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A simplified massive MIMO implemented with pre or post-processing
Physical Communication (
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A simplified massive MIMO implemented with pre or post-processing Mário Marques da Silva a, *, Rui Dinis b a b
Instituto de Telecomunicações, Universidade Autónoma de Lisboa, Autonoma TechLab, Portugal Instituto de Telecomunicações, Universidade Nova, Portugal
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Article history: Received 18 November 2016 Received in revised form 15 March 2017 Accepted 11 June 2017 Available online xxxx Keywords: Massive MIMO Precoding SC-FDE 5G Interference cancellation mm-Wave
a b s t r a c t This paper considers the use of massive multiple input, multiple output (MIMO) combined with singlecarrier with frequency-domain equalization (SC-FDE) modulations, associated to millimeter wave (mmWave) communications using precoding. For the sake of comparison, this paper performs a comparison of pre and post-processing methodology, using the same algorithms. In this paper, we consider three different types of algorithms: Zero Forcing Transmitter (ZFT), Maximum Ratio Transmitter (MRT), and Equal Gain Transmitter (EGT), both of the latter two with iterative detection schemes. The advantage of both MRT and EGT relies on avoiding the computation of pseudo-inverse of matrices. The performance of MRT and EGT are very close to the matched filter bound just after a few iterations of a new proposed interference cancellation, even when the number of receiving antennas is not very high. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Massive MIMO (m-MIMO) schemes involving several tens or even hundreds of antenna elements are expected to be central technologies for 5G (Fifth Generation) systems [1], where higher capacity and spectral efficiency are required [2], as compared to current systems. To avoid implementation complexity, massive MIMO schemes should use simple techniques to separate data streams that avoid matrix inversions inherent to conventional MIMO receivers. mm-Wave communications are expected to be a crucial part of 5G systems due to their increased channel coherence bandwidth, as compared to centimeter wave. The same technological approach is utilized in the ieee 802.11 standard, as in 802.11ad [3]. These systems use carrier frequencies above 30 GHz where we have large unoccupied bandwidth (there are proposals for several bands in the vicinity of 40 GHz, 60 GHz, 70 GHz, or even above [4,5]). However, mm-Wave transmission has important problems like high free-space path losses, very small diffraction effects, huge losses due to obstacles and implementation difficulties, namely with the power amplification [6]. On the other hand, the small wavelength means that we can have small antennas and small-sized antenna aggregates with a large number of elements, facilitating the deployment of m-MIMO schemes [4]. Moreover, the high reflection effects can be used to improve coverage [6]. By taking advantage of these characteristics, we can design mmWave communications with capacities several orders magnitude
* Corresponding author.
E-mail address: [email protected] (M. Marques da Silva).
above current wireless systems. In fact, mm-Wave systems can take full advantage of techniques like small cells networks (pico or femto) and m-MIMO schemes. By combining small cells with m-MIMO systems we can have large gains to cope with propagation losses and/or accommodate a large number of co-channel users, with high frequency reuse [2]. As with other wireless systems, mm-Wave communications should have high power and improved spectral efficiencies, which are conflicting requirements. In general, high spectral efficiency means using large constellations and strictly band-limited signals, which have high power requirements and the inherent high peakto-average power ratio (PAPR) leads to low amplification efficiency [7]. It is well-known that high power and spectral efficiencies are contradictory goals. In fact, increased spectral efficiency means the use of larger constellations, which leads to higher power requirements since the average bit energy for a given minimum Euclidean distance increases with the constellation size. Moreover, in general larger constellations also have higher linearity requirements since the associated signals have higher envelope fluctuations and, consequently, lower amplification efficiency [8]. Block transmission techniques, with appropriate cyclic prefixes and employing Frequency-Domain Equalization (FDE) techniques, have been shown to be suitable for high data rate transmission over severely time-dispersive channels [7]. Orthogonal Frequency Division Multiplexing (OFDM) is the most popular modulation based on this technique. Single Carrier (SC) modulation using FDE is an alternative approach based on this principle. As with OFDM, the data blocks are preceded by a cyclic prefix, long enough to cope with the overall channel length. Due to the lower envelope
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fluctuations of the transmitted signals (and, implicitly lower PAPR), SC-FDE schemes are especially interesting when a low-complexity and efficient power amplification is required [7]. A promising Iterative Block-Decision Feedback Equalization technique (IB-DFE) for SC-FDE was proposed in [8,9] and extended to other diversity [9,10] and spatial multiplexing scenarios [11,12]. These IB-DFE receivers can be regarded as iterative DFE receivers where the feedforward and the feedback operations are implemented in the frequency domain offering much better performance than non-iterative methods [9–11]. IB-DFE receiver can also be regarded as turbo equalization schemes [12,13] that are implemented in the frequency-domain [14]. A disadvantage of the precoding using the Zero Forcing (ZF) algorithm relies on the need to compute the pseudo-inverse channel matrix, for each frequency component, valid for both precoding and post-processing. In this paper, we avoid this by implementing the m-MIMO using MRT for precoding or Maximum Ratio Combining (MRC) for post-processing, and EGT for precoding or Equal Gain Combining (EGC) for post-processing. Note that MRT and MRC are the same algorithms, with the difference of the location where they are implemented. The same rational applies to EGT versus EGC. Since these algorithms originate a certain level of interference, we include an interference cancellation process in the receiver, whose design is based on the IB-DFE receiver, which makes these algorithms performing very close to matched filter bound. In this paper we propose an m-MIMO architecture using an efficient precoding using broadband mm-Wave communications that can employ highly efficient, low-cost saturated amplifiers. For the sake of comparison, this paper performs a comparison with the post-processing methodology, using algorithms similar to those utilized in precoding. This paper is organized as follows: Section 2 describes the system characterization associated to generic SC-FDE signals. Section 3 considers the transmitter structure for the proposed mMIMO using precoding. Section 4 considers the transmitter structure for the proposed m-MIMO using post-processing. Finally, Section 5 analyzes the performance results and Section 6 concludes the paper. 2. System characterization associated to generic SC-FDE signals We consider block transmission schemes and the transmitted block has the form x (t ) =
N −1 ∑
xn hT (t − nTS ) ,
(1)
n=−NG
with TS denoting the symbol duration, NG denoting the number of samples at the cyclic prefix and hT (t ) is the adopted pulse shaping filter. The signal x (t ) is transmitted over a timedispersive channel and the signal at the receiver input is sampled and the cyclic prefix is removed, leading to the timedomain block {yn ; n = 0, 1, . . . , N − 1}, which is then subject to the frequency domain equalization. For SC-FDE schemes, the timedomain block to be transmitted are {xn ; n = 0, 1, . . . , N − 1} denoting the length-N data block to be transmitted, where xn is the nth data symbol, selected from a given constellation (e.g., a QPSK constellation) under an appropriate mapping rule (it is assumed that x−n = xN −n , n = −NG , −NG + 1, . . . , −1). The transmitter frequency-domain block is {Xk ; k = 0, 1, . . . , N − 1} = DFT {xn ; n = 0, 1, . . . , N − 1}. Assuming that the cyclic prefix is longer than the overall channel impulse response of each channel, the frequency-domain block after the FDE block (i.e., the DFT of the received time-domain block, after removing the cyclic prefix) is {yn ; n = 0, 1, . . . , N − 1} = IDFT {Yk ; k = 0, 1, . . . , N − 1}, with Yk = Xk Hk + Nk
(2)
)
–
Fig. 1. Block Diagram of m-MIMO for (a) SC-FDE (b) details of MIMO receiver and interference cancellation using pre-processing.
where {Hk ; k = 0, 1, . . . , N − 1} = DFT {hn ; n = 0, 1, . . . , N − 1} denotes the channel frequency response for the kth subcarrier (the channel is assumed invariant in the frame) and Nk is the frequencydomain block channel noise for that subcarrier. At the output of the FDE we have the samples
˜ Xk =
Yk Hk∗
α + |Hk |2
.
(3)
We assume the frame structure with N subcarriers per block and NT time-domain blocks, each one corresponding to an ‘‘FFT block’’. Assuming the conventional linear FDE for SC schemes, the postprocessing comes,
[ ] (2) ˜ Xk = Yk Hk∗ βk ( ( ))−1 (2) where βk = α + |Hk |2 . As expected, eq (2) ˜ Xk = Xk |Hk |2 βk + Nk .
(4)
(5)
[ ] eq In addition, we define α = E |Nk | /E |Xk |2 . Nk [denotes the ⏐ eq ⏐2 ] ⏐ ⏐ = equivalent noise for detection purposes, with E Nk [ 2 ] (2) [ ] 2 2 2 2σN |Hk | βk , and with σN = E |Nk | /2. [
2
]
The post-processing for OFDM signals is the same as defined in (2) (4) but without multiplying by the βk component. 3. Transmitter structure for the proposed massive MIMO using precoding 3.1. Computation of the precoding coefficient We consider the multi-user massive MIMO scenario depicted in Fig. 1 which concerns the transmission between an emitter with T antennas and a receiver with R antennas. This system can be employed between a Base Station (BS) and a Mobile Terminal (MT) with R receiving antennas, to send multiple streams of data. In either case consider that T ≫R. Finally, this system can also be applied between two MTs, or in the uplink scenario, but it is required that the MT has enough processing to implement the precoding, which is not problematic with the precoding based on MRT and EGT. Without loss of generality, in the signal description we assume the downlink direction. The channels between each transmitting and receiving antenna are assumed to be highly selective in the frequency domain, requiring powerful equalization schemes. For
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this reason, SC-FDE modulations are employed. The BS has a block (r) of N data symbols {xn ; n = 0, 1, . . . , N − 1} to send, which are subject to precoding first. The received block at the rth MT is {y(r) n ; k = 0, 1, . . . , N − 1}. As with other SC-FDE schemes, a cyclic prefix longer than the maximum overall channel impulse response is appended to each transmitted block and removed at the receiver. (r) In this case, the corresponding frequency-domain block {Yk ; k = 0, 1, . . . , N − 1} satisfies
[
(1)
(R)
Yk = Yk , . . . , Yk
]T
= Hk Wk + Nk
(T ) T
(1)
comes Wk = [Wk , . . . , Wk ] , defined by Wk = Bk Xk
(7)
–
3
different transmitting and receiving antennas, the elements outside the main diagonal of Hk Bk
(12)
are much lower than the ones at its diagonal, where (i, i )th element of the matrix B are defined as: ′
1. For MRT: [B]i,i′ = [H]H ′ /T . i,i
2. For EGT: [B]i,i′ = exp j arg [H]i,i′ /T , i.e., they have absolute value 1 and phase identical to the corresponding element of the matrix H.
(6)
where Hk denotes the R × T channel matrix for the kth frequency, (r ,t) with (r , t)th element Hk . T refers to the number of transmitting antennas and R denotes the number of receiving antennas. In this paper it is assumed that channel is known at the transmitting side, as in TDD systems. Considering a precoding approach, the transmitted symbols
)
(
(
))
For SC-FDE signals we could employ a frequency-domain processing with MRT or EGT at each frequency, based on Hk Bk . However, the residual interference levels can still be substantial, especially for moderate values of T /R. To overcome this problem, we propose the iterative interference canceller (receiver) depicted in Fig. 1(b), where
˜ Xk = Yk − Ck Xk .
(13)
The interference cancellation matrix Ck comes defined by
where Bk denotes the T × R precoding matrix, and the data symbols (R) T
(1)
Xk = [Xk , . . . , Xk ] . The precoding matrix Bk can be computed using different algorithms. 1. Using the zero forcing transmitter (ZFT)1 algorithm Bk comes: H Bk = HH k Hk Hk
(
)−1
.
(8)
2. Using the MRT algorithm Bk comes: Bk = HH k /T
(9)
where T stands for the number of transmitting antennas. 3. Using the EGT algorithm Bk comes: Bk = exp j arg HH k
{
(
)}
/T .
Ck = Hk Bk − I
where I is an R × R identity matrix. canceller is implemented using Xk = ] [ This interference X 0 , . . . , X N −1 , with Xk denoting the frequency-domain average values conditioned to the FDE output for the previous iteration [15]. Before defining Xk , let us define the LLRs (Log Likelihood Ratios) I (i) of the ‘‘in-phase bit’’ and the ‘‘quadrature bit’’, associated to xn and Q (i) xn , respectively, given by LIn(i) =
(10)
(14)
LQn (i) =
2
σi2 2
σi2
˜ XnI (i) (15)
˜ XnQ (i)
A disadvantage of the MRT and EGT relating to ZFT relies on the generated interference, which degrades the performance. In order to improve the performance, we consider an iterative receiver.
respectively, with
3.2. Interference cancellation using precoding
σi2 =
N −1 ⏐2 ] ⏐2 1 [⏐ 1 ∑ ⏐ ⌢(i) ⏐x −˜ E ⏐xn − x(ni) ⏐ ≈ Xn(i) ⏐ . n 2 2N
(16)
n=0
Let us consider the frequency domain estimated data symbols (1) (R) T ˜ Xk = [˜ Xk , . . . , ˜ Xk ] . Since the precoding approach considers the
processing at the transmitter side, the detector computes the data (r) (r) symbols obtained from the IDFT of the block {˜ Xk = Yk ; k = 0, 1, . . . , N − 1} with:
˜ xn = IDFT (Yk ) .
(11)
Note that, in the precoding case, it does not need to perform the equalization process, as defined as (4). The estimated bits are obtained by applying the sign function to (11), depending on the modulation scheme. In the case of ZF precoding (that is, ZFT), since interference is not generated, this detection tends to perform well. However, this involves the inversion of a matrix for each frequency component, and the dimensions of these matrices can be very high in massive MIMO systems. Massive MIMO schemes should usually employ simpler receivers. The simplest approach is probably to perform the MRT or EGT. This can be performed either at the receiver or at transmitter side. This paper considers the processing at the transmitter side, i.e, a precoding approach is employed. The proposed MRT or EGT take advantage of the fact that, for massive MIMO systems with T ≫1 with small correlation of the channels between 1 ZFT refers to the ZF algorithm implemented as precoding at the transmitter side.
(σi2 is almost independent of l for large values of N, provided that Hk remains constant for the frame duration). The conditional average values associated with the data symbols are given by
( (i)
xn = tanh
I (i)
Ln
2
)
( + j tanh
Q (i)
Ln
2
) .
(17)
For the first iteration there is no information about the transmitted symbols and Xk = 0. This means that our receiver can be regarded as a simple SC-FDE receiver with an interference cancellation, performed in the frequency domain, of the signals associated to different receiver antennas, while the MRT or EGT processing is performed at the transmitter side (precoding approach). For the subsequent iterations we employ the average values conditioned to the receiver output at the previous iteration to remove the residual intersymbol interference and inter user interference. In general, for moderate-to-high signal-to-noise ratio, the average values conditioned to the receiver output approach the transmitted signals as we increase the number of iterations, which means that the interference cancellation performed by Ck becomes more effective and the performance improves. Moreover, since the average values conditioned to the receiver output can be regarded as soft decisions [15], this reduces significantly error propagation effects in our iterative receiver (in fact, we did not observe error propagation effects).
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)
–
3. Using the EGC receiver, ˜ Xk comes:
{ ( )} ˜ Yk . Xk = exp j arg HH k
(21)
Similar to the precoding case, a disadvantage of the MRC and EGC relating to ZFR relies on the generated interference, which degrades the performance. In order to improve the performance, we consider an iterative receiver, as defined in the following. 4.2. Interference cancellation using post-processing Since the post-processing approach considers the processing at the receiver side, the detector computes the data symbols obtained (r) from the IDFT of the block {˜ Xk ; k = 0, 1, . . . , N − 1} with:
( ) ˜ xn = IDFT ˜ Xk .
Fig. 2. Block Diagram of m-MIMO for (a) SC-FDE (b) details of MIMO receiver and interference cancellation using post-processing.
4. Transmitter structure for the proposed massive MIMO using post-processing 4.1. Computation of the post-processing coefficient We consider the multi-user massive MIMO scenario depicted in Fig. 2 which concerns the uplink transmission between T MTs and a BS with R antennas. For the sake of simplicity, and without loss of generality, we assume a single antenna at each MT. Alternatively, this system can be employed between a MT with T antennas and a BS with R receiving antennas, to send multiple streams of data. In either case we consider that R ≫T. Finally, this system can also be applied between two MTs. Similar to the precoding scenario, SC-FDE modulations are em(t) ployed. The tth MT has a block of N data symbols {xn ; n = (r) 0, 1, . . . , N − 1} to send. The received block at the BS is {yn ; k = 0, 1, . . . , N − 1}. As with other SC-FDE schemes, a cyclic prefix longer than the maximum overall channel impulse response is appended to each transmitted block and removed at the receiver. (r) In this case, the corresponding frequency-domain block {Yk ; k = 0, 1, . . . , N − 1} satisfies
[
(1)
(R)
Yk = Yk , . . . , Yk
]T
= Hk Xk + Nk
(18)
where Hk denotes the R × T channel matrix for the kth frequency, (r ,t ) with (r , t )th element Hk . The transmitted symbols comes Xk =
[
(1)
(T )
Xk , . . . , Xk
]T
.
Let[us consider the ]T frequency domain estimated data symbols (1) (R) ˜ ˜ ˜ Xk = Xk , . . . , Xk . 1. For the Zero Forcing Receiver (ZFR),2 the data symbols can be obtained from the IDFT of the block ˜ Xk , where [16]
)−1 H ( ˜ Xk = HH Hk Yk . k Hk
The estimated bits are obtained by applying the sign function to ˜ xn , depending on the modulation scheme. In the case of ZFR receiver, this involves the inversion of a matrix for each frequency component, and the dimensions of these matrices can be very high in massive MIMO systems. Massive MIMO schemes should usually employ simpler receivers. The simplest approach is probably to perform the MRC or EGC. This take advantage of the fact that, for massive MIMO systems with R ≫1 with small correlation between the channels between different transmit and receiving antennas, the elements outside the main diagonal of AH k Hk
(23)
are much lower than the ones at its diagonal, where (i, i )th element of the matrix A are defined as: ′
1. For MRC: [A]i,i′ = [H]H ′ . i,i
(
(
))
2. For EGC: [A]i,i′ = exp j arg [H]i,i′ , i.e., they have absolute value 1 and phase identical to the corresponding element of the matrix H. For SC-FDE signals we could employ a frequency-domain processing with MRC or EGC at each frequency, based on AH k Hk . However, the residual interference levels can still be substantial, especially for moderate values of T /R. To overcome this problem, we propose the iterative interference canceller (receiver) depicted in Fig. 2(b), where
˜ Xk = AH k Yk − Dk Xk .
(24)
The interference cancellation matrix Dk comes defined by Dk = A H k Hk − I
(25)
where I is an R × R identity matrix. canceller is implemented using Xk = [ This interference ] X 0 , . . . , X N −1 , with Xk denoting the frequency-domain average values conditioned to the FDE output for the previous iteration [15], as defined for the precoding. 5. Performance results
(19)
2. Using the MRC receiver, ˜ Xk comes:
˜ Xk = HH k Yk
(22)
(20)
where R stands for the number of receiving antennas. 2 ZFR refers to the ZF algorithm implemented as post-processing at the receiver side.
In this section we present a set of performance results concerning the proposed m-MIMO scheme using precoding optimized for mm-wave associated to SC-FDE signals. For the sake of comparison, this section performs a comparison with the post-processing methodology, using the same algorithms as those utilized in precoding. We consider Bit Error Rate (BER) performances, which are expressed as a function of Eb /N0 , where N0 is the one-sided power spectral density of the noise and Eb is the energy of the transmitted
Please cite this article in press as: M. Marques da Silva, R. Dinis, A simplified massive MIMO implemented with pre or post-processing, Physical Communication (2017), http://dx.doi.org/10.1016/j.phycom.2017.06.002.
M. Marques da Silva, R. Dinis / Physical Communication (
Fig. 3. BER results with 32 × 8m-MIMO using precoding.
bits (i.e., the degradation due to the useless power spent on the cyclic prefix is not included). Each block has N = 256 symbols selected from a QPSK constellation under a Gray mapping rule (similar results were observed for other values of N, provided that N ≫ 1). Our channel has 16 equal power paths with uncorrelated Rayleigh fading. The channel is assumed to be invariant during the block. The duration of the useful part of the blocks (N symbols) is 1 µs and the cyclic prefix has duration 0.125 µs. For SC-FDE systems we considered the linear FDE (i.e., just the first iteration of the interference canceller) up to four iterations of the interference canceller. Beyond this number, the performance improvement was almost negligible. Linear power amplification is considered at the transmitter and perfect synchronization is assumed at the receiver. Fig. 3 considers BER results for massive MIMO with 32 transmitting antennas and 8 receiving antennas (32 × 8), using precoding. The three proposed algorithms are plotted (ZFT, MRT and EGT). Moreover, the matched filter bound is also plotted. Fig. 3 considers results with and without interference cancellation. In the case without interference cancellation, a regular SC-FDE receiver is considered (that is, a linear FDE receiver). Moreover, when interference cancellation is adopted, an iterative receiver is adopted. From Fig. 3 it is shown that the ZFT achieves a performance very close to the Matched Filter Bound (MFB). It is worth noting that the receiver employed with the ZFT is a regular SC-FDE receiver, without interference cancellation, because the ZFT algorithm does not generate interference. As opposed to the ZFR (post-processing approach), the ZFT precoding (pre-processing) does not generate noise enhancement, because when the processing is applied, the noise does not exist. As previously described, a disadvantage of the ZFT algorithm relies on the need to compute the pseudoinverse of the channel matrix, for each frequency component. To simplify this process, we proposed the use of the MRT and EGT, with the disadvantage of generating a certain level of interference. Fig. 3 shows results for 2 up to 4 iterations of the interference cancellation associated to MRT and EGT. Results with more than 4 iterations are not shown because the performance keeps approximately unchanged, as compared to 4 iterations. It is shown that, with 4 iterations of the interference cancellation, the performance obtained with the MRT approximates that of the ZFT and MFB. Moreover, with 4 iterations of the interference cancellation, the MRT algorithm tends to achieve a performance slightly better than that of the EGT. Fig. 4 considers BER results for massive MIMO with 64 transmitting antennas and 8 receiving antennas (64 × 8), using precoding.
)
–
5
Fig. 4. BER results with 64 × 8 m-MIMO using precoding.
Fig. 5. BER results with 128 × 8 m-MIMO using precoding.
As compared to the previous graphic, we have increased the number of transmitting antennas, while leaving the number of receiving antennas unchanged. As can be seen from the results, with such increase of transmitting antennas, the performance obtained with both MRT and EGT with 4 iterations of the interference cancellation becomes closer to the ZF and MFB. Fig. 5 considers BER results for massive MIMO with 128 transmitting antennas and 8 receiving antennas (128 × 8), using precoding. As compared to the previous graphics, we have increased the number of transmitting antennas, while leaving the number of receiving antennas unchanged. As before, with such increase of transmitting antennas, the performance obtained with both MRT and EGT with 4 iterations of the interference cancellation becomes even closer to the ZFT and MFB. Fig. 6 shows the BER results for the massive MIMO with 32 transmitting antennas and 2 receiving antennas (32 × 2), using precoding. As compared to Fig. 3 (32 × 8), we have reduced the number of receiving antennas, which leads to a performance improvement because the level of interference decreases for MRT and EGT. Note that the level of interference increases with the number of receiving antennas. As expected, it is noticeable that the performance obtained with MRT with 4 iterations of interference cancellation is very close to the MFB and ZFT, even with only 32 transmitting antennas.
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Fig. 6. BER results with 32 × 2 m-MIMO using precoding.
Fig. 7. BER results for m-MIMO with different number of transmit and receiving antennas using Precoding (MRT and EGT have 4 iterations of interference cancellation).
Fig. 7 shows the performance comparison for massive MIMO, using precoding, with different number of transmit and receiving antennas, considering the ZFT. Moreover the MRT and EGT is plotted always with 4 iterations of the interference cancellation, because this represents a signal clear enough of interference (see previous figures). As can be seen, for a certain number of receiving antennas, the increase of transmitting antennas leads to performance improvement. This is visible when we move from 32 × 8 into 128 × 8 configuration. Moreover, the increase of receiving antennas corresponds to a decrease of performance, due to the raise in the level of interference. This is visible when we move from 32 × 2 into 32 × 8 configuration. Finally, it is noticeable that the performance obtained with the ZFT is very insensitive to variations in the number of transmit and receiving antennas, but this is obtained at the cost of a high level of computation associated to the precoding (computation of the pseudo-inverse of a matrix, for each frequency). Fig. 8 considers BER results for massive MIMO using both precoding and post-processing. In the case of precoding the mMIMO adopted comprises 32 transmitting antennas and 8 receiving antennas (32 × 8), while the post-processing comprises 8
)
–
Fig. 8. BER results with m-MIMO using precoding (32 × 8) versus post-processing (8 × 32).
transmitting antennas and 32 receiving antennas (the reciprocal). The three proposed algorithms used in both precoding and postprocessing are ZFT/ZFR, MRT/MRC and EGT/EGC. Moreover, the matched filter bound is also plotted. Fig. 8 considers results with and without interference cancellation. From Fig. 8 it is shown that the ZF in precoding (ZFT) achieves a performance very close to the MFB, while the ZF in post-processing (ZFR) presents a worse performance. It is worth noting that the receiver employed with either precoding or post-processing ZF is a regular SC-FDE receiver, without interference cancellation, because the ZF algorithm does not generate interference. Moreover, as opposed to the ZFR (postprocessing approach), the ZFT (pre-processing) does not generate noise enhancement, because when the processing is applied, the noise does not exist. As previously described, a disadvantage of the ZF algorithm relies on the need to compute the pseudo-inverse of the channel matrix, for each frequency component. To simplify this process, we proposed the use of the MRT/MRC and EGT/EGC (using both pre and post-processing), with the disadvantage of generating a certain level of interference. Fig. 8 shows results for 2 and 4 iterations of the interference cancellation associated to MRT/MRC and EGT/EGC. Results with more than 4 iterations are not shown because the performance keeps approximately unchanged, as compared to 4 iterations (using both pre and post-processing). It is viewed that, for MRT/MRC and EGT/EGC, the post-processing tends to achieve a performance slightly better than those achieved with the pre-processing (precoding). Exceptionally, the results obtained without interference cancellation are the same for both MRT/MRC and EGT/EGC. It is also viewed that the MRT/MRC with interference cancellation always performs better than the EGT/EGC (for the same number of iterations), either in pre-processing or post-processing. Finally, it is viewed that, with 4 iterations of the interference cancellation, the performance obtained with the MRC using post-processing approximates that of the MFB, while the MRT using pre-processing presents a slightly worse performance. Fig. 9 considers BER results for massive MIMO using both preprocessing (precoding) and post-processing. In the case of precoding the m-MIMO adopted comprises 64 transmitting antennas and 8 receiving antennas (64 × 8), while the post-processing comprises 8 transmitting antennas and 64 receiving antennas (the reciprocal). As compared to the previous graphic, we have increased the number of transmit or receiving antennas (precoding or post-processing, respectively), while leaving the other number of antennas unchanged. As can be seen from the results, with such increase of antennas, and for both pre and post-processing
Please cite this article in press as: M. Marques da Silva, R. Dinis, A simplified massive MIMO implemented with pre or post-processing, Physical Communication (2017), http://dx.doi.org/10.1016/j.phycom.2017.06.002.
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References
Fig. 9. BER results with m-MIMO using precoding (64 × 8) versus post-processing (8 × 64).
for MRT/MRC and EGT/EGC, for different number of iterations of the interference cancellation, the performance improves relating to the scenario with 32 antennas (previous graphic). For the case with 4 iterations of the interference cancellation, the MRT/MRC implemented either using the pre-processing or the post-processing achieves a performance very close to the MFB. Moreover, as before, the ZF using the pre-processing (ZFT) performs better than that using post-processing (ZFR). This occurs because the ZFR presents noise enhancement while the pre-processing does not. 6. Conclusions In this paper we considered the massive MIMO using precoding, with different algorithms optimized for mm-Wave. For the sake of comparison, the post-processing methodology was also described, analyzed and compared, using the same algorithms as those utilized in precoding. It was viewed that the precoding ZFT achieves a performance very close to the MFB, while the post-processing ZFR does not, due to the noise enhancement. Moreover, it was described that a disadvantage of the ZF algorithm relies on the need to compute the pseudo-inverse of the channel matrix, for each frequency component. To avoid this and simplify this process, we have proposed the use of the MRT/MRC and EGT/EGC. These two algorithms were described in both pre-processing and post-processing methodologies. A disadvantage of these algorithms rely on a certain level of interference that is generated. To remove this interference, we have proposed a novel iterative interference canceller. It was viewed that the MRT/MRC tends to outperform the EGT/EGC. These algorithms implemented in post-processing achieve a performance slightly better than in the pre-processing methodology. Implementing the MRT/MRC and EGT/EGC algorithms for m-MIMO with mm-Wave, associated to the interference cancellation, we avoid the computation of the pseudo-inverse matrix, and therefore simplify the processing (either pre or post-processing), while achieving a performance very close to the MFB, especially with 4 iterations of the interference canceller. Acknowledgment This work was supported by the Portuguese Foundation for the Science and Technology (FCT) under project UID/EEA/50008/2013.
[1] F. Rusek, D. Persson, B.K. Lau, et al., Scaling up MIMO: opportunities and challenges with very large arrays, IEEE Signal Process. Mag. 30 (1) (2013) 40– 60. [2] F. Boccardi, R. Heath, A. Lozano, T. Marzetta, P. Popovski, Five disruptive technology directions for 5G, IEEE Commun. Mag. 52 (2) (2014) 74–80. [3] IEEE 802.11 Task Group, AD, PHY/MAC Complete Proposal Specification, IEEE 802.11-10/0433r2, May 2010. [4] T.S. Rappaport, Shu Sun, R. Mayzus, Hang Zhao, Y. Azar, K. Wang, G.N. Wong, J.K. Schulz, M. Samimi, F. Gutierrez, Millimeter wave mobile communications for 5G cellular: It will work! IEEE Access 1 (2013) 335, 349. [5] S. Nie, G. MacCartney, S. sun, T. Rappaport, 28 GHz and 73 GHz signal outage study for millimeter wave cellular and backhaul communications, in: IEEE ICC’2014, Sydney, Australia, Jun., 2014. [6] S. Rangan, T.S. Rappaport, E. Erkip, Millimeter-wave cellular wireless networks: Potentials and challenges, Proc. IEEE 102 (3) (2014) 366, 385. [7] D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, B. Eidson, Frequency domain equalization for single-carrier broadband wireless systems, IEEE Commun. Mag. 4 (4) (2002) 58–66. [8] Y. Li, K. Han, C. Dong, A multi-band low-noise transmitter with digital carrier leakage suppression and linearity enhancement, IEEE Trans. Circuits Syst. I 60 (5) (2013). [9] N. Benvenuto, S. Tomasin, Block iterative DFE for single carrier modulation, IEE Electron. Lett. 39 (19) (2002). [10] R. Dinis, A. Gusmão, N. Esteves, On broadband block transmission over strongly frequency-selective fading channels, in: Wireless 2003, Calgary, Canada, July, 2003. [11] R. Dinis, R. Kalbasi, D. Falconer, A. Banihashemi, Iterative layered space-time receivers for single-carrier transmission over severe time-dispersive channels, IEEE Commun. Lett. 8 (9) (2004) 579–581. [12] M. Marques da Silva, A. Correia, R. Dinis, N. Souto, J. Silva, Transmission Techniques for Emergent Multicast and Broadcast Systems, first ed. CRC Press Auerbach Publications, New York, USA, ISBN: 9781439815939, 2010. [13] M. Tuchler, R. Koetter, A. Singer, Turbo equalization: Principles and new results, IEEE Trans. Commun. 50 (2002). [14] A. Gusmão, P. Torres, R. Dinis, N. Esteves, A class of iterative FDE techniques for reduced-CP SC-based block transmission, in: Int. Symposium on Turbo Codes, April, 2006. [15] P. Silva, R. Dinis, Frequency-Domain Multiuser Detection for CDMA Systems, River Publishers, Aalborg, 2012. [16] P. Montezuma, D. Borges, R. Dinis, Low complexity MRC and EGC based receivers for SC-FDE modulations with massive MIMO schemes, in: IEEE GLOBALSIP, Washington DC, Dec., 2016.
Mário Marques da Silva is an Associate Professor and the Director of the Department of Sciences and Technologies at Universidade Autónoma de Lisboa. He is also a Researcher at Instituto de Telecomunicações, in Lisbon, Portugal. He received his B.Sc. in Electrical Engineering in 1992, and the M.Sc. and Ph.D. degrees in Electrical and Computers Engineering (Telecommunications), respectively in 1999 and 2005, both from Instituto Superior Técnico, University of Lisbon. Between 2005 and 2008 he was with NATO Air Command Control & Management Agency (NACMA) in Brussels (Belgium), where he managed the deployable communications of the new Air Command and Control System Program. He has been involved in multiple networking and telecommunications projects. His research interests include networking and mobile communications, namely block transmission techniques (OFDM, SC-FDE), interference cancellation, space-time coding, MIMO systems, smart and adaptive antennas, channel estimation, software defined radio, IP technologies and network security. Mário Marques da Silva is also a Cisco certified CCNA instructor. He is the author of five books entitled Multimedia Communications and Networking, Transmission Techniques for Emergent Multicast and Broadcast Systems, Transmission Techniques for 4G Systems, MIMO Processing for 4G and Beyond: Fundamentals and Evolution and Cable and Wireless Networks: Theory & Practice (all from CRC Press). Moreover, he is author of several dozens of journal and conference papers, a member of IEEE and AFCEA, and reviewer for a number of international scientific IEEE journals and conferences. Finally, he has chaired many conference sessions and has been serving in the organizing committee of relevant EURASIP and IEEE conferences. Links to detailed CV: https://www.it.pt/Members/Index/791 https://www.crcpress.com/authors/i262-mario-marques-da-silva https://www.researchgate.net/profile/Mario_Marques_da_Silva2 http://wirelesscommunication.conferenceseries.com/
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Rui Dinis received the Ph.D. degree from Instituto Superior Técnico (IST), Technical University of Lisbon, Portugal, in 2001. From 2001 to 2008 he was a Professor at IST. Since 2008 he is teaching at FCT-UNL (Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa). He was a researcher at CAPS/IST (Centro de Análise e Processamento de Sinais) from 1992 to 2005; from 2005 to 2008 he was researcher at ISR/IST (Instituto de Sistemas e Robótica); in 2009 he joined the research center IT (Instituto de Telecomunicações). He is serving as editor at IEEE Transactions on Communications in the Transmission Systems area, sub-area of Frequency-Domain Processing and Equalization. He has been involved in several research projects in the broadband wireless communications area. His main research interests include modulation, equalization, channel estimation and synchronization.
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Physical Communication journal homepage: www.elsevier.com/locate/phycom
Full length article
A simplified massive MIMO implemented with pre or post-processing Mário Marques da Silva a, *, Rui Dinis b a b
Instituto de Telecomunicações, Universidade Autónoma de Lisboa, Autonoma TechLab, Portugal Instituto de Telecomunicações, Universidade Nova, Portugal
article
info
Article history: Received 18 November 2016 Received in revised form 15 March 2017 Accepted 11 June 2017 Available online xxxx Keywords: Massive MIMO Precoding SC-FDE 5G Interference cancellation mm-Wave
a b s t r a c t This paper considers the use of massive multiple input, multiple output (MIMO) combined with singlecarrier with frequency-domain equalization (SC-FDE) modulations, associated to millimeter wave (mmWave) communications using precoding. For the sake of comparison, this paper performs a comparison of pre and post-processing methodology, using the same algorithms. In this paper, we consider three different types of algorithms: Zero Forcing Transmitter (ZFT), Maximum Ratio Transmitter (MRT), and Equal Gain Transmitter (EGT), both of the latter two with iterative detection schemes. The advantage of both MRT and EGT relies on avoiding the computation of pseudo-inverse of matrices. The performance of MRT and EGT are very close to the matched filter bound just after a few iterations of a new proposed interference cancellation, even when the number of receiving antennas is not very high. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Massive MIMO (m-MIMO) schemes involving several tens or even hundreds of antenna elements are expected to be central technologies for 5G (Fifth Generation) systems [1], where higher capacity and spectral efficiency are required [2], as compared to current systems. To avoid implementation complexity, massive MIMO schemes should use simple techniques to separate data streams that avoid matrix inversions inherent to conventional MIMO receivers. mm-Wave communications are expected to be a crucial part of 5G systems due to their increased channel coherence bandwidth, as compared to centimeter wave. The same technological approach is utilized in the ieee 802.11 standard, as in 802.11ad [3]. These systems use carrier frequencies above 30 GHz where we have large unoccupied bandwidth (there are proposals for several bands in the vicinity of 40 GHz, 60 GHz, 70 GHz, or even above [4,5]). However, mm-Wave transmission has important problems like high free-space path losses, very small diffraction effects, huge losses due to obstacles and implementation difficulties, namely with the power amplification [6]. On the other hand, the small wavelength means that we can have small antennas and small-sized antenna aggregates with a large number of elements, facilitating the deployment of m-MIMO schemes [4]. Moreover, the high reflection effects can be used to improve coverage [6]. By taking advantage of these characteristics, we can design mmWave communications with capacities several orders magnitude
* Corresponding author.
E-mail address: [email protected] (M. Marques da Silva).
above current wireless systems. In fact, mm-Wave systems can take full advantage of techniques like small cells networks (pico or femto) and m-MIMO schemes. By combining small cells with m-MIMO systems we can have large gains to cope with propagation losses and/or accommodate a large number of co-channel users, with high frequency reuse [2]. As with other wireless systems, mm-Wave communications should have high power and improved spectral efficiencies, which are conflicting requirements. In general, high spectral efficiency means using large constellations and strictly band-limited signals, which have high power requirements and the inherent high peakto-average power ratio (PAPR) leads to low amplification efficiency [7]. It is well-known that high power and spectral efficiencies are contradictory goals. In fact, increased spectral efficiency means the use of larger constellations, which leads to higher power requirements since the average bit energy for a given minimum Euclidean distance increases with the constellation size. Moreover, in general larger constellations also have higher linearity requirements since the associated signals have higher envelope fluctuations and, consequently, lower amplification efficiency [8]. Block transmission techniques, with appropriate cyclic prefixes and employing Frequency-Domain Equalization (FDE) techniques, have been shown to be suitable for high data rate transmission over severely time-dispersive channels [7]. Orthogonal Frequency Division Multiplexing (OFDM) is the most popular modulation based on this technique. Single Carrier (SC) modulation using FDE is an alternative approach based on this principle. As with OFDM, the data blocks are preceded by a cyclic prefix, long enough to cope with the overall channel length. Due to the lower envelope
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fluctuations of the transmitted signals (and, implicitly lower PAPR), SC-FDE schemes are especially interesting when a low-complexity and efficient power amplification is required [7]. A promising Iterative Block-Decision Feedback Equalization technique (IB-DFE) for SC-FDE was proposed in [8,9] and extended to other diversity [9,10] and spatial multiplexing scenarios [11,12]. These IB-DFE receivers can be regarded as iterative DFE receivers where the feedforward and the feedback operations are implemented in the frequency domain offering much better performance than non-iterative methods [9–11]. IB-DFE receiver can also be regarded as turbo equalization schemes [12,13] that are implemented in the frequency-domain [14]. A disadvantage of the precoding using the Zero Forcing (ZF) algorithm relies on the need to compute the pseudo-inverse channel matrix, for each frequency component, valid for both precoding and post-processing. In this paper, we avoid this by implementing the m-MIMO using MRT for precoding or Maximum Ratio Combining (MRC) for post-processing, and EGT for precoding or Equal Gain Combining (EGC) for post-processing. Note that MRT and MRC are the same algorithms, with the difference of the location where they are implemented. The same rational applies to EGT versus EGC. Since these algorithms originate a certain level of interference, we include an interference cancellation process in the receiver, whose design is based on the IB-DFE receiver, which makes these algorithms performing very close to matched filter bound. In this paper we propose an m-MIMO architecture using an efficient precoding using broadband mm-Wave communications that can employ highly efficient, low-cost saturated amplifiers. For the sake of comparison, this paper performs a comparison with the post-processing methodology, using algorithms similar to those utilized in precoding. This paper is organized as follows: Section 2 describes the system characterization associated to generic SC-FDE signals. Section 3 considers the transmitter structure for the proposed mMIMO using precoding. Section 4 considers the transmitter structure for the proposed m-MIMO using post-processing. Finally, Section 5 analyzes the performance results and Section 6 concludes the paper. 2. System characterization associated to generic SC-FDE signals We consider block transmission schemes and the transmitted block has the form x (t ) =
N −1 ∑
xn hT (t − nTS ) ,
(1)
n=−NG
with TS denoting the symbol duration, NG denoting the number of samples at the cyclic prefix and hT (t ) is the adopted pulse shaping filter. The signal x (t ) is transmitted over a timedispersive channel and the signal at the receiver input is sampled and the cyclic prefix is removed, leading to the timedomain block {yn ; n = 0, 1, . . . , N − 1}, which is then subject to the frequency domain equalization. For SC-FDE schemes, the timedomain block to be transmitted are {xn ; n = 0, 1, . . . , N − 1} denoting the length-N data block to be transmitted, where xn is the nth data symbol, selected from a given constellation (e.g., a QPSK constellation) under an appropriate mapping rule (it is assumed that x−n = xN −n , n = −NG , −NG + 1, . . . , −1). The transmitter frequency-domain block is {Xk ; k = 0, 1, . . . , N − 1} = DFT {xn ; n = 0, 1, . . . , N − 1}. Assuming that the cyclic prefix is longer than the overall channel impulse response of each channel, the frequency-domain block after the FDE block (i.e., the DFT of the received time-domain block, after removing the cyclic prefix) is {yn ; n = 0, 1, . . . , N − 1} = IDFT {Yk ; k = 0, 1, . . . , N − 1}, with Yk = Xk Hk + Nk
(2)
)
–
Fig. 1. Block Diagram of m-MIMO for (a) SC-FDE (b) details of MIMO receiver and interference cancellation using pre-processing.
where {Hk ; k = 0, 1, . . . , N − 1} = DFT {hn ; n = 0, 1, . . . , N − 1} denotes the channel frequency response for the kth subcarrier (the channel is assumed invariant in the frame) and Nk is the frequencydomain block channel noise for that subcarrier. At the output of the FDE we have the samples
˜ Xk =
Yk Hk∗
α + |Hk |2
.
(3)
We assume the frame structure with N subcarriers per block and NT time-domain blocks, each one corresponding to an ‘‘FFT block’’. Assuming the conventional linear FDE for SC schemes, the postprocessing comes,
[ ] (2) ˜ Xk = Yk Hk∗ βk ( ( ))−1 (2) where βk = α + |Hk |2 . As expected, eq (2) ˜ Xk = Xk |Hk |2 βk + Nk .
(4)
(5)
[ ] eq In addition, we define α = E |Nk | /E |Xk |2 . Nk [denotes the ⏐ eq ⏐2 ] ⏐ ⏐ = equivalent noise for detection purposes, with E Nk [ 2 ] (2) [ ] 2 2 2 2σN |Hk | βk , and with σN = E |Nk | /2. [
2
]
The post-processing for OFDM signals is the same as defined in (2) (4) but without multiplying by the βk component. 3. Transmitter structure for the proposed massive MIMO using precoding 3.1. Computation of the precoding coefficient We consider the multi-user massive MIMO scenario depicted in Fig. 1 which concerns the transmission between an emitter with T antennas and a receiver with R antennas. This system can be employed between a Base Station (BS) and a Mobile Terminal (MT) with R receiving antennas, to send multiple streams of data. In either case consider that T ≫R. Finally, this system can also be applied between two MTs, or in the uplink scenario, but it is required that the MT has enough processing to implement the precoding, which is not problematic with the precoding based on MRT and EGT. Without loss of generality, in the signal description we assume the downlink direction. The channels between each transmitting and receiving antenna are assumed to be highly selective in the frequency domain, requiring powerful equalization schemes. For
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this reason, SC-FDE modulations are employed. The BS has a block (r) of N data symbols {xn ; n = 0, 1, . . . , N − 1} to send, which are subject to precoding first. The received block at the rth MT is {y(r) n ; k = 0, 1, . . . , N − 1}. As with other SC-FDE schemes, a cyclic prefix longer than the maximum overall channel impulse response is appended to each transmitted block and removed at the receiver. (r) In this case, the corresponding frequency-domain block {Yk ; k = 0, 1, . . . , N − 1} satisfies
[
(1)
(R)
Yk = Yk , . . . , Yk
]T
= Hk Wk + Nk
(T ) T
(1)
comes Wk = [Wk , . . . , Wk ] , defined by Wk = Bk Xk
(7)
–
3
different transmitting and receiving antennas, the elements outside the main diagonal of Hk Bk
(12)
are much lower than the ones at its diagonal, where (i, i )th element of the matrix B are defined as: ′
1. For MRT: [B]i,i′ = [H]H ′ /T . i,i
2. For EGT: [B]i,i′ = exp j arg [H]i,i′ /T , i.e., they have absolute value 1 and phase identical to the corresponding element of the matrix H.
(6)
where Hk denotes the R × T channel matrix for the kth frequency, (r ,t) with (r , t)th element Hk . T refers to the number of transmitting antennas and R denotes the number of receiving antennas. In this paper it is assumed that channel is known at the transmitting side, as in TDD systems. Considering a precoding approach, the transmitted symbols
)
(
(
))
For SC-FDE signals we could employ a frequency-domain processing with MRT or EGT at each frequency, based on Hk Bk . However, the residual interference levels can still be substantial, especially for moderate values of T /R. To overcome this problem, we propose the iterative interference canceller (receiver) depicted in Fig. 1(b), where
˜ Xk = Yk − Ck Xk .
(13)
The interference cancellation matrix Ck comes defined by
where Bk denotes the T × R precoding matrix, and the data symbols (R) T
(1)
Xk = [Xk , . . . , Xk ] . The precoding matrix Bk can be computed using different algorithms. 1. Using the zero forcing transmitter (ZFT)1 algorithm Bk comes: H Bk = HH k Hk Hk
(
)−1
.
(8)
2. Using the MRT algorithm Bk comes: Bk = HH k /T
(9)
where T stands for the number of transmitting antennas. 3. Using the EGT algorithm Bk comes: Bk = exp j arg HH k
{
(
)}
/T .
Ck = Hk Bk − I
where I is an R × R identity matrix. canceller is implemented using Xk = ] [ This interference X 0 , . . . , X N −1 , with Xk denoting the frequency-domain average values conditioned to the FDE output for the previous iteration [15]. Before defining Xk , let us define the LLRs (Log Likelihood Ratios) I (i) of the ‘‘in-phase bit’’ and the ‘‘quadrature bit’’, associated to xn and Q (i) xn , respectively, given by LIn(i) =
(10)
(14)
LQn (i) =
2
σi2 2
σi2
˜ XnI (i) (15)
˜ XnQ (i)
A disadvantage of the MRT and EGT relating to ZFT relies on the generated interference, which degrades the performance. In order to improve the performance, we consider an iterative receiver.
respectively, with
3.2. Interference cancellation using precoding
σi2 =
N −1 ⏐2 ] ⏐2 1 [⏐ 1 ∑ ⏐ ⌢(i) ⏐x −˜ E ⏐xn − x(ni) ⏐ ≈ Xn(i) ⏐ . n 2 2N
(16)
n=0
Let us consider the frequency domain estimated data symbols (1) (R) T ˜ Xk = [˜ Xk , . . . , ˜ Xk ] . Since the precoding approach considers the
processing at the transmitter side, the detector computes the data (r) (r) symbols obtained from the IDFT of the block {˜ Xk = Yk ; k = 0, 1, . . . , N − 1} with:
˜ xn = IDFT (Yk ) .
(11)
Note that, in the precoding case, it does not need to perform the equalization process, as defined as (4). The estimated bits are obtained by applying the sign function to (11), depending on the modulation scheme. In the case of ZF precoding (that is, ZFT), since interference is not generated, this detection tends to perform well. However, this involves the inversion of a matrix for each frequency component, and the dimensions of these matrices can be very high in massive MIMO systems. Massive MIMO schemes should usually employ simpler receivers. The simplest approach is probably to perform the MRT or EGT. This can be performed either at the receiver or at transmitter side. This paper considers the processing at the transmitter side, i.e, a precoding approach is employed. The proposed MRT or EGT take advantage of the fact that, for massive MIMO systems with T ≫1 with small correlation of the channels between 1 ZFT refers to the ZF algorithm implemented as precoding at the transmitter side.
(σi2 is almost independent of l for large values of N, provided that Hk remains constant for the frame duration). The conditional average values associated with the data symbols are given by
( (i)
xn = tanh
I (i)
Ln
2
)
( + j tanh
Q (i)
Ln
2
) .
(17)
For the first iteration there is no information about the transmitted symbols and Xk = 0. This means that our receiver can be regarded as a simple SC-FDE receiver with an interference cancellation, performed in the frequency domain, of the signals associated to different receiver antennas, while the MRT or EGT processing is performed at the transmitter side (precoding approach). For the subsequent iterations we employ the average values conditioned to the receiver output at the previous iteration to remove the residual intersymbol interference and inter user interference. In general, for moderate-to-high signal-to-noise ratio, the average values conditioned to the receiver output approach the transmitted signals as we increase the number of iterations, which means that the interference cancellation performed by Ck becomes more effective and the performance improves. Moreover, since the average values conditioned to the receiver output can be regarded as soft decisions [15], this reduces significantly error propagation effects in our iterative receiver (in fact, we did not observe error propagation effects).
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)
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3. Using the EGC receiver, ˜ Xk comes:
{ ( )} ˜ Yk . Xk = exp j arg HH k
(21)
Similar to the precoding case, a disadvantage of the MRC and EGC relating to ZFR relies on the generated interference, which degrades the performance. In order to improve the performance, we consider an iterative receiver, as defined in the following. 4.2. Interference cancellation using post-processing Since the post-processing approach considers the processing at the receiver side, the detector computes the data symbols obtained (r) from the IDFT of the block {˜ Xk ; k = 0, 1, . . . , N − 1} with:
( ) ˜ xn = IDFT ˜ Xk .
Fig. 2. Block Diagram of m-MIMO for (a) SC-FDE (b) details of MIMO receiver and interference cancellation using post-processing.
4. Transmitter structure for the proposed massive MIMO using post-processing 4.1. Computation of the post-processing coefficient We consider the multi-user massive MIMO scenario depicted in Fig. 2 which concerns the uplink transmission between T MTs and a BS with R antennas. For the sake of simplicity, and without loss of generality, we assume a single antenna at each MT. Alternatively, this system can be employed between a MT with T antennas and a BS with R receiving antennas, to send multiple streams of data. In either case we consider that R ≫T. Finally, this system can also be applied between two MTs. Similar to the precoding scenario, SC-FDE modulations are em(t) ployed. The tth MT has a block of N data symbols {xn ; n = (r) 0, 1, . . . , N − 1} to send. The received block at the BS is {yn ; k = 0, 1, . . . , N − 1}. As with other SC-FDE schemes, a cyclic prefix longer than the maximum overall channel impulse response is appended to each transmitted block and removed at the receiver. (r) In this case, the corresponding frequency-domain block {Yk ; k = 0, 1, . . . , N − 1} satisfies
[
(1)
(R)
Yk = Yk , . . . , Yk
]T
= Hk Xk + Nk
(18)
where Hk denotes the R × T channel matrix for the kth frequency, (r ,t ) with (r , t )th element Hk . The transmitted symbols comes Xk =
[
(1)
(T )
Xk , . . . , Xk
]T
.
Let[us consider the ]T frequency domain estimated data symbols (1) (R) ˜ ˜ ˜ Xk = Xk , . . . , Xk . 1. For the Zero Forcing Receiver (ZFR),2 the data symbols can be obtained from the IDFT of the block ˜ Xk , where [16]
)−1 H ( ˜ Xk = HH Hk Yk . k Hk
The estimated bits are obtained by applying the sign function to ˜ xn , depending on the modulation scheme. In the case of ZFR receiver, this involves the inversion of a matrix for each frequency component, and the dimensions of these matrices can be very high in massive MIMO systems. Massive MIMO schemes should usually employ simpler receivers. The simplest approach is probably to perform the MRC or EGC. This take advantage of the fact that, for massive MIMO systems with R ≫1 with small correlation between the channels between different transmit and receiving antennas, the elements outside the main diagonal of AH k Hk
(23)
are much lower than the ones at its diagonal, where (i, i )th element of the matrix A are defined as: ′
1. For MRC: [A]i,i′ = [H]H ′ . i,i
(
(
))
2. For EGC: [A]i,i′ = exp j arg [H]i,i′ , i.e., they have absolute value 1 and phase identical to the corresponding element of the matrix H. For SC-FDE signals we could employ a frequency-domain processing with MRC or EGC at each frequency, based on AH k Hk . However, the residual interference levels can still be substantial, especially for moderate values of T /R. To overcome this problem, we propose the iterative interference canceller (receiver) depicted in Fig. 2(b), where
˜ Xk = AH k Yk − Dk Xk .
(24)
The interference cancellation matrix Dk comes defined by Dk = A H k Hk − I
(25)
where I is an R × R identity matrix. canceller is implemented using Xk = [ This interference ] X 0 , . . . , X N −1 , with Xk denoting the frequency-domain average values conditioned to the FDE output for the previous iteration [15], as defined for the precoding. 5. Performance results
(19)
2. Using the MRC receiver, ˜ Xk comes:
˜ Xk = HH k Yk
(22)
(20)
where R stands for the number of receiving antennas. 2 ZFR refers to the ZF algorithm implemented as post-processing at the receiver side.
In this section we present a set of performance results concerning the proposed m-MIMO scheme using precoding optimized for mm-wave associated to SC-FDE signals. For the sake of comparison, this section performs a comparison with the post-processing methodology, using the same algorithms as those utilized in precoding. We consider Bit Error Rate (BER) performances, which are expressed as a function of Eb /N0 , where N0 is the one-sided power spectral density of the noise and Eb is the energy of the transmitted
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M. Marques da Silva, R. Dinis / Physical Communication (
Fig. 3. BER results with 32 × 8m-MIMO using precoding.
bits (i.e., the degradation due to the useless power spent on the cyclic prefix is not included). Each block has N = 256 symbols selected from a QPSK constellation under a Gray mapping rule (similar results were observed for other values of N, provided that N ≫ 1). Our channel has 16 equal power paths with uncorrelated Rayleigh fading. The channel is assumed to be invariant during the block. The duration of the useful part of the blocks (N symbols) is 1 µs and the cyclic prefix has duration 0.125 µs. For SC-FDE systems we considered the linear FDE (i.e., just the first iteration of the interference canceller) up to four iterations of the interference canceller. Beyond this number, the performance improvement was almost negligible. Linear power amplification is considered at the transmitter and perfect synchronization is assumed at the receiver. Fig. 3 considers BER results for massive MIMO with 32 transmitting antennas and 8 receiving antennas (32 × 8), using precoding. The three proposed algorithms are plotted (ZFT, MRT and EGT). Moreover, the matched filter bound is also plotted. Fig. 3 considers results with and without interference cancellation. In the case without interference cancellation, a regular SC-FDE receiver is considered (that is, a linear FDE receiver). Moreover, when interference cancellation is adopted, an iterative receiver is adopted. From Fig. 3 it is shown that the ZFT achieves a performance very close to the Matched Filter Bound (MFB). It is worth noting that the receiver employed with the ZFT is a regular SC-FDE receiver, without interference cancellation, because the ZFT algorithm does not generate interference. As opposed to the ZFR (post-processing approach), the ZFT precoding (pre-processing) does not generate noise enhancement, because when the processing is applied, the noise does not exist. As previously described, a disadvantage of the ZFT algorithm relies on the need to compute the pseudoinverse of the channel matrix, for each frequency component. To simplify this process, we proposed the use of the MRT and EGT, with the disadvantage of generating a certain level of interference. Fig. 3 shows results for 2 up to 4 iterations of the interference cancellation associated to MRT and EGT. Results with more than 4 iterations are not shown because the performance keeps approximately unchanged, as compared to 4 iterations. It is shown that, with 4 iterations of the interference cancellation, the performance obtained with the MRT approximates that of the ZFT and MFB. Moreover, with 4 iterations of the interference cancellation, the MRT algorithm tends to achieve a performance slightly better than that of the EGT. Fig. 4 considers BER results for massive MIMO with 64 transmitting antennas and 8 receiving antennas (64 × 8), using precoding.
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Fig. 4. BER results with 64 × 8 m-MIMO using precoding.
Fig. 5. BER results with 128 × 8 m-MIMO using precoding.
As compared to the previous graphic, we have increased the number of transmitting antennas, while leaving the number of receiving antennas unchanged. As can be seen from the results, with such increase of transmitting antennas, the performance obtained with both MRT and EGT with 4 iterations of the interference cancellation becomes closer to the ZF and MFB. Fig. 5 considers BER results for massive MIMO with 128 transmitting antennas and 8 receiving antennas (128 × 8), using precoding. As compared to the previous graphics, we have increased the number of transmitting antennas, while leaving the number of receiving antennas unchanged. As before, with such increase of transmitting antennas, the performance obtained with both MRT and EGT with 4 iterations of the interference cancellation becomes even closer to the ZFT and MFB. Fig. 6 shows the BER results for the massive MIMO with 32 transmitting antennas and 2 receiving antennas (32 × 2), using precoding. As compared to Fig. 3 (32 × 8), we have reduced the number of receiving antennas, which leads to a performance improvement because the level of interference decreases for MRT and EGT. Note that the level of interference increases with the number of receiving antennas. As expected, it is noticeable that the performance obtained with MRT with 4 iterations of interference cancellation is very close to the MFB and ZFT, even with only 32 transmitting antennas.
Please cite this article in press as: M. Marques da Silva, R. Dinis, A simplified massive MIMO implemented with pre or post-processing, Physical Communication (2017), http://dx.doi.org/10.1016/j.phycom.2017.06.002.
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Fig. 6. BER results with 32 × 2 m-MIMO using precoding.
Fig. 7. BER results for m-MIMO with different number of transmit and receiving antennas using Precoding (MRT and EGT have 4 iterations of interference cancellation).
Fig. 7 shows the performance comparison for massive MIMO, using precoding, with different number of transmit and receiving antennas, considering the ZFT. Moreover the MRT and EGT is plotted always with 4 iterations of the interference cancellation, because this represents a signal clear enough of interference (see previous figures). As can be seen, for a certain number of receiving antennas, the increase of transmitting antennas leads to performance improvement. This is visible when we move from 32 × 8 into 128 × 8 configuration. Moreover, the increase of receiving antennas corresponds to a decrease of performance, due to the raise in the level of interference. This is visible when we move from 32 × 2 into 32 × 8 configuration. Finally, it is noticeable that the performance obtained with the ZFT is very insensitive to variations in the number of transmit and receiving antennas, but this is obtained at the cost of a high level of computation associated to the precoding (computation of the pseudo-inverse of a matrix, for each frequency). Fig. 8 considers BER results for massive MIMO using both precoding and post-processing. In the case of precoding the mMIMO adopted comprises 32 transmitting antennas and 8 receiving antennas (32 × 8), while the post-processing comprises 8
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Fig. 8. BER results with m-MIMO using precoding (32 × 8) versus post-processing (8 × 32).
transmitting antennas and 32 receiving antennas (the reciprocal). The three proposed algorithms used in both precoding and postprocessing are ZFT/ZFR, MRT/MRC and EGT/EGC. Moreover, the matched filter bound is also plotted. Fig. 8 considers results with and without interference cancellation. From Fig. 8 it is shown that the ZF in precoding (ZFT) achieves a performance very close to the MFB, while the ZF in post-processing (ZFR) presents a worse performance. It is worth noting that the receiver employed with either precoding or post-processing ZF is a regular SC-FDE receiver, without interference cancellation, because the ZF algorithm does not generate interference. Moreover, as opposed to the ZFR (postprocessing approach), the ZFT (pre-processing) does not generate noise enhancement, because when the processing is applied, the noise does not exist. As previously described, a disadvantage of the ZF algorithm relies on the need to compute the pseudo-inverse of the channel matrix, for each frequency component. To simplify this process, we proposed the use of the MRT/MRC and EGT/EGC (using both pre and post-processing), with the disadvantage of generating a certain level of interference. Fig. 8 shows results for 2 and 4 iterations of the interference cancellation associated to MRT/MRC and EGT/EGC. Results with more than 4 iterations are not shown because the performance keeps approximately unchanged, as compared to 4 iterations (using both pre and post-processing). It is viewed that, for MRT/MRC and EGT/EGC, the post-processing tends to achieve a performance slightly better than those achieved with the pre-processing (precoding). Exceptionally, the results obtained without interference cancellation are the same for both MRT/MRC and EGT/EGC. It is also viewed that the MRT/MRC with interference cancellation always performs better than the EGT/EGC (for the same number of iterations), either in pre-processing or post-processing. Finally, it is viewed that, with 4 iterations of the interference cancellation, the performance obtained with the MRC using post-processing approximates that of the MFB, while the MRT using pre-processing presents a slightly worse performance. Fig. 9 considers BER results for massive MIMO using both preprocessing (precoding) and post-processing. In the case of precoding the m-MIMO adopted comprises 64 transmitting antennas and 8 receiving antennas (64 × 8), while the post-processing comprises 8 transmitting antennas and 64 receiving antennas (the reciprocal). As compared to the previous graphic, we have increased the number of transmit or receiving antennas (precoding or post-processing, respectively), while leaving the other number of antennas unchanged. As can be seen from the results, with such increase of antennas, and for both pre and post-processing
Please cite this article in press as: M. Marques da Silva, R. Dinis, A simplified massive MIMO implemented with pre or post-processing, Physical Communication (2017), http://dx.doi.org/10.1016/j.phycom.2017.06.002.
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References
Fig. 9. BER results with m-MIMO using precoding (64 × 8) versus post-processing (8 × 64).
for MRT/MRC and EGT/EGC, for different number of iterations of the interference cancellation, the performance improves relating to the scenario with 32 antennas (previous graphic). For the case with 4 iterations of the interference cancellation, the MRT/MRC implemented either using the pre-processing or the post-processing achieves a performance very close to the MFB. Moreover, as before, the ZF using the pre-processing (ZFT) performs better than that using post-processing (ZFR). This occurs because the ZFR presents noise enhancement while the pre-processing does not. 6. Conclusions In this paper we considered the massive MIMO using precoding, with different algorithms optimized for mm-Wave. For the sake of comparison, the post-processing methodology was also described, analyzed and compared, using the same algorithms as those utilized in precoding. It was viewed that the precoding ZFT achieves a performance very close to the MFB, while the post-processing ZFR does not, due to the noise enhancement. Moreover, it was described that a disadvantage of the ZF algorithm relies on the need to compute the pseudo-inverse of the channel matrix, for each frequency component. To avoid this and simplify this process, we have proposed the use of the MRT/MRC and EGT/EGC. These two algorithms were described in both pre-processing and post-processing methodologies. A disadvantage of these algorithms rely on a certain level of interference that is generated. To remove this interference, we have proposed a novel iterative interference canceller. It was viewed that the MRT/MRC tends to outperform the EGT/EGC. These algorithms implemented in post-processing achieve a performance slightly better than in the pre-processing methodology. Implementing the MRT/MRC and EGT/EGC algorithms for m-MIMO with mm-Wave, associated to the interference cancellation, we avoid the computation of the pseudo-inverse matrix, and therefore simplify the processing (either pre or post-processing), while achieving a performance very close to the MFB, especially with 4 iterations of the interference canceller. Acknowledgment This work was supported by the Portuguese Foundation for the Science and Technology (FCT) under project UID/EEA/50008/2013.
[1] F. Rusek, D. Persson, B.K. Lau, et al., Scaling up MIMO: opportunities and challenges with very large arrays, IEEE Signal Process. Mag. 30 (1) (2013) 40– 60. [2] F. Boccardi, R. Heath, A. Lozano, T. Marzetta, P. Popovski, Five disruptive technology directions for 5G, IEEE Commun. Mag. 52 (2) (2014) 74–80. [3] IEEE 802.11 Task Group, AD, PHY/MAC Complete Proposal Specification, IEEE 802.11-10/0433r2, May 2010. [4] T.S. Rappaport, Shu Sun, R. Mayzus, Hang Zhao, Y. Azar, K. Wang, G.N. Wong, J.K. Schulz, M. Samimi, F. Gutierrez, Millimeter wave mobile communications for 5G cellular: It will work! IEEE Access 1 (2013) 335, 349. [5] S. Nie, G. MacCartney, S. sun, T. Rappaport, 28 GHz and 73 GHz signal outage study for millimeter wave cellular and backhaul communications, in: IEEE ICC’2014, Sydney, Australia, Jun., 2014. [6] S. Rangan, T.S. Rappaport, E. Erkip, Millimeter-wave cellular wireless networks: Potentials and challenges, Proc. IEEE 102 (3) (2014) 366, 385. [7] D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, B. Eidson, Frequency domain equalization for single-carrier broadband wireless systems, IEEE Commun. Mag. 4 (4) (2002) 58–66. [8] Y. Li, K. Han, C. Dong, A multi-band low-noise transmitter with digital carrier leakage suppression and linearity enhancement, IEEE Trans. Circuits Syst. I 60 (5) (2013). [9] N. Benvenuto, S. Tomasin, Block iterative DFE for single carrier modulation, IEE Electron. Lett. 39 (19) (2002). [10] R. Dinis, A. Gusmão, N. Esteves, On broadband block transmission over strongly frequency-selective fading channels, in: Wireless 2003, Calgary, Canada, July, 2003. [11] R. Dinis, R. Kalbasi, D. Falconer, A. Banihashemi, Iterative layered space-time receivers for single-carrier transmission over severe time-dispersive channels, IEEE Commun. Lett. 8 (9) (2004) 579–581. [12] M. Marques da Silva, A. Correia, R. Dinis, N. Souto, J. Silva, Transmission Techniques for Emergent Multicast and Broadcast Systems, first ed. CRC Press Auerbach Publications, New York, USA, ISBN: 9781439815939, 2010. [13] M. Tuchler, R. Koetter, A. Singer, Turbo equalization: Principles and new results, IEEE Trans. Commun. 50 (2002). [14] A. Gusmão, P. Torres, R. Dinis, N. Esteves, A class of iterative FDE techniques for reduced-CP SC-based block transmission, in: Int. Symposium on Turbo Codes, April, 2006. [15] P. Silva, R. Dinis, Frequency-Domain Multiuser Detection for CDMA Systems, River Publishers, Aalborg, 2012. [16] P. Montezuma, D. Borges, R. Dinis, Low complexity MRC and EGC based receivers for SC-FDE modulations with massive MIMO schemes, in: IEEE GLOBALSIP, Washington DC, Dec., 2016.
Mário Marques da Silva is an Associate Professor and the Director of the Department of Sciences and Technologies at Universidade Autónoma de Lisboa. He is also a Researcher at Instituto de Telecomunicações, in Lisbon, Portugal. He received his B.Sc. in Electrical Engineering in 1992, and the M.Sc. and Ph.D. degrees in Electrical and Computers Engineering (Telecommunications), respectively in 1999 and 2005, both from Instituto Superior Técnico, University of Lisbon. Between 2005 and 2008 he was with NATO Air Command Control & Management Agency (NACMA) in Brussels (Belgium), where he managed the deployable communications of the new Air Command and Control System Program. He has been involved in multiple networking and telecommunications projects. His research interests include networking and mobile communications, namely block transmission techniques (OFDM, SC-FDE), interference cancellation, space-time coding, MIMO systems, smart and adaptive antennas, channel estimation, software defined radio, IP technologies and network security. Mário Marques da Silva is also a Cisco certified CCNA instructor. He is the author of five books entitled Multimedia Communications and Networking, Transmission Techniques for Emergent Multicast and Broadcast Systems, Transmission Techniques for 4G Systems, MIMO Processing for 4G and Beyond: Fundamentals and Evolution and Cable and Wireless Networks: Theory & Practice (all from CRC Press). Moreover, he is author of several dozens of journal and conference papers, a member of IEEE and AFCEA, and reviewer for a number of international scientific IEEE journals and conferences. Finally, he has chaired many conference sessions and has been serving in the organizing committee of relevant EURASIP and IEEE conferences. Links to detailed CV: https://www.it.pt/Members/Index/791 https://www.crcpress.com/authors/i262-mario-marques-da-silva https://www.researchgate.net/profile/Mario_Marques_da_Silva2 http://wirelesscommunication.conferenceseries.com/
Please cite this article in press as: M. Marques da Silva, R. Dinis, A simplified massive MIMO implemented with pre or post-processing, Physical Communication (2017), http://dx.doi.org/10.1016/j.phycom.2017.06.002.
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Rui Dinis received the Ph.D. degree from Instituto Superior Técnico (IST), Technical University of Lisbon, Portugal, in 2001. From 2001 to 2008 he was a Professor at IST. Since 2008 he is teaching at FCT-UNL (Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa). He was a researcher at CAPS/IST (Centro de Análise e Processamento de Sinais) from 1992 to 2005; from 2005 to 2008 he was researcher at ISR/IST (Instituto de Sistemas e Robótica); in 2009 he joined the research center IT (Instituto de Telecomunicações). He is serving as editor at IEEE Transactions on Communications in the Transmission Systems area, sub-area of Frequency-Domain Processing and Equalization. He has been involved in several research projects in the broadband wireless communications area. His main research interests include modulation, equalization, channel estimation and synchronization.
Please cite this article in press as: M. Marques da Silva, R. Dinis, A simplified massive MIMO implemented with pre or post-processing, Physical Communication (2017), http://dx.doi.org/10.1016/j.phycom.2017.06.002.