Iterative timing-induced interference suppression in a two-tier OFDMA uplink network

Digital Signal Processing 81 (2018) 90–99

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Digital Signal Processing www.elsevier.com/locate/dsp

Iterative timing-induced interference suppression in a two-tier OFDMA uplink network Mohammad Pourmoazen a , Mohammad Movahhedian b,∗ , Bahare S. Mousavitabar a a b

Department for Engineering and Technology, Imam Khomeini International University, Qazvin, Iran Mobile Communication Company of Iran (MCI), Tehran, Iran

a r t i c l e

i n f o

Article history: Available online 23 July 2018 Keywords: Femtocell Orthogonal Frequency-Division Multiple Access (OFDMA) Uplink Inter-Carrier Interference (ICI) Precoder Automatic gain controller Equalizer Iterative algorithm

a b s t r a c t Consider a scenario in a two-tier cellular network wherein all subscribers adjust their transmission-times to be synchronously received at the macro base-station (MBS). This transmission timing arrangement causes asynchronous reception of signals and inter-carrier interference (ICI) at the femto base-station (FBS). In this paper, an iterative interference suppression scheme for reducing the ICI at the FBS is presented. By assuming a number of macro-users (MUs) and a single femto-user (FU), the mean square error (MSE) cost-function is first defined, based on which, the closed-forms for 3 underlying parameters, i.e., precoder, equalizer and the automatic gain controller are then derived by proposing a partial derivative-based sub-optimization scheme. To counteract the interrelation of the aforementioned parameters, an iterative algorithm is further proposed which results in finding a local-optimum point of the cost-function. To demonstrate the successful interference suppression performance of the proposed scheme, a per-subcarrier interference power analysis is also derived. The simulation results demonstrate a reasonable convergence after 6 iterations. Moreover, for the proposed scheme, a close bit error rate (BER) performance to that of a system without any timing-induced interference at low and medium SNRs (i.e., <20 dB) and a comparable performance at higher SNRs (i.e., 20 dB & <30 dB) are observed. © 2018 Elsevier Inc. All rights reserved.

1. Introduction The increasing appetite of cellular users for higher data-rates and sustainable QoS is showing no signs of slowing down over the past decades. On the other hand, more than 50% of voice-calls and 70% of data-download [1] are happening at the indoor environments. Therefore, a more localized solution for the provision of higher capacity particularly to the indoor cellular subscribers had to be proposed by mobile operators. One of the promising solutions was to deploy low-power-short-range nodes, a.k.a., smallcells within the macrocell coverage and as a typical example, femtocells. Femtocell is a base station with stringent transmit power constraint, i.e., 10 to 100 mW and hence a shorter coverage range, i.e. 10 to 30 meters [2] that is often bought and installed by the end-users and could be connected to the core of cellular network through a broadband connection by means of the digital subscriber line (DSL), cable modem or via a separate radio frequency backhaul link. The advantages of using femtocells within the cellular net-

*

Corresponding author. E-mail addresses: [email protected] (M. Pourmoazen), [email protected] (M. Movahhedian), [email protected] (B.S. Mousavitabar). https://doi.org/10.1016/j.dsp.2018.05.014 1051-2004/© 2018 Elsevier Inc. All rights reserved.

work are in several folds. While the use of femtocells can offload a considerable amount of data from macrocells, particularly in the areas with higher localized data-demanding subscribers, they also play an important role in expanding the coverage and increasing the overall network capacity, in comparison with the traditional single-tier cellular networks [1–4]. On the other hand, the latest 3GPP standardized multiple-access scheme that is used as the air-interface on the front-haul link of cellular networks is called orthogonal frequency-division multipleaccess (OFDMA) [5–10]. OFDMA is a promising scheme due to its higher resilience to frequency-selective fading, higher flexibility in scheduling of physical resource blocks to different subscribers based on their channel fading status and the relative ease of hardware implementation at the TX and RX sides. Besides its positive points, OFDMA is extremely vulnerable to timing misalignments. If the timing misalignment is greater than the cyclic prefix (CP), the orthogonality between subcarriers would be destroyed and the inter-carrier interference (ICI) as well as the inter-symbol interference (ISI) would occur [11–13]. Consider a scenario wherein a number of cellular subscribers are connected to a two-tier OFDMA-based network, consisting of both macro and femto base stations. In such a scenario, the aforementioned subscribers need to set their uplink transmission time-

M. Pourmoazen et al. / Digital Signal Processing 81 (2018) 90–99

origins in a way to ensure all transmitted signals are received at the macro base-station (MBS) in a time-synchronous manner. This transmission timing constraint generally causes asynchronous reception of these signals at an arbitrary femto base-station (FBS) [14] and hence cross-tier interference, i.e. the interference between MBS and FBS, would occur if the timing misalignments of the corresponding macro-users (MUs) are greater than the pre-specified CP length. Several papers in the literature have considered this problem so far [15–24]. These research works could be divided into two general categories, based on their undertaken approach. Category I: The schemes within this category generally concentrate on the analysis of the timing-induced interference. The most significant works within this category are listed as follows. The analysis of spectrum opportunities detection in the presence of timing misalignment in the OFDMA cognitive radios [15]. Hamdi et al. considered the interference induced by timing misalignment in an OFDMA-based ad-hoc network [16]. They showed that the spectral efficiency can be maximized by adequate guard-intervals and also positioning the fast Fourier transform (FFT) windows in a dynamic manner, for both subband and interleaved subcarrier allocation schemes. In [17], the geometrical 2D contour over which the MUs could generate ICI on the uplink direction was determined. Moreover, the critical distance between the MBS and the FBS, beyond which the FBS would undergo ICI was calculated. A more accurate derivation for the aforementioned contour (than the one in [17]) was proposed in [18]. Moreover, the probability of an MU causing ICI to a given FBS was derived. The results of this research showed that the use of open-access femtocells could help in reducing the uplink interference induced by the timing misalignments. The cumulative distribution function (CDF) belonging to the arrival-times of the MUs’ signals at the FBS was derived in [19]. Wang et al. in [20] made an in-detail analysis of the timinginduced interference and based on that derived the close-forms for the average ICI power and the probability mass function (PMF) for the above-mentioned arrival-times by exploitation of a more accurate CDF form than [19]. As the last step in this direction, ICI and IBI (inter-block interference) were analyzed in the uplink direction of heterogeneous cellular networks where multiple macrocells are considered in [21]. Category II: On the other hand, the approaches within the second category have suggested some interference mitigating schemes to prevent the ICI induced by the timing-misalignments. Within this category, one of the suggested methods for mitigating the ICI is to increase the CP-length to become greater than required for combating the ISI arisen from the collective effect of both the multipath fading and the timing-offsets [22]. This method maintains the orthogonality between subcarriers at the receiver at the cost of an effective reduction in the spectral efficiency. As the second example within this category, the authors in [23] proposed an approach where the synchronization point at the FBS is set to the instance of first arriving signal. Their proposed method is of a reasonable complexity but further ICI suppression would require some others appropriate accompanying schemes. Looking at it from another perspective, performing synchronization with respect to this point could increase the probability of the ICI occurrence due to the fact that the arrival-time of the first arriving signal is generally earlier than the first arriving MU. This issue would in turn increase the chance of having larger relative-delays than the CP length. As the best performing approach in this category, Wang et al. in [24] proposed a precoding scheme by maximizing femtocell uplink capacity in an OFDMA two-tier network. Based on this method, the effect of interference induced by timing-misalignments is reduced. Despite demonstrating good results in terms of femtocell uplink capacity, an important drawback of this scheme is the se-

91

vere degradation in ICI suppression behavior on the last two subcarriers, in the presence of one femto-user. As stated earlier, most of the research works so far either concentrate on timing-induced interference analysis (i.e., Category I above) or they propose ICI mitigating algorithms (i.e., Category II above). To the best of our knowledge, very few works are proposed so far with the purpose of interference suppression to counteract the adverse effects of timing-induced ICI in a two-tier OFDMA uplink network. To further clarify the difference between the proposed scheme and the above two categories, the schemes within the first category do not often propose a particular algorithm to counteract the detrimental effect of timing-induced interference. Instead, they mostly concentrate on formulating the interference signal as well as the measurement of the interference power and how it would affect the overall system performance. On the other hand, within the second category, the concentration is made upon proposing some pre-processing interference mitigating schemes to prevent the occurrence of timing-induced interference. In contrary, the research work presented here would belong to a third category within this context, in the sense that it proposes a post-processing iterative interference suppression scheme with the following details. This paper presents an iterative scheme for the suppression of timing-induced ICI in a two-tier macro-femto OFDMA uplink network. The major contributions of this paper are in three folds as follows. 1– By assuming a number of MUs and a single precoded femtouser (FU), the mean square error (MSE) cost-function is first defined, based on which, the closed-forms for 3 underlying parameters, i.e., the precoder matrix, the joint deprecoder–equalizer matrix and the gain controller scalar are then derived by proposing a partial derivative-based sub-optimization scheme. 2– It is observed from the closed-forms that the abovementioned three parameters are inter-related to each other which calls for an appropriate post-processing technique. As a possible solution, an iterative interference suppression scheme is proposed with a reasonable convergence behavior (i.e., 6 iterations) which achieves a bit error rate (BER) performance result close to an interference-free scenario at low and medium SNRs (i.e., <20 dB). For higher SNRs (>20 dB and <30 dB), the BER performance is comparable to the interference-free scenario even for the distances as large as 900 m between MBS and FBS. 3– To further demonstrate the effectiveness of the proposed iterative scheme in terms of interference suppression, the ICI power induced by MUs’ timing-misalignments is derived on a persubcarrier basis. By taking advantage of the close-form for the ICI power, it is semi-analytically shown that the proposed scheme could enhance the signal-to-interference-plus-noise ratio (SINR) indicator by ≈ 0.8 dB at SNR = 30 dB and ≈0.3 dB at SNR = 25 dB for distances as large as 900 m between MBS and FBS. The rest of this paper is organized as follows. The system model for a two-tier OFDMA uplink network is presented in section 2. Section 3 contains our proposed iterative interference suppression scheme. We analyze SINR on a per-subcarrier basis in section 4. In section 5, the simulation results are described. Finally, conclusions are drawn in Notation. In this paper, column vectors and matrices are denoted by lower-case and upper-case boldface italic letters, respectively. [.] T , [.]∗ and [.] H denote matrix transposition, conjugation and conjugate transposition, respectively. tr(.) refers to the sum of diagonal elements of the enclosed matrix. The matrix I N stands for the N × N identity matrix and 0 N × M refers to an N × M zero matrix. Moreover, C N × M denotes the N × M complex matrices and R N × M refers to the N × M real matrices. We represent the complex Gaussian distribution with a mean μ and a variance σ 2 by

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M. Pourmoazen et al. / Digital Signal Processing 81 (2018) 90–99

Table 1 Variables used in this paper. Variables

Description

Variables

Description

a

Path loss exponent

T (k)

Number of subcarriers assigned to kth user

c

Speed of light

T rx

d(k)

Distance between kth MU and the FBS

trx

Arrival time of kth user signal

f x (x)

Marginal probability density function of x

Ts

Sampling period

f xy (x, y )

Joint probability density function of x and y

ttx

EH

Equalizer matrix

w

F

FFT matrix

xm

(k)

mth OFDM block of kth user of transmitted signal

h(k) (n)

nth channel tap of kth user

ym

mth OFDM block of the received signal at the FBS

H (k)

Toeplitz channel matrix between kth user and the FBS

Y m (l)

Received signal at the lth subcarrier of the mth block

J (int+n)

Power of interference and noise on the jth subcarrier of mth block of the FU

z

Interference and noise terms

K

Number of MUs

μ ρ ω η

Lagrangian coefficient

(k)

Discrete arrival time of kth user signal

(k)

(k)

Transmission time of kth user signal Noise vector

Lagrangian function

L

Channel length

M

Number of OFDM blocks in each frame

N

Number of subcarriers

N cp

Cyclic prefix length Precoding matrix

λf λm

Average received SNR level of the FU at the FBS

P r (k)

Distance between kth MU and the MBS

σ w2

Noise variance

R

Macrocell coverage radius

θ (k)

Angle of kth user placement

Rf

Distance between the FBS and the MBS on the X-axis

ξ (k)

Discrete-time relative delay of kth user

R zz

Covariance matrix of z

γ (k)

Transmitted power of kth user

(k)

mth data block of kth user

(k)

Ordered subcarrier-index set assigned to kth user

(k)

Data symbol transmitted over the jth subcarrier of the mth block of the kth user

 Rx

CP removing matrix

(0)

mth precoded data block of the FU

T x

CP inserting matrix

sˆ m

(0)

mth block of the FU detected signal

ϒ(k)

Modeling relative discrete-time delay of kth user

Sˆ m ( j )

jth subcarrier of the mth block of the FU detected signal

ϒ pre

Modeling interference from previous OFDM block of kth user

SINRm ( j )

SINR on the jth subcarrier of the mth block of the FU

(k)

Frequency mapping matrix of kth user

sm

Sm ( j) s´m

(0)

Automatic gain controller MSE function Average received SNR level of the MU at the MBS

(k)

CN(μ, σ 2 ). Finally, n(.), E [.], ||.|| and . stand for the number of elements belonging to the enclosed set, expectation, the Euclidean norm and the integer ceiling, respectively. All variables used in this paper are summarized in Table 1. 2. System model Consider the uplink direction of a two-tier OFDMA-based mobile cellular network. Without loss of generality and for the sake of clear presentation, it is assumed that the cellular network of our interest consists of one MBS with K MUs and one FBS that only serves one FU [18]. The MBS coverage area has radius of R. By considering polar coordinates, according to Fig. 1, the MBS is assumed to be located at (0, 0) and kth MU is located at (r (k) , θ (k) ) where 1 ≤ k ≤ K . Without loss of generality, the FBS is located at ( R f , 0). It is also assumed that all MUs are uniformly distributed in the macrocell coverage [18]. Consequently, the joint probability density function of r (k) and θ (k) is f r θ (r , θ) = π rR 2 where 0 ≤ r ≤ R and 0 ≤ θ ≤ 2π with marginal probability density functions f r (r ) =

2r R2

Fig. 1. Schematic representation of the relative positions of MBS, FBS and their corresponding user equipments.

d(k) =

(k)

trx =

mits its signal at time ttx = R −cr , where c is the speed of light. As the MU signals are transmitted in a way to comply with the timing-synchronization requirements of the MBS, they are not necessarily received at the FBS synchronously. According to Fig. 1, the distance between the kth MU and the FBS can be given by

T rx =

(k)

(r (k) )2 + R 2f − 2r (k) R f cos θ (k) . Thus, the kth MU signal is

received at the FBS at the time

and f θ (θ) = 21π . In order to have simultaneous reception of all signals belonging to different MUs at the MBS, the user farther away from the MBS transmits its signal earlier than the user closer to the MBS [25]. Without loss of generality, assume that the MU which is located on the border of the macrocell, transmits its signal at time zero [18]. Therefore, the kth MU which located at radius r (k) , trans(k)



R − r (k) + d(k) c

.

(1) (0)

It is supposed that 0th user is the FU and its arrival time is trx while users with indexes of 1 to K are the MUs and their arrival (1) (K ) times are expressed by trx to trx . The discrete arrival time of kth user signal is

 (k)

(k) 

trx

Ts

,

(2)

where T s is the sampling period. The FBS synchronization time (0) is set at trx . It is assumed that the arrival time of the FU signal is equal to first discrete arrival time of the MU signal which

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93

(0) (0) where s´m ∈ C T ×1 is the mth precoded data block of the FU. Power constraint condition is satisfied for precoded signal

    ( 0) ( 0) E ||´sm ||2 = E || P sm ||2 tr( P P H γ (0) ) = γ (0) T (0) .

(5)

The FU’s precoded data symbol blocks and the MU’s data symbol blocks are mapped to own subcarriers set



(k)

xm =

( 0)

if k = 0

(k)

if k = 0 ,

(0) s´ m (k) sm

where (k) ∈ R N × T which equals to Fig. 2. The signal arrival times belonging to the FU and MUs and the corresponding induced timing misalignments.

(0)

(1)

⎡

(k)

(k)

sm =



(0)



T

(k) (k) (k) γ (k) S m (1), S m (2), . . . , S m ( T (k) ) ,

(3) (k)

where 1 ≤ m ≤ M, γ (k) is the transmitted power, S m ( j ) is the data symbol transmitted over the jth subcarrier of mth block of kth user and data symbols are assumed to be independent random variables with zero mean and unit variance. The fractional power control is used in this paper which indicates that the transmitted power of different MUs is chosen in such a way that their SNR level in the MBS will be equal to a desired level λm [26]. Hence, 2 (k) a the transmitted power of kth MU is γ (k) = λm σ w (r ) , where σ w2 is noise variance and 1 ≤ k ≤ K . This rule is true for the FU where 2 its transmitted power is γ (0) = λ f σ w (d(0) )a and λ f is the received SNR level of the FU at the FBS. (0) (0) A precoding matrix P ∈ C T × T is applied to all data symbols 1 belonging to the FU ( 0)

( 0)

s´ m = P sm ,

(4)

I T (k)

⎤ ⎥ ⎦

(7)

0( N − (k) (1)− T (k) +1)× T (k)

means trx = min{ T rx , . . . , T rx } [20]. Therefore, the discrete-time relative delay of kth user is ξ (k) = T rx − trx . In a multipath channel with length L, the discrete-time relative delay of kth user is (k) (0) ξ (k) = T rx − trx + L − 1 where ( L − 1) corresponds to the length of channel image. It should be noted that the fractional timing misalignment can be incorporated into channel impulse response and hence be compensated by channel equalization techniques. If ξ (k) ≤ N cp , the orthogonality between subcarriers is preserved and hence there is no interference. If ξ (k) > N cp , the FFT window of the FU (desired signal) would overlap with previous OFDM block of the kth MU, inducing ISI and ICI. The cyclic structure is not maintained for this MU and orthogonality between subcarriers is lost (see Fig. 2). Throughout this paper, it is assumed that all users are well synchronized along the frequency direction and hence there is no interference induced by the carrier frequency offsets (CFOs). It is assumed that our system has N subcarriers. (k) is the ordered subcarrier-index set assigned to kth user with n( (k) ) = T (k) K  subcarriers where k=1 (k) = {0, 1, ..., N − 1} and (k) ( j ) = φ where k = j. There are M OFDM blocks in each frame. The data stream of kth user after serial to parallel conversion at the mth block can be given as

is the frequency mapping matrix of kth user

0( (k) (1)−1)× T (k)

⎢ (k) = ⎣

(K )

(k)

(6)

and (k) (1) denotes the first element of (k) . The data blocks are modulated over the whole allocated bandwidth, by taking N-point inverse fast Fourier transform (IFFT) from each OFDM block. Then, the CP is appended to the beginning of each block where N cp ≥ L − 1. In the next step, the signal is transmitted through the physical channel and then the CP is removed from the blocks at the receiver. Finally, we perform users data decomposition through FFT. The mth OFDM block of the received signal at the FBS is given in the matrix form by

ym = [Y m (1), Y m (2), . . . , Y m ( N )] T

=

K 

(k)

F  Rx ϒ(k) H (k)  T x F H xm

(8)

k =0

+

K  k =1

(k)

(k)

F  Rx ϒ pre H (k)  T x F H xm−1 + F  Rx w ,

where Y m (l) is the received signal at the lth subcarrier of the mth block. F ∈ C N × N denotes the FFT matrix where 2π (n)(l) 1 F (n, l) = √ e − j N , 0 ≤ n, l ≤ N − 1. (9) N  T  T x = [0 N cp ×( N −N cp ) I N cp ] T I N ∈ R(N +N cp )× N and  Rx = [0 N × N cp I N ] ∈ R N ×( N +N cp ) are the CP inserting and CP removing matrices, respectively. H (k) ∈ C( N + N cp )×( N + N cp ) is a Toeplitz ma-

trix, which represents the channel impulse responses between kth user and the FBS. Its first column is [h(k) (1), h(k) (2), . . . , h(k) ( L ), 0, . . . , 0] T where

h(k) (n) = (d(k) )−a/2

L 

(k)

g i δ(n − i ).

d(k) is the distance between kth user and the FBS, a is the path loss exponent, L is the number of channel taps and δ(.) is the (k) delta Dirac function. It is assumed that g i is a random vari-



able with zero mean and variance 1

In LTE, the initial connectivity of a user-equipment (UE) is performed through the following steps [22]. 1– UE needs to synchronize with the network at the slot-level through primary synchronization signal (PSS) and at the frame-level via the secondary synchronization signal (SSS). Using both PSS and SSS, UE is able to derive its physical cell ID (PCI). 2– Upon completion of UE synchronization in the downlink direction, the UE is required to synchronize in the uplink direction through random access channel (RACH) procedure. There are generally two types of RACH procedure as follows, non-contention-based and contention-based procedures.

(10)

i =1

σi2 = E | g i(k) |2



where the

power is normalized to unity. w ∈ C N ×1 is the noise vector where 2 w ∼ CN(0 N ×1 , σ w I N ). Finally, the relative discrete-time delay and

It is important to note here that in this paper the precoding process, which is performed on all OFDM data symbols of the UE (e.g., the FU as in this paper), can change the aforementioned preamble pattern sent through the uplink RACH channel. This issue calls for a more complicated design of precoding matrix at the transmitter side, which is not within the research scope of this paper.

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M. Pourmoazen et al. / Digital Signal Processing 81 (2018) 90–99

the interference from previous OFDM block are modeled by ϒ(k) ∈ (k) R(N +N cp )×( N +N cp ) and ϒ pre ∈ R(N +N cp )×( N +N cp ) , respectively, where

 ϒ(k) = 0ξT(k) ×( N + N

 cp )

I N + N cp −ξ (k)

0( N + N cp −ξ (k) )×ξ (k)

T T (11)



η = E ||ˆs − s||2

  = E ||ω−1 E H ( P s + z ) − s||2    = tr ω−2 γ E H  P P H  H E + E H R zz E −ω

and (k)

ϒ pre =



0ξ (k) ×( N + N cp −ξ (k) )

I ξ (k)

T

T

0T

( N + N cp −ξ (k) )× N B

. (12)

−1





H



−1

H

H



(17)



γ E P − ω γ P  E + γ I T ,

where R zz is the covariance matrix and equals to

R zz =

3. Iterative interference suppression through precoding, automatic gain control and equalization



K 

γ (k) (k) [(k) ] H +

k =1

K 

k) k) H γ (k) (pre [(pre ] + σ w2 I T (0) .

k =1

(18) In this section, we propose an interference suppression scheme together with an iterative algorithm to reduce the effect of MUs’ interference at the FBS. It is supposed that the channel impulse responses and all user’s time delay are known at the transmitter and the receiver sides [24,27]. By plugging (4) and (6) into (8), performing FU subcarrier selection and finally multiplying equalizer and automatic gain controller with the received signals, the mth block of the FU detected signal is given by

Also, the power constraint condition in (5) must be considered in (17) by Lagrangian coefficient μ ∈ R [28]

ρ ( P , E , ω, μ) 

    = tr ω−2 γ E H  P P H  H E + E H R zz E − ω−1 γ E H  P      − ω−1 γ P H  H E + γ I T + μ γ tr( P P H ) − γ T .

sˆ m = ω−1 E H [(0) ] T ym ( 0)

=ω

−1

+ω

H

( 0) T

E [

−1



E

H

] F  Rx ϒ

 K k =1

+

K  k =1

(19) ( 0)

H



( 0)

H

( 0)

T x F 



( 0)

For finding the best candidates for P , ω and E that will be resulting in the interference suppression and according to the requirements contained in [28], we take the derivative of ρ with respect to P , ω, E and μ and then set each of them to zero through the following 4 steps.

P sm

(0) (k)

[(0) ]T F  Rx ϒ(k) H (k)  T x F H (k) sm    (k)

(13)

∂ρ = tr( P P H ) − T = 0, ∂μ

k) (k) [(0) ]T F  Rx ϒ(pre H (k)  T x F H (k) sm−1    (k)

 ( 0) T + [ ] F  Rx w ,

 pre

tr( P P H ) = T .

(0)

sˆ = ω−1 E H ( P s + z ),

K  k =1

(21)

Step 2:

   ∂ρ = tr − 2ω−3 γ E H  P P H  H E + E H R zz E ∂ω   + ω −2 γ E H  P + P H  H E = 0,

(22)

(14) which can be written as

where

z=

(20)

which results in

where E H ∈ C T × T is the equalizer matrix performing joint deprecoding and channel equalization. The transmit power constraint for the precoder is met by choosing ω ∈ R+ . We can rewrite (13) in the linear form as (0)

Step 1:



(k)

(k) sm +

K  k =1



tr E H  P P H  H E + (k) (k)

 pre sm−1 + [(0) ]T F  Rx w

(15)

=

denoting the interference and noise terms. The indexes m and (0) are omitted for the sake of simplification in (14). 3.1. Designing precoder, automatic gain controller and equalizer

ω 2

 

H



1

γ



tr E H R zz E



H

H

tr E  P + tr P  E





(23)

.

Step 3:

 ∗  T ∂ρ = ω−2 γ  H E E H  P − ω−1 γ E H  + μγ P ∗ = 0, ∂P (24)

We can derive the precoder P , automatic gain controller the equalizer E H by minimizing MSE criterion

ω and

  { P , E , ω} = argmin E ||ˆs − s||2 P , E ,ω

  subject to : E || P s||2 = γ T . The MSE function can be expanded as

which can be written as

 H E E H  P + μω2 P = ω H E . (16)

(25)

Equation (25) can be rewritten in the below form

 H E E H  P¯ + α P¯ =  H E , where

α = μω and 2

(26)

M. Pourmoazen et al. / Digital Signal Processing 81 (2018) 90–99

Table 2 Iterative algorithm for finding P ,

The convergence of the proposed algorithm can be justified through the following explanation. According to the dependence of P and ω to P¯ in (27) and (29) and convexity of the MSE function η over P¯ and E [29], the updated P¯ and E always decrease η , means

ω and E .

Initialization: Set the iteration number i = 0. P (0) = I T and ω(0) = 1. 1. i = i + 1



2. E (i ) = ω(i − 1)  P (i − 1) P H (i − 1) H + γ1 R zz   3.

−1

γT



4. P¯ (i ) =  H E (i ) E H (i ) + α (i ) I T



−1





(36)

(27)

4. SINR analysis

(28)

In this section, the interference suppression behavior of the proposed algorithm is analyzed by measuring the SINR on a persubcarrier basis. According to (13), the jth (1 ≤ j ≤ T (0) ) subcarrier of the mth block of the FU detected signal can be expressed as

P¯ can be obtained from (26) as

 − 1 P¯ =  H E E H  + α I T H E .

With respect to (21), we have tr( P P H ) = ω2 tr( P¯ P¯ ) = T . Consequently, H

Sˆ m ( j ) = ( 0)

T tr( P¯ P¯ ) H

(29)

,

multiplying P H in (25) from the left results in

P H  H E E H  P + μω2 P H P = ω P H  H E .

H

H

tr( P  E ) = tr( E  P ).



α = μω =



K  

(k) γ (k) ω−1 E Hj (jk) S m ( j)





Multi-User Interference (MUI) T   (0)

+

( 0) γ (0) ω−1 E Hj (0) P n S m (n)

n =1 n= j







Intra-band ICI induced by FU

+

(37)

K  T (k)  

(k) γ (k) ω−1 E Hj n(k) S m (n)

k =1 n =1 n= j

(32)

.

γT



k =1

(31)



( 0) γ (0) ω−1 E Hj (0) P j S m ( j)





(30)

Taking trace of (30), using (21) and (31) and finally subtracting obtained equation from (23) yields

tr E H R zz E



Signal of Interest

+

According to (30), the diagonal elements of ( P H  H E ) are real. Consequently,

2





Consequently, in each iteration, η is decreased. Since η is lowerbounded by zero, it converges to a local optimum point of our optimization problem.

P¯ = ω−1 P .

H

(35)

η E (i ), P¯ (i ) ≤ η E (i ), P¯ (i − 1) .

 H E (i )

ω (i ) = H tr( P¯ (i ) P¯ (i )) 6. P (i ) = ω(i ) P¯ (i ) 7. Go back to 1 until convergence of (17) 8. End

ω=





η E (i ), P¯ (i − 1) ≤ η E (i − 1), P¯ (i − 1) ,

T

5.







 P (i − 1)

tr E H (i ) R zz E (i )

α (i ) =

95







ICI induced by MUs

Step 4:

 ∗ ∂ρ = ω−2 γ  P P H  H E + ω−2 [ R zz E ]∗ ∂E − ω−1 γ [ P H  H ]T = 0.

(k)

(33)

E = ω  P P H H +

1

γ

R zz

− 1

P.

+

k =1 n =1

k) (k) γ (k) ω−1 E Hj (pre S (n) n m −1







ISI

+ ω−1 E Hj [(0) ]T F  Rx w ,   

After some simplification, E can be derived as



T K   

Noise

(34)

3.2. Iterative scheme It is seen from (27), (28), (29) and (34) that P , ω and E are completely dependent upon each other and hence cannot mathematically be expressed independently. Therefore, we propose an iterative algorithm for finding the steady-state of P , ω and E in Table 2. The basic idea of this algorithm is to search the best E using (34) when ω and therefore P are given and then updating ω and P using (27), (28) and (29) according to the most updated E . The iteration continues until the MSE function in (17) converges.

where we have distinguished between signal of interest and interference terms. Also, the subscripts j and n represent the column index of the corresponding matrix. The SINR on the jth subcarrier of the mth block of the FU can be expressed as

SINRm ( j ) =

γ (0) ω−2 E Hj (0) P j P Hj [(0) ] H E j J (int+n)

.

(38)

J (int+n) is the power of interference and noise that can be derived as

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M. Pourmoazen et al. / Digital Signal Processing 81 (2018) 90–99

Table 3 Simulation parameters.

J (int+n) =

K 

Parameter

Value

Number of subcarriers (N) Number of MUs ( K ) CP length (N cp ) Channel length ( L ) Macrocell radius ( R ) Sampling duration ( T s ) Path loss exponent (a)

256 8 10 6 1000 m 0.2 μs 3

γ (k) ω−2 E Hj (jk) [(jk) ] H E j

k =1







MUI Power (0)

+

T 

γ (0) ω−2 E Hj (0) P n P nH [(0) ] H E j

n =1 n= j





Fig. 3. Interference suppression performance of the proposed scheme in terms of MSE (η ) versus SNR (λ f ) at R f = 600 m & R f = 900 m, for 6 iterations and λm = λf .



FU ICI Power

+

T (k) K  

γ (k) ω−2 E Hj n(k) [n(k) ] H E j

k =1 n =1 n= j





(39)



MUs ICI Power (k)

+

K  T  k =1 n =1

k) (k) γ (k) ω−2 E Hj (pre [ pre n ] H E j n







ISI Power

+ σ w2 ω−2 E Hj E j ,    Noise Power

where in (38) and (39), the expectation is taken over signals and noise. 5. Simulation results In this section, computer simulations are derived to evaluate the performance of the proposed algorithm. Matlab is used as the simulating software. The quadrature phase shift keying (QPSK) modulation is employed in the uplink direction of an OFDMA system. The simulation parameters are listed in Table 3 which are in-line with those of Wang et al. in [20]. We employ multipath Rayleigh fading channel with exponential power-delay profile (PDP) σi2 , where σi2 = σ02 e −i /4 for 1 ≤ i ≤ L [16]. Block subcarrier assignment scheme is used for subcarrier allocation to each user. The number of subcarriers allocated to the FU is n( (0) ) = T (0) = 16 with a subcarrier-index set given by (0) = {121, 122, . . . , 136}. All MUs are allocated equal number of subcarriers, i.e., n( (k) ) = 30 with 1 ≤ k ≤ K [20]. It should be noted that all results are based on averaging over many realizations of users’ distribution. The interference suppression performance of the proposed scheme together with no-ICI (i.e., a fully-synchronous system) & no-interference-treatment scenarios, in terms of MSE (η ) versus SNR (λ f ) at R f = 600 m & R f = 900 m, for 6 iterations and λ f = λm is plotted in Fig. 3. The following observations are evident. First, in the absence of any interference-suppressing scheme, the MSE of the transmitted symbols tends to establish an error floor for high SNRs, i.e. >25 dB at R f = 900 m. This observation further justifies the motivation behind the problem considered in this paper. Second, by taking advantage of the proposed ICI suppression scheme, a close MSE performance to that of a fully synchronized

system for small and medium SNRs (i.e., <20 dB) and a comparable one for higher SNRs (i.e., >20 dB & <30 dB) are achieved. Therefore, as opposed to the no-interference treatment scenario, the proposed scheme successfully cancels out a considerable portion of MUs’ interfering signals, which is particularly of interest at high SNRs. Third, for the sake of performance comparison, the simulation of the state-of-the-art is also provided. Based on explanation provided in Section 1, Category I schemes only concentrate on the analysis of the timing-induced interference and do not propose some specific methods to counteract the interference. Within the Category II, the CP-based family takes advantage of an increase in the CP-length which in turn significantly reduces the spectral efficiency and hence cannot be used in the standardized wireless metropolitan area networks (see [22] for more details). Moreover, as the interference mitigation scheme presented in [24] outperforms the older method [23], the former research work is chosen to be compared with our simulation results. Interestingly it can be observed that this scheme shows a more degraded performance than that of no-interference-treatment scenario. This observation can be justified by the fact that firstly, in [24] the precoder and equalizer matrices are not designed to optimize the MSE costfunction, but to optimize the uplink throughput function. Secondly, in the presence of one FU, the orthogonality condition of the precoder matrix does limit the interference suppression performance of this scheme on the last two subcarriers. In Fig. 4, the convergence behavior of the proposed scheme in terms of MSE versus SNR at R f = 900 m and for λ f = λm is evaluated. It is observed that after 0 iteration, the proposed method is likely to result in an error-floor for asymptotically high SNRs. This is because, as stated earlier (see Section 3), due to high dependency of the unknown parameters to each other, i.e., the precoder matrix, the matrix of joint deprecoder–equalizer and the gain controller scalar, in the absence of the iterative algorithm, the MSE cost-function cannot attain a local optimum-point. However, by taking advantage of the proposed iterative scheme and increasing the number of iterations to at least 6, the aforementioned target parameters tend to some candidate values that would result in a local-optimum point for the MSE cost-function. Fig. 5 illustrates the Average SINR on a per-subcarrier basis with and without the proposed interference-suppressing method at R f = 900 m and for two SNRs of 25 dB and 30 dB and for λ f = λm . The following points are of importance.

M. Pourmoazen et al. / Digital Signal Processing 81 (2018) 90–99

Fig. 4. The convergence behavior of the proposed scheme in terms of MSE versus SNR (λ f ) at R f = 900 m and for λm = λ f .

Fig. 5. Average SINR on a per-subcarrier basis at R f = 900 m and for λm = λ f .

First, for two scenarios of no-interference-treatment and the proposed scheme, the interference induced by the MUs’ timingmisalignments has a more adverse impact on the boundaries of FU’s frequency-band. This fact is due to a reason of higher impact of ICI belonging to interfering MUs present on the frequency-bands adjacent to the user of interest (i.e., FU) within the context of subband OFDMA networks. Second, it is evident that the proposed iterative scheme has successfully improved the SINR indicator by ≈0.8 dB at SNR = 30 dB and ≈0.3 dB at SNR = 25 dB over all subcarriers. These results are also in-line with the results of Fig. 3 on the fact that the proposed scheme’s capability on suppressing the ICI is of a more significance at higher SNRs. Third, despite demonstrating a better SINR performance over most of subcarriers, the state-of-the-art scheme in [24] is severely under-performed over the last 2 subcarriers of the FU’s band. As mentioned earlier in Section 2, this is due to the fact that in the presence of one FU, the precoder matrix does not fulfill the full orthogonality condition and this will in turn significantly degrade the interference suppression performance of this scheme on the last two subcarriers. Fig. 6 presents the overall system performance in terms of FU’s BER vs. SNR at different R f s with and without the proposed scheme and for λ f = λm . As it was the case with Fig. 3, in the absence of any interference treatment scheme, the error-rate becomes significant by forming up an error-floor for SNRs greater than 20 dB. In contrary, the proposed iterative scheme closely follows the performance of a fully-synchronized system (i.e., a fully

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Fig. 6. Overall system performance in terms of femtocell BER vs. SNR (λ f ) at different R f s and for λm = λ f .

Fig. 7. Overall system performance in terms of femtocell BER vs. SNR (λ f ) at different R f s and for λm = 4λ f .

synchronous system) up to SNR = 20 dB. For larger SNRs (i.e., >20 dB & <30 dB), the proposed method suppresses a considerable portion of the induced interference by demonstrating comparable results to the no-ICI scenario. As a clarifying example, the proposed scheme can achieve an uncoded BER = 8 × 10−5 at SNR = 30 dB while the same BER is achieved by a fully synchronized system with approximately 2 dB power difference. It is particularly important to note that the amount of performance degradation over 2 subcarriers in [24], as presented in Fig. 5, is large enough to cause a close performance to that of nointerference-treatment scenario at R f = 600 m and a comparable performance with that at R f = 900 m. Finally, to evaluate the performance of the proposed scheme in presence of higher interference power belonging to MUs as compared to FU’s power, Fig. 7 is drawn to illustrate the overall system performance in terms of FU’s BER versus SNR, where it is assumed λm = 4λ f . It is observed that increasing the received power of macro (i.e., interfering) users relative to the power of femto (i.e., the desired) user, affect all performance curves i.e., “nointerference treatment”, “the state-of-the-art scheme as in [24]” and our proposed scheme. However, the adverse effect of increasing multiuser interference power is more realizable on the state-of-the-art scheme. It is evident that by increasing the received power of interfering users, both state-of-the-art scheme and “no-interference treatment scenario” establish error floors at high

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M. Pourmoazen et al. / Digital Signal Processing 81 (2018) 90–99

SNRs, i.e., > 28 dB, whereas our proposed scheme does not establish an error floor and shows a BER performance of 2.5 × 10−4 at SNR = 30 dB and R f = 600 meters. This observation proves that our proposed scheme is more resilient toward the increased multiuser interference power. 6. Conclusion In this paper, an iterative scheme for suppressing the MUs’ timing-induced interference for an OFDMA uplink femtocell network was presented. By assuming a number of MUs and a single precoded FU, the MSE cost-function was first defined, based on which, the closed-forms for 3 underlying parameters, i.e., the precoder matrix, the joint deprecoder–equalizer matrix and the gain controller scalar were then derived by proposing a partial derivative-based sub-optimization scheme. To overcome the interrelation of 3 aforementioned parameters, a post-processing iterative interference suppression algorithm was further proposed with a reasonable convergence behavior, i.e., 6 iterations, which resulted in finding a local optimum point of the cost-function with respect to the unknown parameters. To evaluate the interference suppression performance of the proposed method, a per-subcarrier based SINR analysis was also derived. The simulation results showed that the overall system performance of the proposed method was close to that of a system without any timing-induced interference at low and medium SNRs (i.e. <20 dB) and comparable to that at higher SNRs (i.e., >20 dB & <30 dB), even for distances as large as 900 meters between MBS and FBS. It was also shown that the proposed scheme could enhance the SINR indicator by ≈0.8 dB at SNR = 30 dB and ≈0.3 at SNR = 25 dB for the same distance between MBS and FBS. Acknowledgments The authors would like to thank the respected Editor-in-Chief, Prof. Ercan Engin Kuruoglu and anonymous reviewers for the efficient review process and extremely consecutive and supportive comments. References [1] D. Lopez-Perez, I. Guvenc, G. de la Roche, M. Kountouris, Enhanced intercell interference coordination challenges in heterogeneous networks, IEEE Trans. Wirel. Commun. 18 (3) (2011) 22–30. [2] V. Chandrasekhar, J.G. Andrews, A. Gatherer, Femtocell networks: a survey, IEEE Commun. Mag. 46 (9) (2008) 59–67. [3] Y. Sun, R.P. Jover, X. Wang, Uplink interference mitigation for OFDMA femtocell networks, IEEE Trans. Wirel. Commun. 11 (2) (2011) 614–625. [4] G. Mansfield, Femtocells in the US market business drivers and consumer propositions, in: Femto Cells Europe Conference, 2008. [5] M.M.U. Gul, S. Lee, X. Ma, Carrier frequency offset estimation for OFDMA uplink using null sub-carriers, Digit. Signal Process. 29 (2014) 127–137. [6] M. Movahhedian, Y. Ma, R. Tafazolli, Blind CFO estimation for linearly precoded OFDMA uplink, IEEE Trans. Signal Process. 58 (9) (2010) 4698–4710. [7] C. Ahn, D. Har, T. Omori, K. Hashimito, Frequency symbol spreading based adaptive subcarrier block selection for OFDMA system, Digit. Signal Process. 22 (3) (2012) 518–525. [8] A. Ahmed, W. Osman, T. Abdulrahman, Orthogonal frequency division multiple access system analysis using bit error rate, in: Third International Conference on Next Generation Mobile Applications, Services and Technologies, 2009, pp. 211–214. [9] J. Li, X. Wu, R. Laroia, OFDMA Mobile Broadband Communications: A Systems Approach, Cambridge University Press, 2013. [10] H. Zhou, B. Li, Z. Yan, M. Yang, Q. Qu, An OFDMA based multiple access protocol with QoS guarantee for next generation WLAN, in: IEEE International Conference on Signal Processing, Communications and Computing, ICSPCC, 2015, pp. 1–6. [11] S.C. Yang, OFDMA System Analysis and Design, Artech House, 2010. [12] M. Park, K. Ko, H. Yoo, D. Hong, Performance analysis of OFDMA uplink systems with symbol timing misalignment, IEEE Commun. Lett. 7 (8) (2003) 376–378. [13] E. Bala, L.J. Cimini, On the uplink synchronization of OFDMA systems, in: IEEE Military Communications Conference, MILCOM, 2005, pp. 1133–1139.

[14] M.E. Sahin, I. Guvenc, M.R. Jeong, H. Arslan, Handling CCI and ICI in OFDMA femtocell networks through frequency scheduling, IEEE Trans. Consum. Electron. 55 (4) (2009) 1936–1944. [15] M.E. Sahin, I. Guvenc, H. Arslan, Opportunity detection for OFDMA-based cognitive radio systems with timing misalignment, IEEE Trans. Wirel. Commun. 8 (10) (2009) 5300–5313. [16] K.H. Hamdi, Precise interference analysis of OFDMA time-asynchronous wireless ad-hoc networks, IEEE Trans. Wirel. Commun. 9 (1) (2010) 134–144. [17] P. Tarasak, T.Q.S. Quek, F. Chin, Closed access OFDMA femtocells under timing misalignment, in: IEEE Global Telecommunications Conference, GLOBECOM, 2010, pp. 1–5. [18] P. Tarasak, T.Q.S. Quek, F. Chin, Uplink timing misalignment in open and closed access OFDMA femtocell networks, IEEE Commun. Lett. 15 (9) (2011) 926–928. [19] I. Guvenc, Statistics of macrocell-synchronous femtocell-asynchronous users’ delays for improved femtocell uplink receiver design, IEEE Commun. Lett. 13 (4) (2009) 239–241. [20] H. Wang, R. Song, S.-H. Leung, Analysis of uplink intercarrier interference in OFDMA femtocell networks, IEEE Trans. Veh. Technol. 64 (3) (2015) 998–1013. [21] H. Wang, R. Song, S.-H. Leung, Analysis of uplink ICI and IBI in heterogeneous cellular networks with multiple macrocells, IEEE Commun. Lett. 21 (1) (2017) 212–215. [22] E. Dahlman, S. Parkvall, J. Skold, 4G LTE/LTE-Advanced for Mobile Broadband, Academic Press, 2013. [23] I. Guvenc, S. Tombaz, M.E. Sahin, H. Arslan, H.A. Cirpan, ICI-minimizing blind uplink time synchronization for OFDMA-based cognitive radio systems, in: IEEE Global Telecommunications Conference, GLOBECOM, 2009, pp. 1–6. [24] H. Wang, R. Song, S.-H. Leung, Mitigation of uplink ICI and IBI in OFDMA twotier networks, IEEE Trans. Veh. Technol. 65 (8) (2016) 6244–6258. [25] Ieee 802.16e standard, http://www.ieee802.org/16/pubs/80216e.html. [26] H. Wang, R. Song, S.-H. Leung, Optimal uplink access in cognitive femtocell networks with adaptive modulation, IEEE Commun. Lett. 20 (5) (2016) 1050–1053. [27] E. Hossain, L.B. Le, D. Niyato, Radio Resource Management in Multi-Tier Cellular Wireless Networks, John Wiley & Sons, 2013. [28] S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. [29] H. Shen, B. Li, M. Tao, X. Wang, MSE-based transceiver designs for the mimo interference channel, IEEE Trans. Wirel. Commun. 9 (11) (2010) 3480–3489.

Mohammad Pourmoazen received the B.S. degree in electrical engineering from Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran, in 2011 and the M.S. degree in telecommunications engineering with the top-rank from Imam Khomeini International University (IKIU), Qazvin, Iran, in 2013. From 2015 to 2017, he was a research assistant within the department of electrical and electronic engineering, IKIU. His main research interests are in the areas of signal processing advances in wireless communications, estimation, synchronization, detection techniques and interference cancellation in OFDMA-based cellular networks. Mohammad Movahhedian received the Ph.D. degree in electrical engineering from the institute for communication systems (ICS), University of Surrey, UK, in 2010. He was chosen as the distinguished Bachelor of Engineering student by the IET and hence was awarded the IET manufacturing engineering prize in 2006. In 2009, he was chosen as the best PhD candidate, within the department of electronic engineering, University of Surrey, UK. Since October 2012, he has been acting as a senior management consultant at the mobile communication company of Iran (MCI), the largest mobile network operator in the middle-east, providing consultancy to the C-levels on improving the overall QoE through the optimum deployment of cutting-edge technologies and solutions. He also leads a group of talented engineers at the MCI’s Research and Development Centre, in close collaboration with the RAN equipment vendors, with an overall objective of improving subscriber’s QoE, particularly in the direction of design and deployment of 5G networks. Dr Movahhedian’s research interests span over a wide range of physical, system and network layer aspects of emerging wireless communication networks, including statistical signal processing, massive MIMO channel modeling, radio resource scheduling, service-oriented network slicing, network automation through AI, QoE enhancement through data-analytics, and distributed intelligence through mobile-edge computing. Bahare Sadat Mousavitabar received a B.S. degree in computer software engineering, a second B.S. degree in electrical engineering and the M.S. degree in telecommunications engineering, all from Imam Khomeini

M. Pourmoazen et al. / Digital Signal Processing 81 (2018) 90–99

International University (IKIU), Qazvin, Iran, in 2012, 2013, and 2015 respectively. Currently, she is working as an ICT engineer at the mobile communication company of Iran (MCI) and has participated in several national

99

ICT projects. Her main research interests are statistical signal processing, estimation and synchronization techniques, and Interference suppression in OFDMA and GFDMA-based cellular networks.