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Coded cooperation diversity for uncoded oversampled OFDM systems
ARTICLE IN PRESS Signal Processing 89 (2009) 1370–1378
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Coded cooperation diversity for uncoded oversampled OFDM systems Alireza Rahmati, Paeiz Azmi Electrical and Computer Engineering Department, Tarbiat Modares University, Tehran, Iran
a r t i c l e i n f o
abstract
Article history: Received 12 November 2007 Received in revised form 15 December 2008 Accepted 12 January 2009 Available online 25 January 2009
Recently, user-cooperation diversity has been introduced as an effective scheme that can bring about antenna diversity in wireless networks. In this paper, we introduce a coded cooperation diversity technique for single antenna uncoded orthogonal frequency division multiplexing (OFDM) systems, in which implementation of coded cooperation is provided by the oversampling potential in OFDM, instead of using extra channel coding. In fact, zero-padding followed by IFFT in OFDM is similar to oversampling and could be an alternative to applying correction codes. Furthermore, we use this oversampling to implement an iterative receiver at the partner terminal. This receiver works based on the nonuniform sampling theorem for reconstructing of lost symbols. The lost symbols appear at the partner terminal of cooperative network because of dividing each OFDM block into two segments through the puncturing at the user terminal of the cooperative network. We provide simulation results for our proposed scenario, and observe significant gains over the non-cooperative oversampled OFDM systems without any need whatever for using extra channel coding. & 2009 Elsevier B.V. All rights reserved.
Keywords: Coded cooperation diversity Orthogonal frequency division multiplexing (OFDM) Oversampling Iterative reconstruction method
1. Introduction Signal quality in mobile radio channels is severely affected by undesirable channel quality due to the effects of multi-path fading, in which mobile users experience strong variations in signal attenuation during a given call. Recently, user-cooperation diversity has been emerged as a new form of spatial diversity, whereby diversity gains are attained via cooperation of sparse terminals in wireless networks. This diversity technique enables terminals, where it is not easy to be equipped by multiple antennas due to size and cost limitations, to obtain higher data rates which are less prone to channel variations [1–3]. Coded cooperation scheme using channel coding for cooperative systems has been proposed in [4–6], for its efficient usage of the available bandwidth. This cooperative transmission
Corresponding author.
E-mail address: [email protected] (P. Azmi). 0165-1684/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2009.01.010
protocol should be implemented in state-of-the-art transmission technologies, such as orthogonal frequency division multiplexing (OFDM), that has recently received substantial attention in the areas of wireless communication systems for its simple implementation with FFT/IFFT pairs, efficient use of the available bandwidth, and robustness to frequency selective fading [7,8]. For the first time in this paper, we will use the oversampling potential for implementing the coded cooperative diversity in OFDM systems as an alternative for using formal channel coding. In fact, the oversampling can act as an error-correction code without the need for the complex Viterbi decoding algorithm used in decoding convolutional codes in the conventional coded cooperative systems. Oversampling is performed by padding the QAM modulating sequence with some zeros before IFFT at the transmitter of OFDM systems to provide oversampled OFDM systems, a special case of the precoded OFDM systems, known as the zero-padded OFDM (ZP-OFDM) systems by the papers of the past [9,10]. However,
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oversampling can be considered for providing other properties as well, such as decreasing edge effects of OFDM signal in frequency domain, channel estimation, and PAPR reduction, as explored in [11–14]. The oversampling in our proposed cooperative system is used for two reasons. First, this oversampling provides a special DFT code (or a Reed Solomon code in real field) without any need for using extra channel coding which is mandatory for putting the coded cooperative diversity schemes into practice. We use the oversampling potential secondly to reconstruct the lost QAM modulated symbols of each OFDM symbol at the partner terminal. In fact, our cooperative scheme partitions each user’s OFDM symbol into the two segments through puncturing. So, the partner terminal should reconstruct user’s OFDM symbol from a received version which has lost some of its QAM modulated symbols. However, if the average symbol rate of the remaining QAM modulated symbols stays above the Nyquist rate, as the nonuniform sampling theorem states, complete recovery of each OFDM symbol would be possible [15]. This perfect reconstruction can be guaranteed at the partner terminal if the high enough oversampling factor is chosen at the user terminal. Therefore, using the iterative receiver working base on the nonuniform sampling theory at the partner terminal can be a proper choice for its simple implementation. The rest of this paper is organized as follows. In Section 2, the oversampled OFDM system and the iterative receiver included in our coded cooperative scheme are reviewed. In Section 3, we describe the proposed coded cooperation model in the oversampled OFDM system. Simulation results illustrating the performance of the oversampled OFDM for the coded cooperation scenario are presented in Section 4. Section 5 is dedicated to concluding remarks and future works. 2. Iterative receiver for oversampled OFDM systems
Fig. 1 gives the simplified model of oversampled OFDM transmitter. Let c stand for the information symbols after the QAM modulation and segmentation into blocks with size K, c ¼ ½c1 ; c2 ; . . . ; cK T
L can be considered as an oversampling factor and in the case of the conventional OFDM system, L ¼ 1, corresponding to the Nyquist symbol rate. Let N be the number of subcarriers in the OFDM system. Hence, N symbols of c0 are transmitted at the same time in one OFDM symbol s, which is a N-point IFFT transformed version of c. It has been shown that s is a special DFT coded version of c that can be expressed as [15–17] s ¼ Gc
2.2. Iterative receiver One can estimate s from its punctured version, t, perfectly by the iterative receiver shown in Fig. 2 if a high oversampling factor, L, is chosen at the transmission side. This iterative receiver works based on the nonuniform sampling theorem [15]. Hence, as long as the average symbol rate of t stays above the Nyquist rate, perfect reconstruction of s would be possible. This iterative receiver consists of two main blocks, namely filtering and iterative reconstruction. 2.3. Linear filtering The filtering stage begins by removing the interference among different symbols that can be carried out by time domain ZF equalization:
(1)
c
s
c
t
QAM 0
IFFT
P
Fig. 1. Transmitter of the oversampled OFDM system.
(3)
where t is the punctured vector at the transmitter after N-point IFFT modulator (time domain transmitted signal), H ¼ diagðH1 ; H2 ; . . . ; HN Þ, a diagonal matrix with diagonal elements ðH1 ; H2 ; . . . ; HN Þ, is the channel in the time domain and v0 is N 1 AWGN noise. Note that multipath effects of quasi-static Rayleigh fading channel can be
Then ðL 1ÞK trailing zeros are padded after each c to form a N 1 column vector of c0 ¼ ½c1 ; c2 ; . . . ; cK ; 0; . . . ; 0T .
S / P
(2)
where G is the generator matrix. In the next section, we will see that in the proposed coded cooperation scheme, the oversampled OFDM transmitter partitions s into the two segments through N N puncturing matrix of P and sends only one of these segments. The channel is assumed to be quasi-static frequency selective Rayleigh fading corrupted by N 1 additive white Gaussian noise (AWGN) vector of v ¼ ½v1 ; v2 ; . . . ; vN T at the receiver.
bt ¼ t þ H1 v0
2.1. Oversampled OFDM transmitter
1371
Fig. 2. The Iterative receiver for oversampled OFDM system.
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3. Proposed coded cooperation diversity for OFDM systems 3.1. Medium access and level of cooperation
Fig. 3. LPF processing in the filtering stage.
Fig. 4. Iterative reconstruction method.
removed completely by using the cyclic prefix (CP), so fading effects of each subchannel can be considered only by a scalar product as explained in Eq. (3) similar to that in [14]. This stage is finished by applying the low pass filtering to bt, depicted by the LPF block in Fig. 2. This LPF block may alleviate a high noise level of H1 v0 by erasing erasures corresponding to the zero padded positions of the oversampled OFDM signal as depicted in Fig. 3 and expressed as follows: 2
3T K zfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflffl{ 0 0 0 0 0 6 7 tb0 ¼ FNbt ¼ 4bt 1 ; bt 2 ; . . . ; bt K ; bt Kþ1 ; . . . ; bt N 5 |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
(4)
Erasures
3T K zfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflffl{ 0 0 0 6 7 te0 ¼ 4bt 1 ; bt 2 ; . . . ; bt K ; 0; . . . ; 05 |fflfflfflffl{zfflfflfflffl}
Consider the wireless network depicted in Fig. 5, in which both terminals T 1 and T 2 cooperate and transmit to a single destination D. The inter-user and uplink channels are subject to frequency selective Rayleigh fading. We assume that terminals transmit on orthogonal TDMA channels similar to [1,4,6], which not only allows the terminals to transmit and receive on different channels but also enables the destination and the two terminals to separately detect each other in the cooperative mode. The modified TDMA implementation of this system for our OFDM system is shown in Fig. 6, where for simplicity only the cooperative level of 50% is depicted. The level of cooperation for OFDM systems is the percentage of the total subcarriers per each OFDM symbol that the user transmits for its partner. Each T 1 and T 2 terminals act as the user terminal and as the partner terminal during its own time slot. In direct transmission, each user transmits its OFDM symbol via N subcarriers during its whole own time slot while for the cooperative scheme each user simultaneously sends a combination of its own data and the partner’s data, as shown in Fig. 6. Particularly, in fullcooperation (50% cooperation) scheme, each terminal simultaneously transmits half of its OFDM symbol on N=2 subcarriers and half of the partner’s OFDM symbol on the remaining N=2 subcarriers during its own time slot. Note that this cooperative scheme is a special case of coded cooperative diversity based on superposition modulation for OFDM systems. Recently, new DF scheme based on superposition modulation for a single carrier system has been proposed in [19]. This spectrally efficient
2
(5)
T1
Erasures
D et ¼ FH te0 ¼ ½et 1 ; et 2 ; . . . ; et N T N
(6)
T2
where FN denotes N-point FFT operator.
Fig. 5. Cooperation system model.
2.4. Iterative reconstruction Reconstruction of s from et can be performed by the iterative method depicted in Fig. 4, a special case of general ones proposed by [15,18] 8 iþ1 i
N/2
N/2
N/2
N/2
Terminal T1
T1 bits
T2 bits
RX T2
Inactive
Terminal T2
RX T1
Inactive
T2 bits
T1 bits
T1 Slot
T2 Slot
Fig. 6. Coded cooperation implementation for oversampled OFDM system using TDMA.
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employed for partitioning of each user’s OFDM symbol into the two frames in the cooperative transmission. Block diagram of each partner terminal during its own time slot in the cooperative level of 50% is precisely depicted in Fig. 8. In this block diagram, after filtering stage, the partner terminal tries to recover the whole of the user’s OFDM symbol from the received segment by the iterative reconstruction method with P ¼ P1 (Fig. 4), explained in Section 2. If the partner terminal manages to recover user’s OFDM symbol successfully (as indicated by the CRC bits) sends the remaining of the OFDM symbol for the user through the puncturing block of P2 within its time slot. Furthermore, the partner terminal simultaneously sends the first segment of its own OFDM symbol provided by the puncturing matrix of P1 during its own time slot. Note that P1 and P2 are N N puncturing matrixes, e.g. for N ¼ 4 and 50% cooperation, P1 and P2 can be considered as follows:
cooperative protocol is based on superposition modulation which allows each user to transmit its own information and relay the data from the partner simultaneously. 3.2. Oversampling and proposed coded cooperative diversity Fig. 7 shows the user terminal to implement the proposed coded cooperative diversity for the oversampled OFDM systems for sending half of its own OFDM symbol. This block diagram includes cyclic redundancy check (CRC) coder block, the oversampled OFDM transmitter block, and puncturing matrix block of P1 . The receiver is informed by CRC bits for detection process corresponding to the cooperative or non-cooperative transmission mode. The oversampled OFDM transmitter block is explained in Section 2 and is utilized in our scenario because of the oversampling potential. Conventional methods [4,5] use channel coding like convolutional codes for both partitioning a user’s OFDM symbol and detection and correction of errors, whereas we apply the oversampling factor L to c and obtain s, its Reed Solomon coded version in real field, instead of using extra channel coding and so avoid wasting bandwidth. The puncturing matrix, P1 , is
0
1
1
0
0
0
B0 B P1 ¼ B @0
0
0
0
1
0C C C 0A
0
0
0
0
0 and
1
0
0
0
0
B0 B P2 ¼ B @0
1
0
0
0
0C C C 0A
0
0
0
1
Fig. 7. The user terminal in the coded cooperative diversity.
CRC check Symbols received From User
Z F
L P F
Iterative Reconstruc.
2
1 2
P2
N-1 N
N
Partner's DATA
CRC
Oversampled OFDM Trasmitted
1 2
YES
P1
1 2
N-1 N
N
1 2
N
Fig. 8. The partner terminal in the coded cooperative diversity.
NO
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100
10−1
BER
10−2
10−3
75% cooperation 50%cooperation 25%cooperation
10−4
Unpunctured
10−5 (511,130) BCH coded OFDM Oversampled OFDM using iterative receiver
10−6 5
10
15 (Eb/N0)T1−T2(dB)
20
25
Fig. 9. BER performance of both a (511,130) BCH coded OFDM and the proposed iterative oversampled OFDM versus Eb =N 0 at the partner terminal for different levels of cooperation.
Hence, the user only transmits the odd QAM modulated symbols of its OFDM symbol and the even modulated symbols should be transmitted for the user terminal by the partner. If the partner terminal cannot recover user’s OFDM symbol successfully (as indicated by the CRC bits) automatically revert back to a non-cooperative mode and transmits its OFDM symbol via N subcarriers during its whole own time slot. 4. Results and discussion We evaluate the performance of the oversampled OFDM system in the proposed coded cooperation scenario, compared to the non-cooperative scheme through simulations over multipath Rayleigh fading channels with zero mean and variance 1. The system parameters that we assumed in the simulation, unless specified otherwise, were K ¼ 32 length of the CRC coded block with Graymapped 16-QAM modulation on each entry, L ¼ 4 the oversampling factor as in [11,14] for PAPR reduction considerations, N ¼ 128 the number of subcarriers, and i ¼ 10 the number of iteration employed at the iterative receiver of the partner terminal. A 16-bit CRC code with generator polynomial given by coefficients 15935 (hexadecimal notation) is considered for our simulations. 4.1. The oversampling factor and the level of cooperation Due to the puncturing process at the user terminal T 1 , the partner terminal T 2 should reconstruct the lost symbols of each user’s OFDM block from the remaining
ones. If we denote P as the probability of lost, then it has been shown that the inverse of the 1 P is the sampling rate normalized by the Nyquist rate, needed for errorless transmission [15]. Hence, the oversampling factor of L ¼ 4 ensures errorless transmission even if 3=4 of the samples of each OFDM block are lost. Therefore, up to the cooperation level of 75% is guaranteed in our cooperative system thanks to the oversampling factor of L ¼ 4, where the puncturing process discards 3=4 of each OFDM symbol. To demonstrate the iterative receiver efficiency at the partner terminal Fig. 9 is provided, where the average T 1 ’s BER versus Eb =N0 of the T 1 –T 2 inter-user channel in the partner terminal is shown. Performance of BCH coded OFDM with the same bandwidth is also shown in Fig. 9. Here, T 2 uses the iterative receiver/BCH decoder and different probability of lost P ¼ 1=4; 1=2; 3=4, corresponding to the various cooperation levels of 25%, 50%, and 75%, respectively, are applied in T 1 terminal. It is worth noting that unlike our scheme most of the channel codes cannot recover the data from its severely punctured version, e.g., OFDM transmission that relies on using a BCH code shown in Fig. 9 yields perfect reconstruction only for cooperation level of 25%. Because of that conventional cooperative systems use some complex special channel codes, e.g., RCPC codes for data reconstruction at the partner terminal. To show the convergence rate of the iterative receiver at the partner terminal, for a given level of cooperation, different number of iterations i ¼ 1, 2, 3, 4, 5, 10, and 100 are considered as shown in Fig. 10. The iterative receiver improves the BER performance significantly as more iterations are carried out. Observe also that the performance
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1375
100
BER
10−1
Iteration=1 Iteration=2 Iteration=3 Iteration=4 Iteration=5 Iteration=10 Iteration=100
10−2
10−3 0
5
10
15
20
25
SNRT1−T2(dB) Fig. 10. BER versus SNR at the partner terminal for different number of iterations.
for the iterations with the values of i ¼ 10 and 100 are close together that implies the fast convergence rate of our proposed scheme. 4.2. Detection policy at the destination terminal At the destination terminal, two different strategies can be devised for the detection of each user’s OFDM symbol. One of them can be easily performed by combining the received signals from both the user and the partner terminals in two consecutive time slot similar to that in [19]. The better manner, which also alleviates the Rayleigh fading channel nulls, uses the iterative receiver at the destination. This receiver is the same as the iterative ones introduced in Section 2 except the discarding matrix O which should be included before the iterative reconstruction block of Fig. 2. The destination discards the deep faded symbols of each OFDM symbol by the discarding matrix O which is a N N diagonal matrix with o ¼ ½o1 ; o2 ; . . . ; oN on its diagonal with ( 1 kHi kXl oi ¼ , 0 O:W where l is the discarding threshold and H ¼ diag½H1 ; H2 ; . . . ; HN is the time domain channel vector. Also, the discarding matrix of O should be substituted for P in the iterative reconstruction method shown in Fig. 4. Fig. 11 compares the performance of the coded cooperation system using the simple detector with one employing the iterative detector with l ¼ 0:1 at the destination terminal for both a poor inter-user channel (0 dB) and one with average SNR of 40 dB. The T 2 -destination uplink
channel is assumed 3 dB better than the T 1 -destination uplink channel, and the level of cooperation is 50%. Note that the cooperation improves the BER performance significantly, but the performance of both coded cooperation scenarios at the average inter-user SNR of 0 dB nears the performance of non-cooperative system depicted by Fig. 11. One can observe that better BER performance can be achieved with the employment of the proposed iterative detector, rather than the simple one in the cooperation scheme. Particularly, about 9 dB gain in SNR over the simple detector at a bit error rate of 103 can be achieved by the iterative receiver. Performance of space time coded cooperation in OFDM system with the same bandwidth and cooperation level of 50% for perfect interuser channel is also shown in Fig. 11. As Fig. 11 shows, space time coded cooperation shows little better performance than our proposed cooperative scheme, but this negligible profit is obtained at the expense of including comparatively complicated RCPC codes for recovering the data from its punctured version at the partner terminal. Furthermore, various cooperation levels which can simply be provided in our cooperative method by changing the oversampling factor, L, cannot easily be obtained in space time cooperation. Performance of DF scheme for OFDM system based on superposition modulation with the same bandwidth and cooperation level is also shown in Fig. 11, where BCH codes are applied at the cooperative terminals. The inter-user and uplink channels are assumed to be similar to those considered in our proposed coded cooperative scheme. Due to the error propagation, the performance of DF cooperation system at the average inter-user SNR of 0 dB is very poor, and at the average inter-user SNR of 40 dB the performance of DF cooperation
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10−1
10−2
BER
10−3
10−4 0dB Interuser SNR 40dB Interuser SNR Non−cooperativemode
10−5
DF cooperation system based on superposition Non−iterative oversampled OFDM in 50% cooperation scheme
10−6
Iterative oversampled OFDM in 50% cooperation scheme Space time coded cooperation
10−7 0
5
10
15
20
25
SNRT1−destination(dB) Fig. 11. T 1 ’s BER versus the T 1 -destination uplink channel SNR for the coded cooperative diversity in the oversampled OFDM system using the simple and the iterative detector with l ¼ 0:1 at the destination. Space time coded cooperation with the same bandwidth for perfect inter-user channel is also shown. Performance of DF scheme for OFDM system based on superposition modulation with the same bandwidth and cooperation level is also compared, where BCH codes are applied at the cooperative terminals.
system approaches the performance of non-cooperative oversampled OFDM system. As a result, although both the DF cooperation system and our proposed coded cooperative scheme are based on superposition modulation, our proposed scheme for oversampled OFDM system yields significant gains over the DF scheme for BCH coded OFDM system (see Fig. 11). This result could be predicted from Fig. 9, which shows the merit of using oversampling in OFDM.
of l for discarding high quality symbols and reconstructing them via iterative scheme. In other words, by discarding symbols via choosing a high value for l, we lose very much useful information needed for symbol recovery. At low SNRs, however, choosing a low value for l results in such a burst of weak symbols that using the iterative receiver based on nonuniform sampling theorem cannot improve the performance because of the large number of missing symbols. Therefore, it seems that for a given SNR there is only one optimum value for l, as can be seen by dotted curve in Fig 13.
4.3. l in oversampled OFDM system One important issue in our proposed iterative receiver described in Section 4.2 is selecting the proper value for l. Fig. 12 shows the average BER versus SNR for our proposed cooperative scheme using the iterative receiver for average inter-user channel SNR of 0 dB, which corresponds to the non-cooperative case. The figure shows curves generated through simulations corresponding to different discarding thresholds l ¼ 0; 0:05; 0:1; 0:15; 0:2; 0:25 in Rayleigh fading channel. Notice that the l ¼ 0 reduces to the case of the non-cooperative oversampled OFDM system. It can also be seen that at high SNR ð417 dBÞ the iterative receiver with l ¼ 0:1 performs the best in Rayleigh fading channel with zero mean and variance 1. As Fig. 13 illustrates, proper value of l relates inversely to the channel SNR and it should be decreased by increasing the SNR for obtaining the best performance. At high SNRs, the number of symbols with good enough quality increases and there is no need for choosing a high value
4.4. Performance improvement with cooperation by iterative receiver at destination terminal Fig. 14 compares the performance of the coded cooperation scenario using the iterative detector with l ¼ 0:1 at 75%, 50%, and 25%, for both a poor inter-user channel and one with average SNR of 40 dB. The user uplink channels have equal average SNR. When the interuser channel is poor, both users never cooperate, and consequently the closest case to the non-cooperation (25%) yields better performance. However, when the interuser channel is perfect (40 dB) all cases perform the same. 5. Conclusions and future works In this paper, we proposed a novel coded cooperation scenario for OFDM systems by using the oversampling as an error-correction code based on superposition
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100 λ=0 λ = 0.05 λ = 0.1 λ = 0.15 λ = 0.2 λ = 0.25
BER
10−1
10−2
10−3
10−4 4
6
8
10
12
14
16
18
20
SNR (dB) Fig. 12. BER versus SNR for iterative oversampled OFDM system for different values of l.
100
10−1
10−2
BER
10−3
10−4 SNR=5, λmin = 0.35
10−5
SNR=10, λmin = 0.25 SNR=15, λmin = 0.15
10−6
SNR=20, λmin = 0.1 SNR=25, λmin = 0.06
10−7 0
0.2
0.4
0.6
0.8
1
λ Fig. 13. BER versus l for iterative oversampled OFDM system for different channel SNRs.
modulation. In our scheme, the oversampling which is usually applied for PAPR reduction is employed at the partner terminal to iteratively recover the data from its punctured version. All the processing of our scheme is performed at the receiver without requiring any modification at the transmitter and without any need for using
extra channel coding that may use the very long interleaving for decoding. This potentially can save more bandwidth for the transmission. Also, we proposed two detection strategies in the destination terminal. Simulation results reveal the significant BER improvements of proposed methods compared to the non-cooperative ones
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10−4 75%cooperation 50%cooperation 25%cooperation
10−5
0dB interuser SNR 40dB interuser SNR
10−6 0
5
10
15
20
25
SNRT1−destination(dB) Fig. 14. T 1 ’s BER versus the T 1 -destination uplink channel SNR for the coded cooperative diversity in the oversampled OFDM system using the iterative detector with l ¼ 0:1 at the destination for different levels of cooperation.
over the Rayleigh fading channels. Although the oversampled OFDM transmitter considered in our scheme falls under a broad class of linear transmitters, the iterative receiver employed in our proposed scheme is a nonlinear receiver based on the nonuniform sampling theorem. Performance analysis of this nonlinear receiver in OFDM systems is not a straight-forward task and closed form representation for the performance of our proposed scheme will be derived in our future works. References [1] J.N. Laneman, D.N.C. Tse, G.W. Wornell, Cooperative diversity in wireless networks: efficient protocols and outage behavior, IEEE Trans. Inf. Theory 50 (12) (December 2004) 3062–3080. [2] A. Sendonaris, E.E.B. Aazhang, User cooperation diversity—part i: system description, IEEE Trans. Commun. 51 (11) (November 2003) 1927–1938. [3] A. Sendonaris, E.E.B. Aazhang, User cooperation diversity—part ii: implementation aspects and performance analysis, IEEE Trans. Commun. 51 (11) (November 2003) 1939–1948. [4] T.E. Hunter, A. Nosratinia, Cooperative diversity through coding, in: Proceedings of IEEE ISIT, Laussane, Switzerland, July 2002, p. 220. [5] P.S.R. Liu, E. Soljanin, User cooperation with punctured turbo codes, in: Proceedings of 41st Allerton Conference on Communication, Control, and Computing, Monticello, IL, October 2003. [6] A. Stefanov, E. Erkip, Cooperative coding for wireless networks, IEEE Trans. Commun. 52 (9) (September 2004) 1470–1476. [7] J.A.C. Bingham, Modulation for data transmission: an idea whose time has come, IEEE Commun. Mag. 28 (5) (May 1990) 5–14.
[8] F.V. Nee, R. Prasad, OFDM for Wireless Multimedia Communications, Artech House, Boston, MA, 2000. [9] J.S.J. Wang, Z.-X. Yang, L. Yang, J. Wang, Frames theoretic analysis of zero-padding OFDM over deep fading wireless channels, IEEE Trans. Broadcast. 52 (6) (June 2006) 252–260. [10] X.-G. Xia, Precoded and vector OFDM robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems, IEEE Trans. Commun. 49 (8) (August 2001) 1363–1374. [11] R. O’Neill, L. Lopes, Envelope variations and spectral splatter in clipped multicarrier signals, in: Proceedings of Conference on Personal Indoor Mobile Ratio, September 1995. [12] Z. Dlugaszewski, K. Wesolowski, WHT/OFDM—an improved OFDM transmission method for selective fading channels, in: Proc. Symposium on Communications and Vehicular Technology, vol. 19, Leuven, Belgium, October 2000, pp. 144–149. [13] H. Schulze, C. Luders, Theory and Applications of OFDM and CDMA, Wiley, New Jersey, 2005. [14] R. AliHemmati, P. Azmi, Iterative reconstruction-based method for clipping noise suppression in OFDM systems, IEE Proc. Commun. 152 (8) (August 2005) 452–456. [15] F. Marvasti, Theory and Practice of Nonuniform Sampling, Kluwer Academic/Plenum Publishers, New York, 2001. [16] J.K. Wolf, Redundancy, the discrete fourier transform, and impulse noise cancellation, IEEE Trans. Commun. 31 (3) (March 1983) 458–461. [17] F. Marvasti, M. Hasan, S. Talebi, Efficient algorithms for burst error recovery using FFT and other transform kernels, IEEE Trans. Signal Process. 47 (4) (April 1999) 1065–1075. [18] F. Marvasti, An iterative method to compensate for the interpolation distortion, IEEE Trans. Acoust. Speech Signal Process 37 (10) (October 1989) 1617–1621. [19] E.G. Larsson, B.R. Vojcic, Cooperative transmit diversity based on superposition modulation, IEEE Commun. Lett. 9 (9) (September 2005) 778–780.
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Coded cooperation diversity for uncoded oversampled OFDM systems Alireza Rahmati, Paeiz Azmi Electrical and Computer Engineering Department, Tarbiat Modares University, Tehran, Iran
a r t i c l e i n f o
abstract
Article history: Received 12 November 2007 Received in revised form 15 December 2008 Accepted 12 January 2009 Available online 25 January 2009
Recently, user-cooperation diversity has been introduced as an effective scheme that can bring about antenna diversity in wireless networks. In this paper, we introduce a coded cooperation diversity technique for single antenna uncoded orthogonal frequency division multiplexing (OFDM) systems, in which implementation of coded cooperation is provided by the oversampling potential in OFDM, instead of using extra channel coding. In fact, zero-padding followed by IFFT in OFDM is similar to oversampling and could be an alternative to applying correction codes. Furthermore, we use this oversampling to implement an iterative receiver at the partner terminal. This receiver works based on the nonuniform sampling theorem for reconstructing of lost symbols. The lost symbols appear at the partner terminal of cooperative network because of dividing each OFDM block into two segments through the puncturing at the user terminal of the cooperative network. We provide simulation results for our proposed scenario, and observe significant gains over the non-cooperative oversampled OFDM systems without any need whatever for using extra channel coding. & 2009 Elsevier B.V. All rights reserved.
Keywords: Coded cooperation diversity Orthogonal frequency division multiplexing (OFDM) Oversampling Iterative reconstruction method
1. Introduction Signal quality in mobile radio channels is severely affected by undesirable channel quality due to the effects of multi-path fading, in which mobile users experience strong variations in signal attenuation during a given call. Recently, user-cooperation diversity has been emerged as a new form of spatial diversity, whereby diversity gains are attained via cooperation of sparse terminals in wireless networks. This diversity technique enables terminals, where it is not easy to be equipped by multiple antennas due to size and cost limitations, to obtain higher data rates which are less prone to channel variations [1–3]. Coded cooperation scheme using channel coding for cooperative systems has been proposed in [4–6], for its efficient usage of the available bandwidth. This cooperative transmission
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E-mail address: [email protected] (P. Azmi). 0165-1684/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2009.01.010
protocol should be implemented in state-of-the-art transmission technologies, such as orthogonal frequency division multiplexing (OFDM), that has recently received substantial attention in the areas of wireless communication systems for its simple implementation with FFT/IFFT pairs, efficient use of the available bandwidth, and robustness to frequency selective fading [7,8]. For the first time in this paper, we will use the oversampling potential for implementing the coded cooperative diversity in OFDM systems as an alternative for using formal channel coding. In fact, the oversampling can act as an error-correction code without the need for the complex Viterbi decoding algorithm used in decoding convolutional codes in the conventional coded cooperative systems. Oversampling is performed by padding the QAM modulating sequence with some zeros before IFFT at the transmitter of OFDM systems to provide oversampled OFDM systems, a special case of the precoded OFDM systems, known as the zero-padded OFDM (ZP-OFDM) systems by the papers of the past [9,10]. However,
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oversampling can be considered for providing other properties as well, such as decreasing edge effects of OFDM signal in frequency domain, channel estimation, and PAPR reduction, as explored in [11–14]. The oversampling in our proposed cooperative system is used for two reasons. First, this oversampling provides a special DFT code (or a Reed Solomon code in real field) without any need for using extra channel coding which is mandatory for putting the coded cooperative diversity schemes into practice. We use the oversampling potential secondly to reconstruct the lost QAM modulated symbols of each OFDM symbol at the partner terminal. In fact, our cooperative scheme partitions each user’s OFDM symbol into the two segments through puncturing. So, the partner terminal should reconstruct user’s OFDM symbol from a received version which has lost some of its QAM modulated symbols. However, if the average symbol rate of the remaining QAM modulated symbols stays above the Nyquist rate, as the nonuniform sampling theorem states, complete recovery of each OFDM symbol would be possible [15]. This perfect reconstruction can be guaranteed at the partner terminal if the high enough oversampling factor is chosen at the user terminal. Therefore, using the iterative receiver working base on the nonuniform sampling theory at the partner terminal can be a proper choice for its simple implementation. The rest of this paper is organized as follows. In Section 2, the oversampled OFDM system and the iterative receiver included in our coded cooperative scheme are reviewed. In Section 3, we describe the proposed coded cooperation model in the oversampled OFDM system. Simulation results illustrating the performance of the oversampled OFDM for the coded cooperation scenario are presented in Section 4. Section 5 is dedicated to concluding remarks and future works. 2. Iterative receiver for oversampled OFDM systems
Fig. 1 gives the simplified model of oversampled OFDM transmitter. Let c stand for the information symbols after the QAM modulation and segmentation into blocks with size K, c ¼ ½c1 ; c2 ; . . . ; cK T
L can be considered as an oversampling factor and in the case of the conventional OFDM system, L ¼ 1, corresponding to the Nyquist symbol rate. Let N be the number of subcarriers in the OFDM system. Hence, N symbols of c0 are transmitted at the same time in one OFDM symbol s, which is a N-point IFFT transformed version of c. It has been shown that s is a special DFT coded version of c that can be expressed as [15–17] s ¼ Gc
2.2. Iterative receiver One can estimate s from its punctured version, t, perfectly by the iterative receiver shown in Fig. 2 if a high oversampling factor, L, is chosen at the transmission side. This iterative receiver works based on the nonuniform sampling theorem [15]. Hence, as long as the average symbol rate of t stays above the Nyquist rate, perfect reconstruction of s would be possible. This iterative receiver consists of two main blocks, namely filtering and iterative reconstruction. 2.3. Linear filtering The filtering stage begins by removing the interference among different symbols that can be carried out by time domain ZF equalization:
(1)
c
s
c
t
QAM 0
IFFT
P
Fig. 1. Transmitter of the oversampled OFDM system.
(3)
where t is the punctured vector at the transmitter after N-point IFFT modulator (time domain transmitted signal), H ¼ diagðH1 ; H2 ; . . . ; HN Þ, a diagonal matrix with diagonal elements ðH1 ; H2 ; . . . ; HN Þ, is the channel in the time domain and v0 is N 1 AWGN noise. Note that multipath effects of quasi-static Rayleigh fading channel can be
Then ðL 1ÞK trailing zeros are padded after each c to form a N 1 column vector of c0 ¼ ½c1 ; c2 ; . . . ; cK ; 0; . . . ; 0T .
S / P
(2)
where G is the generator matrix. In the next section, we will see that in the proposed coded cooperation scheme, the oversampled OFDM transmitter partitions s into the two segments through N N puncturing matrix of P and sends only one of these segments. The channel is assumed to be quasi-static frequency selective Rayleigh fading corrupted by N 1 additive white Gaussian noise (AWGN) vector of v ¼ ½v1 ; v2 ; . . . ; vN T at the receiver.
bt ¼ t þ H1 v0
2.1. Oversampled OFDM transmitter
1371
Fig. 2. The Iterative receiver for oversampled OFDM system.
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3. Proposed coded cooperation diversity for OFDM systems 3.1. Medium access and level of cooperation
Fig. 3. LPF processing in the filtering stage.
Fig. 4. Iterative reconstruction method.
removed completely by using the cyclic prefix (CP), so fading effects of each subchannel can be considered only by a scalar product as explained in Eq. (3) similar to that in [14]. This stage is finished by applying the low pass filtering to bt, depicted by the LPF block in Fig. 2. This LPF block may alleviate a high noise level of H1 v0 by erasing erasures corresponding to the zero padded positions of the oversampled OFDM signal as depicted in Fig. 3 and expressed as follows: 2
3T K zfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflffl{ 0 0 0 0 0 6 7 tb0 ¼ FNbt ¼ 4bt 1 ; bt 2 ; . . . ; bt K ; bt Kþ1 ; . . . ; bt N 5 |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
(4)
Erasures
3T K zfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflffl{ 0 0 0 6 7 te0 ¼ 4bt 1 ; bt 2 ; . . . ; bt K ; 0; . . . ; 05 |fflfflfflffl{zfflfflfflffl}
Consider the wireless network depicted in Fig. 5, in which both terminals T 1 and T 2 cooperate and transmit to a single destination D. The inter-user and uplink channels are subject to frequency selective Rayleigh fading. We assume that terminals transmit on orthogonal TDMA channels similar to [1,4,6], which not only allows the terminals to transmit and receive on different channels but also enables the destination and the two terminals to separately detect each other in the cooperative mode. The modified TDMA implementation of this system for our OFDM system is shown in Fig. 6, where for simplicity only the cooperative level of 50% is depicted. The level of cooperation for OFDM systems is the percentage of the total subcarriers per each OFDM symbol that the user transmits for its partner. Each T 1 and T 2 terminals act as the user terminal and as the partner terminal during its own time slot. In direct transmission, each user transmits its OFDM symbol via N subcarriers during its whole own time slot while for the cooperative scheme each user simultaneously sends a combination of its own data and the partner’s data, as shown in Fig. 6. Particularly, in fullcooperation (50% cooperation) scheme, each terminal simultaneously transmits half of its OFDM symbol on N=2 subcarriers and half of the partner’s OFDM symbol on the remaining N=2 subcarriers during its own time slot. Note that this cooperative scheme is a special case of coded cooperative diversity based on superposition modulation for OFDM systems. Recently, new DF scheme based on superposition modulation for a single carrier system has been proposed in [19]. This spectrally efficient
2
(5)
T1
Erasures
D et ¼ FH te0 ¼ ½et 1 ; et 2 ; . . . ; et N T N
(6)
T2
where FN denotes N-point FFT operator.
Fig. 5. Cooperation system model.
2.4. Iterative reconstruction Reconstruction of s from et can be performed by the iterative method depicted in Fig. 4, a special case of general ones proposed by [15,18] 8 iþ1 i
N/2
N/2
N/2
N/2
Terminal T1
T1 bits
T2 bits
RX T2
Inactive
Terminal T2
RX T1
Inactive
T2 bits
T1 bits
T1 Slot
T2 Slot
Fig. 6. Coded cooperation implementation for oversampled OFDM system using TDMA.
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employed for partitioning of each user’s OFDM symbol into the two frames in the cooperative transmission. Block diagram of each partner terminal during its own time slot in the cooperative level of 50% is precisely depicted in Fig. 8. In this block diagram, after filtering stage, the partner terminal tries to recover the whole of the user’s OFDM symbol from the received segment by the iterative reconstruction method with P ¼ P1 (Fig. 4), explained in Section 2. If the partner terminal manages to recover user’s OFDM symbol successfully (as indicated by the CRC bits) sends the remaining of the OFDM symbol for the user through the puncturing block of P2 within its time slot. Furthermore, the partner terminal simultaneously sends the first segment of its own OFDM symbol provided by the puncturing matrix of P1 during its own time slot. Note that P1 and P2 are N N puncturing matrixes, e.g. for N ¼ 4 and 50% cooperation, P1 and P2 can be considered as follows:
cooperative protocol is based on superposition modulation which allows each user to transmit its own information and relay the data from the partner simultaneously. 3.2. Oversampling and proposed coded cooperative diversity Fig. 7 shows the user terminal to implement the proposed coded cooperative diversity for the oversampled OFDM systems for sending half of its own OFDM symbol. This block diagram includes cyclic redundancy check (CRC) coder block, the oversampled OFDM transmitter block, and puncturing matrix block of P1 . The receiver is informed by CRC bits for detection process corresponding to the cooperative or non-cooperative transmission mode. The oversampled OFDM transmitter block is explained in Section 2 and is utilized in our scenario because of the oversampling potential. Conventional methods [4,5] use channel coding like convolutional codes for both partitioning a user’s OFDM symbol and detection and correction of errors, whereas we apply the oversampling factor L to c and obtain s, its Reed Solomon coded version in real field, instead of using extra channel coding and so avoid wasting bandwidth. The puncturing matrix, P1 , is
0
1
1
0
0
0
B0 B P1 ¼ B @0
0
0
0
1
0C C C 0A
0
0
0
0
0 and
1
0
0
0
0
B0 B P2 ¼ B @0
1
0
0
0
0C C C 0A
0
0
0
1
Fig. 7. The user terminal in the coded cooperative diversity.
CRC check Symbols received From User
Z F
L P F
Iterative Reconstruc.
2
1 2
P2
N-1 N
N
Partner's DATA
CRC
Oversampled OFDM Trasmitted
1 2
YES
P1
1 2
N-1 N
N
1 2
N
Fig. 8. The partner terminal in the coded cooperative diversity.
NO
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100
10−1
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10−3
75% cooperation 50%cooperation 25%cooperation
10−4
Unpunctured
10−5 (511,130) BCH coded OFDM Oversampled OFDM using iterative receiver
10−6 5
10
15 (Eb/N0)T1−T2(dB)
20
25
Fig. 9. BER performance of both a (511,130) BCH coded OFDM and the proposed iterative oversampled OFDM versus Eb =N 0 at the partner terminal for different levels of cooperation.
Hence, the user only transmits the odd QAM modulated symbols of its OFDM symbol and the even modulated symbols should be transmitted for the user terminal by the partner. If the partner terminal cannot recover user’s OFDM symbol successfully (as indicated by the CRC bits) automatically revert back to a non-cooperative mode and transmits its OFDM symbol via N subcarriers during its whole own time slot. 4. Results and discussion We evaluate the performance of the oversampled OFDM system in the proposed coded cooperation scenario, compared to the non-cooperative scheme through simulations over multipath Rayleigh fading channels with zero mean and variance 1. The system parameters that we assumed in the simulation, unless specified otherwise, were K ¼ 32 length of the CRC coded block with Graymapped 16-QAM modulation on each entry, L ¼ 4 the oversampling factor as in [11,14] for PAPR reduction considerations, N ¼ 128 the number of subcarriers, and i ¼ 10 the number of iteration employed at the iterative receiver of the partner terminal. A 16-bit CRC code with generator polynomial given by coefficients 15935 (hexadecimal notation) is considered for our simulations. 4.1. The oversampling factor and the level of cooperation Due to the puncturing process at the user terminal T 1 , the partner terminal T 2 should reconstruct the lost symbols of each user’s OFDM block from the remaining
ones. If we denote P as the probability of lost, then it has been shown that the inverse of the 1 P is the sampling rate normalized by the Nyquist rate, needed for errorless transmission [15]. Hence, the oversampling factor of L ¼ 4 ensures errorless transmission even if 3=4 of the samples of each OFDM block are lost. Therefore, up to the cooperation level of 75% is guaranteed in our cooperative system thanks to the oversampling factor of L ¼ 4, where the puncturing process discards 3=4 of each OFDM symbol. To demonstrate the iterative receiver efficiency at the partner terminal Fig. 9 is provided, where the average T 1 ’s BER versus Eb =N0 of the T 1 –T 2 inter-user channel in the partner terminal is shown. Performance of BCH coded OFDM with the same bandwidth is also shown in Fig. 9. Here, T 2 uses the iterative receiver/BCH decoder and different probability of lost P ¼ 1=4; 1=2; 3=4, corresponding to the various cooperation levels of 25%, 50%, and 75%, respectively, are applied in T 1 terminal. It is worth noting that unlike our scheme most of the channel codes cannot recover the data from its severely punctured version, e.g., OFDM transmission that relies on using a BCH code shown in Fig. 9 yields perfect reconstruction only for cooperation level of 25%. Because of that conventional cooperative systems use some complex special channel codes, e.g., RCPC codes for data reconstruction at the partner terminal. To show the convergence rate of the iterative receiver at the partner terminal, for a given level of cooperation, different number of iterations i ¼ 1, 2, 3, 4, 5, 10, and 100 are considered as shown in Fig. 10. The iterative receiver improves the BER performance significantly as more iterations are carried out. Observe also that the performance
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100
BER
10−1
Iteration=1 Iteration=2 Iteration=3 Iteration=4 Iteration=5 Iteration=10 Iteration=100
10−2
10−3 0
5
10
15
20
25
SNRT1−T2(dB) Fig. 10. BER versus SNR at the partner terminal for different number of iterations.
for the iterations with the values of i ¼ 10 and 100 are close together that implies the fast convergence rate of our proposed scheme. 4.2. Detection policy at the destination terminal At the destination terminal, two different strategies can be devised for the detection of each user’s OFDM symbol. One of them can be easily performed by combining the received signals from both the user and the partner terminals in two consecutive time slot similar to that in [19]. The better manner, which also alleviates the Rayleigh fading channel nulls, uses the iterative receiver at the destination. This receiver is the same as the iterative ones introduced in Section 2 except the discarding matrix O which should be included before the iterative reconstruction block of Fig. 2. The destination discards the deep faded symbols of each OFDM symbol by the discarding matrix O which is a N N diagonal matrix with o ¼ ½o1 ; o2 ; . . . ; oN on its diagonal with ( 1 kHi kXl oi ¼ , 0 O:W where l is the discarding threshold and H ¼ diag½H1 ; H2 ; . . . ; HN is the time domain channel vector. Also, the discarding matrix of O should be substituted for P in the iterative reconstruction method shown in Fig. 4. Fig. 11 compares the performance of the coded cooperation system using the simple detector with one employing the iterative detector with l ¼ 0:1 at the destination terminal for both a poor inter-user channel (0 dB) and one with average SNR of 40 dB. The T 2 -destination uplink
channel is assumed 3 dB better than the T 1 -destination uplink channel, and the level of cooperation is 50%. Note that the cooperation improves the BER performance significantly, but the performance of both coded cooperation scenarios at the average inter-user SNR of 0 dB nears the performance of non-cooperative system depicted by Fig. 11. One can observe that better BER performance can be achieved with the employment of the proposed iterative detector, rather than the simple one in the cooperation scheme. Particularly, about 9 dB gain in SNR over the simple detector at a bit error rate of 103 can be achieved by the iterative receiver. Performance of space time coded cooperation in OFDM system with the same bandwidth and cooperation level of 50% for perfect interuser channel is also shown in Fig. 11. As Fig. 11 shows, space time coded cooperation shows little better performance than our proposed cooperative scheme, but this negligible profit is obtained at the expense of including comparatively complicated RCPC codes for recovering the data from its punctured version at the partner terminal. Furthermore, various cooperation levels which can simply be provided in our cooperative method by changing the oversampling factor, L, cannot easily be obtained in space time cooperation. Performance of DF scheme for OFDM system based on superposition modulation with the same bandwidth and cooperation level is also shown in Fig. 11, where BCH codes are applied at the cooperative terminals. The inter-user and uplink channels are assumed to be similar to those considered in our proposed coded cooperative scheme. Due to the error propagation, the performance of DF cooperation system at the average inter-user SNR of 0 dB is very poor, and at the average inter-user SNR of 40 dB the performance of DF cooperation
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10−1
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DF cooperation system based on superposition Non−iterative oversampled OFDM in 50% cooperation scheme
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Iterative oversampled OFDM in 50% cooperation scheme Space time coded cooperation
10−7 0
5
10
15
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SNRT1−destination(dB) Fig. 11. T 1 ’s BER versus the T 1 -destination uplink channel SNR for the coded cooperative diversity in the oversampled OFDM system using the simple and the iterative detector with l ¼ 0:1 at the destination. Space time coded cooperation with the same bandwidth for perfect inter-user channel is also shown. Performance of DF scheme for OFDM system based on superposition modulation with the same bandwidth and cooperation level is also compared, where BCH codes are applied at the cooperative terminals.
system approaches the performance of non-cooperative oversampled OFDM system. As a result, although both the DF cooperation system and our proposed coded cooperative scheme are based on superposition modulation, our proposed scheme for oversampled OFDM system yields significant gains over the DF scheme for BCH coded OFDM system (see Fig. 11). This result could be predicted from Fig. 9, which shows the merit of using oversampling in OFDM.
of l for discarding high quality symbols and reconstructing them via iterative scheme. In other words, by discarding symbols via choosing a high value for l, we lose very much useful information needed for symbol recovery. At low SNRs, however, choosing a low value for l results in such a burst of weak symbols that using the iterative receiver based on nonuniform sampling theorem cannot improve the performance because of the large number of missing symbols. Therefore, it seems that for a given SNR there is only one optimum value for l, as can be seen by dotted curve in Fig 13.
4.3. l in oversampled OFDM system One important issue in our proposed iterative receiver described in Section 4.2 is selecting the proper value for l. Fig. 12 shows the average BER versus SNR for our proposed cooperative scheme using the iterative receiver for average inter-user channel SNR of 0 dB, which corresponds to the non-cooperative case. The figure shows curves generated through simulations corresponding to different discarding thresholds l ¼ 0; 0:05; 0:1; 0:15; 0:2; 0:25 in Rayleigh fading channel. Notice that the l ¼ 0 reduces to the case of the non-cooperative oversampled OFDM system. It can also be seen that at high SNR ð417 dBÞ the iterative receiver with l ¼ 0:1 performs the best in Rayleigh fading channel with zero mean and variance 1. As Fig. 13 illustrates, proper value of l relates inversely to the channel SNR and it should be decreased by increasing the SNR for obtaining the best performance. At high SNRs, the number of symbols with good enough quality increases and there is no need for choosing a high value
4.4. Performance improvement with cooperation by iterative receiver at destination terminal Fig. 14 compares the performance of the coded cooperation scenario using the iterative detector with l ¼ 0:1 at 75%, 50%, and 25%, for both a poor inter-user channel and one with average SNR of 40 dB. The user uplink channels have equal average SNR. When the interuser channel is poor, both users never cooperate, and consequently the closest case to the non-cooperation (25%) yields better performance. However, when the interuser channel is perfect (40 dB) all cases perform the same. 5. Conclusions and future works In this paper, we proposed a novel coded cooperation scenario for OFDM systems by using the oversampling as an error-correction code based on superposition
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100 λ=0 λ = 0.05 λ = 0.1 λ = 0.15 λ = 0.2 λ = 0.25
BER
10−1
10−2
10−3
10−4 4
6
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SNR (dB) Fig. 12. BER versus SNR for iterative oversampled OFDM system for different values of l.
100
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10−4 SNR=5, λmin = 0.35
10−5
SNR=10, λmin = 0.25 SNR=15, λmin = 0.15
10−6
SNR=20, λmin = 0.1 SNR=25, λmin = 0.06
10−7 0
0.2
0.4
0.6
0.8
1
λ Fig. 13. BER versus l for iterative oversampled OFDM system for different channel SNRs.
modulation. In our scheme, the oversampling which is usually applied for PAPR reduction is employed at the partner terminal to iteratively recover the data from its punctured version. All the processing of our scheme is performed at the receiver without requiring any modification at the transmitter and without any need for using
extra channel coding that may use the very long interleaving for decoding. This potentially can save more bandwidth for the transmission. Also, we proposed two detection strategies in the destination terminal. Simulation results reveal the significant BER improvements of proposed methods compared to the non-cooperative ones
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10−5
0dB interuser SNR 40dB interuser SNR
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SNRT1−destination(dB) Fig. 14. T 1 ’s BER versus the T 1 -destination uplink channel SNR for the coded cooperative diversity in the oversampled OFDM system using the iterative detector with l ¼ 0:1 at the destination for different levels of cooperation.
over the Rayleigh fading channels. Although the oversampled OFDM transmitter considered in our scheme falls under a broad class of linear transmitters, the iterative receiver employed in our proposed scheme is a nonlinear receiver based on the nonuniform sampling theorem. Performance analysis of this nonlinear receiver in OFDM systems is not a straight-forward task and closed form representation for the performance of our proposed scheme will be derived in our future works. References [1] J.N. Laneman, D.N.C. Tse, G.W. Wornell, Cooperative diversity in wireless networks: efficient protocols and outage behavior, IEEE Trans. Inf. Theory 50 (12) (December 2004) 3062–3080. [2] A. Sendonaris, E.E.B. Aazhang, User cooperation diversity—part i: system description, IEEE Trans. Commun. 51 (11) (November 2003) 1927–1938. [3] A. Sendonaris, E.E.B. Aazhang, User cooperation diversity—part ii: implementation aspects and performance analysis, IEEE Trans. Commun. 51 (11) (November 2003) 1939–1948. [4] T.E. Hunter, A. Nosratinia, Cooperative diversity through coding, in: Proceedings of IEEE ISIT, Laussane, Switzerland, July 2002, p. 220. [5] P.S.R. Liu, E. Soljanin, User cooperation with punctured turbo codes, in: Proceedings of 41st Allerton Conference on Communication, Control, and Computing, Monticello, IL, October 2003. [6] A. Stefanov, E. Erkip, Cooperative coding for wireless networks, IEEE Trans. Commun. 52 (9) (September 2004) 1470–1476. [7] J.A.C. Bingham, Modulation for data transmission: an idea whose time has come, IEEE Commun. Mag. 28 (5) (May 1990) 5–14.
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