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A low-complexity receiver for iterative parallel interference cancellation and decoding in MIMO–OFDM systems
Int. J. Electron. Commun. (AEÜ) 62 (2008) 68 – 71 www.elsevier.de/aeue
LETTER
A low-complexity receiver for iterative parallel interference cancellation and decoding in MIMO–OFDM systems Wenfeng Lin∗ , Chen He Department of Electronic Engineering, Shanghai Jiao Tong University, 800 Dong Chuang Road Shanghai 200240 China Received 10 September 2006; accepted 6 February 2007
Abstract A novel low-complexity iterative receiver for coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems is proposed in this letter. The soft-in soft-out (SISO) detector is simply a parallel interference cancellation (PIC)–maximum ratio combining (MRC) operation. However, system performance would be degraded because of ignoring the existence of the residual interference from other transmit antennas. In our scheme, the log likelihood ratios (LLRs) of encoded bits after channel decoding are multiplied by a constant factor to achieve a performance gain. The constant factor is optimized according to the extrinsic information transfer (EXIT) chart. Simulation results show that the proposed iterative receiver can significantly improve the system performance and converge to the matched filter bound (MFB) with low computational complexity at high signal-to-noise ratios (SNRs). 䉷 2007 Elsevier GmbH. All rights reserved. Keywords: MIMO–OFDM; Iterative; PIC–MRC; EXIT
1. Introduction In recent years, multiple-input multiple-output (MIMO) communication system has received considerable attention because of its potential to improve the system performance and capacity. To achieve this advantage, turbo Bell Laboratories Layered Space–Time (BLAST) techniques are developed for flat fading MIMO systems [1]. In [2], turbo equalization is developed to combat the frequency selective channels. But it has a huge increase in complexity for the large number of receive antennas and long delay spreads due to the matrix inversion. Thus, orthogonal frequency division multiplexing (OFDM) techniques would be more attractive for wideband signals, which can transfer frequency selective channels in time domain to flat fading channels in frequency ∗ Corresponding author. Tel.: +86 021 34204587.
E-mail addresses: [email protected] (W. Lin), [email protected] (C. He). 1434-8411/$ - see front matter 䉷 2007 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2007.02.002
domain. In order to further reduce the complexity of the MMSE detector, the soft-in soft-out (SISO) detector is simply a parallel interference cancellation (PIC)–maximum ratio combining (MRC) operation in this letter. After channel decoding, the log likelihood ratios (LLRs) are multiplied by a constant factor to achieve a performance gain. Simulation results show that our scheme can substantially improve system performance and converge to the matched filter bound (MFB).
2. System model The MIMO–OFDM system is equipped with Nt transmit antennas and Nr receive antennas. After cyclic prefix removal and fast Fourier transform (FFT) demodulation, the received vector at the kth subcarrier can be expressed as yk = Hk xk + nk ,
(1)
W. Lin, C. He / Int. J. Electron. Commun. (AEÜ) 62 (2008) 68 – 71
where Hk is an Nr × Nt channel matrix, in which the (i, j )th element, hk (i, j ), is the fading coefficient between the jth transmit antenna and the ith receive antenna. xk = [xk,1 , xk,2 , . . . , xk,Nt ]T is the Nt × 1 transmitted symbol vector; nk is the zero mean complex Gaussian noise with variance 2 per complex dimension.
69
x
+
+ Channel Decoder
Interleaver
DeInterleaver
+
+
FFT
CP Removal
FFT
CP Removal
PICMRC
SISO Decoder
3. Low complexity iterative detection and decoding
Fig. 1. MIMO–OFDM iterative receiver.
Fig. 1 shows the proposed PIC–MRC based iterative receiver. At each iteration, the SISO detector performs PIC and MRC, as H zk,n = hk,n (yk − Hk x¯ k + x¯k,n hk,n ),
(2)
where n denotes the transmit antenna index and hk,n is the nth column of Hk . x¯ k = [x¯k,1 , x¯k,2 , . . . , x¯k,Nt ]T is the mean value of transmitted symbol vector. With the a priori information fed back from the channel decoder, it is calculated as [3] x¯k,n = E[xk,n ] = (d)P (xk,n = (d)), (3) d∈S
where P (xk,n =(d)) is the function of a priori information La (dk,n (i)), i = 1, 2, . . . , Mc , Mc is the number of bits per constellation symbol. d is an Mc × 1 vector of data bits with its entity dk,n (i) and (d) is a constellation symbol which is obtained using the mapping function. S is the set of possible values of d. Then we have [3] P (xk,n = (d)) =
Mc 1 i=1
2
· tanh
1 + (2dk,n (i) − 1)
1 La (dk,n (i)) . 2
(4)
To extract the extrinsic information of the transmitted bits, the PIC–MRC detector output is approximated as Gaussian. The mean and the variance are computed as [3]. Therefore, computational complexity is significantly reduced because matrix inversion in [1] is avoided. However, the MRC operation would result in large performance loss because of residual co-antennas interference, especially at the first iteration when no priori information is available. Thus we could obtain the LLRs of transmitted bits. Then they are fed to the channel decoder after deinterleaving. In order to improve the system performance, the LLRs of the channel decoder output are multiplied by a constant factor . It is optimized according to the extrinsic information transfer (EXIT) chart of the SISO decoder. The EXIT chart is an effective technique to examine the convergence property of iterative detection and decoding [4]. It models receiver components as devices mapping a sequence of a priori information La to a new sequence of extrinsic information Le . Using the input a priori
information, the channel decoder estimates the LLRs Le of encoded bits. Then they are multiplied by a constant factor in the proposed scheme. To optimize the constant factor , the mutual information between the extrinsic information Le and the encoded bits C is computed as [5] Ie (Le ; C) = 1 −
N 1 log2 [1 + exp(−c(n)Le (n))], N
(5)
n=1
where N is the number of encoded bits and and c(n) is the nth bit of the encoded bit sequence C. The constant factor is set to the minimum value that can almost result in the maximum mutual information Ie (Le ; C).
4. Simulation results In this section, we demonstrate the performance of the proposed iterative receiver. The system parameters are as follows. Eight transmit antennas and eight receive antennas are employed. The carrier frequency is 2.0 GHz and the bandwidth is 5 MHz. The system has 512 subcarriers with 64 cyclic prefix. Information bits are encoded using a rate- 21 recursive systematic convolution (RSC) code with a generation function (7, 5). Encoded bits are randomly interleaved and QPSK modulated. The channel model is the international telecommunicational union (ITU) “vehicular A” (VA) and mobile velocity is 30 km/h. Perfect channel state information is available at the receiver. We define the signal-tonoise ratio (SNR) per receive antenna and per subcarrier to be 10 log10 (Nt Es /2 ), where Es is the symbol energy.We first show the EXIT charts of the channel decoder under different in Fig. 2, where = 1.0 corresponds to the conventional channel decoder. It can be observed that = 2.5 is an approximately optimal solution. At the low input mutual information region, it maximizes the output mutual information Ie (Le ; C), which could reduce the SNR threshold requiring for the turbo cliff region. Further increase of would not improve the output mutual information at that region. However, the output mutual information Ie (Le ; C) is nearly the same at the high input mutual information region under different . If is set too small, more iterations are needed for the iterative receiver to converge, which would be computationally inefficient.
70
W. Lin, C. He / Int. J. Electron. Commun. (AEÜ) 62 (2008) 68 – 71 1 0.9 0.8 0.7
Ie(Ia)
0.6 0.5 0.4 PIC-MRC MMSE Channel Decoder α=1.0 Channel Decoder α=2.0 Channel Decoder α=2.5 Channel Decoder α=3.0
0.3 0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
Ia(Ie)
Fig. 2. Receiver EXIT charts, at SNR = 5 dB.
5. Conclusions
100
In this letter, we have proposed a novel low-complexity iterative receiver for coded MIMO–OFDM systems. The SISO detector is simply a PIC–MRC operation. After channel decoding, the LLRs of encoded bits are multiplied by a constant factor to achieve a performance gain. Simulation results show that the proposed iterative receiver can obtain significant performance gain and converge to the MFB with low computational complexity at high SNRs.
10-1
BER
10-2 10-3
10
The matched filter bound (MFB) is also presented as a lower bound of BER of the iterative receiver. For the conventional PIC–MRC detector, an error floor can be observed. The BER performance of the proposed PIC–MRC detector is much better than that of the conventional one after two iterations and converges to the MFB at high SNRs. Five iterations is needed for the MMSE [1] detector to converge and then the simulation result is also shown in Fig. 3. Comparing the propose PIC–MRC detector with the MMSE detector at the fifth iteration, the performance loss is only 0.5 dB at BER of 10−4 . But our scheme is much simpler than the MMSE [1] detector since the matrix inversion is avoided. Though the constant factor is optimized under the VA channel, we find that = 2.5 is also effective for other channels, such as “vehicular A” (VB), “pedestrian A” (PA) and “pedestrian B” (PB). We don’t give the simulation results due to the page limit.
Iteration=1 Iteration=2 Iteration=3 Iteration=4 Iteration=5 Iteration=6 MMSE [1] MFB
-4
10-5 10-6 2
3
Acknowledgements 4
5
6
7
SNR(dB)
Fig. 3. BER performance comparison of iterative receiver for 8×8 MIMO–OFDM systems (VA).
If → ∞, it reduces the SISO decoder to a hard-decision decoder, resulting in performance loss. The EXIT charts of the PIC–MRC detector and the MMSE detector at SNR = 5 dB are also given in Fig. 2. For the MMSE detector, the mutual information input to the channel decoder is already high enough at the first iteration. At that region, the LLRs multiplication by a constant factor would not improve mutual information of channel decoder output. Thus no optimization of is needed for the MMSE detector. However, for the PIC–MRC detector, the mutual information input to the channel decoder is still low at the first iteration. Thus our scheme would improve the system performance of the PIC–MRC detector. The bit error rate (BER) performance of the conventional PIC–MRC detector (=1.0, dashed line) is compared with that of the proposed one ( = 2.5, solid line) in Fig. 3. Six iterations are implemented in both schemes.
This research was supported by the Science and Technology Committee of Shanghai Municipality (under Grant nos. 06DZ15013 and 03DZ15010) and Shanghai Research Center for Wireless Communications.
References [1] Sellathurai M, Haykin S. Turbo-blast for wireless communications: theory and experiments. IEEE Trans Signal Process 2002;50:2538–46. [2] Abe T, Matsumoto T. Space–time turbo equalization in frequency selective mimo channels. IEEE Trans Vehicular Technol 2003;52:469–75. [3] Tuchler M, Singer AC, Koetter R. Minimum mean squared error equalization using a prior information. IEEE Trans Signal Process 2002;50:673–83. [4] Brink ST. Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Trans Commun 2001;40:1727–37. [5] Tuchler M, Hagenauer J. Exit charts of irregular codes, Conference on Information Sciences and Systems, 2002.
W. Lin, C. He / Int. J. Electron. Commun. (AEÜ) 62 (2008) 68 – 71
Wenfeng Lin was born in Quanzhou, China, 1978. He received his M.S. degree in Circuit and System from XiDian University, Xi’an, China, in 2004. He is currently pursuiting his Ph.D. degree in the Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai. His research interests include wireless communications and signal processing, primarily on the iterative algorithms and adaptive modulation and coding. Chen He graduated from Southeast University of China and obtained his B.E. degree and his M.E. degree in electronic engineering in 1982 and 1985, respectively, and then, he joined the Department of Electronic Engineering in Southeast University of China from 1985. He visited Tokushima University of Japan as a foreign researcher from October 1990 to September 1991 and obtained his Ph.D. degree from
71
Tokushima University of Japan in electronics system in 1994. He jointed the Department of Electronic Engineering in Shanghai Jiao Tong University of China from 1996. He visited the Communication Research Laboratory of Japan from December 1999 to December 2000 as a research fellow. Now, he is a professor of Shanghai Jiao Tong University of China. His current research interests are wireless communication systems and intelligent information processing.
LETTER
A low-complexity receiver for iterative parallel interference cancellation and decoding in MIMO–OFDM systems Wenfeng Lin∗ , Chen He Department of Electronic Engineering, Shanghai Jiao Tong University, 800 Dong Chuang Road Shanghai 200240 China Received 10 September 2006; accepted 6 February 2007
Abstract A novel low-complexity iterative receiver for coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems is proposed in this letter. The soft-in soft-out (SISO) detector is simply a parallel interference cancellation (PIC)–maximum ratio combining (MRC) operation. However, system performance would be degraded because of ignoring the existence of the residual interference from other transmit antennas. In our scheme, the log likelihood ratios (LLRs) of encoded bits after channel decoding are multiplied by a constant factor to achieve a performance gain. The constant factor is optimized according to the extrinsic information transfer (EXIT) chart. Simulation results show that the proposed iterative receiver can significantly improve the system performance and converge to the matched filter bound (MFB) with low computational complexity at high signal-to-noise ratios (SNRs). 䉷 2007 Elsevier GmbH. All rights reserved. Keywords: MIMO–OFDM; Iterative; PIC–MRC; EXIT
1. Introduction In recent years, multiple-input multiple-output (MIMO) communication system has received considerable attention because of its potential to improve the system performance and capacity. To achieve this advantage, turbo Bell Laboratories Layered Space–Time (BLAST) techniques are developed for flat fading MIMO systems [1]. In [2], turbo equalization is developed to combat the frequency selective channels. But it has a huge increase in complexity for the large number of receive antennas and long delay spreads due to the matrix inversion. Thus, orthogonal frequency division multiplexing (OFDM) techniques would be more attractive for wideband signals, which can transfer frequency selective channels in time domain to flat fading channels in frequency ∗ Corresponding author. Tel.: +86 021 34204587.
E-mail addresses: [email protected] (W. Lin), [email protected] (C. He). 1434-8411/$ - see front matter 䉷 2007 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2007.02.002
domain. In order to further reduce the complexity of the MMSE detector, the soft-in soft-out (SISO) detector is simply a parallel interference cancellation (PIC)–maximum ratio combining (MRC) operation in this letter. After channel decoding, the log likelihood ratios (LLRs) are multiplied by a constant factor to achieve a performance gain. Simulation results show that our scheme can substantially improve system performance and converge to the matched filter bound (MFB).
2. System model The MIMO–OFDM system is equipped with Nt transmit antennas and Nr receive antennas. After cyclic prefix removal and fast Fourier transform (FFT) demodulation, the received vector at the kth subcarrier can be expressed as yk = Hk xk + nk ,
(1)
W. Lin, C. He / Int. J. Electron. Commun. (AEÜ) 62 (2008) 68 – 71
where Hk is an Nr × Nt channel matrix, in which the (i, j )th element, hk (i, j ), is the fading coefficient between the jth transmit antenna and the ith receive antenna. xk = [xk,1 , xk,2 , . . . , xk,Nt ]T is the Nt × 1 transmitted symbol vector; nk is the zero mean complex Gaussian noise with variance 2 per complex dimension.
69
x
+
+ Channel Decoder
Interleaver
DeInterleaver
+
+
FFT
CP Removal
FFT
CP Removal
PICMRC
SISO Decoder
3. Low complexity iterative detection and decoding
Fig. 1. MIMO–OFDM iterative receiver.
Fig. 1 shows the proposed PIC–MRC based iterative receiver. At each iteration, the SISO detector performs PIC and MRC, as H zk,n = hk,n (yk − Hk x¯ k + x¯k,n hk,n ),
(2)
where n denotes the transmit antenna index and hk,n is the nth column of Hk . x¯ k = [x¯k,1 , x¯k,2 , . . . , x¯k,Nt ]T is the mean value of transmitted symbol vector. With the a priori information fed back from the channel decoder, it is calculated as [3] x¯k,n = E[xk,n ] = (d)P (xk,n = (d)), (3) d∈S
where P (xk,n =(d)) is the function of a priori information La (dk,n (i)), i = 1, 2, . . . , Mc , Mc is the number of bits per constellation symbol. d is an Mc × 1 vector of data bits with its entity dk,n (i) and (d) is a constellation symbol which is obtained using the mapping function. S is the set of possible values of d. Then we have [3] P (xk,n = (d)) =
Mc 1 i=1
2
· tanh
1 + (2dk,n (i) − 1)
1 La (dk,n (i)) . 2
(4)
To extract the extrinsic information of the transmitted bits, the PIC–MRC detector output is approximated as Gaussian. The mean and the variance are computed as [3]. Therefore, computational complexity is significantly reduced because matrix inversion in [1] is avoided. However, the MRC operation would result in large performance loss because of residual co-antennas interference, especially at the first iteration when no priori information is available. Thus we could obtain the LLRs of transmitted bits. Then they are fed to the channel decoder after deinterleaving. In order to improve the system performance, the LLRs of the channel decoder output are multiplied by a constant factor . It is optimized according to the extrinsic information transfer (EXIT) chart of the SISO decoder. The EXIT chart is an effective technique to examine the convergence property of iterative detection and decoding [4]. It models receiver components as devices mapping a sequence of a priori information La to a new sequence of extrinsic information Le . Using the input a priori
information, the channel decoder estimates the LLRs Le of encoded bits. Then they are multiplied by a constant factor in the proposed scheme. To optimize the constant factor , the mutual information between the extrinsic information Le and the encoded bits C is computed as [5] Ie (Le ; C) = 1 −
N 1 log2 [1 + exp(−c(n)Le (n))], N
(5)
n=1
where N is the number of encoded bits and and c(n) is the nth bit of the encoded bit sequence C. The constant factor is set to the minimum value that can almost result in the maximum mutual information Ie (Le ; C).
4. Simulation results In this section, we demonstrate the performance of the proposed iterative receiver. The system parameters are as follows. Eight transmit antennas and eight receive antennas are employed. The carrier frequency is 2.0 GHz and the bandwidth is 5 MHz. The system has 512 subcarriers with 64 cyclic prefix. Information bits are encoded using a rate- 21 recursive systematic convolution (RSC) code with a generation function (7, 5). Encoded bits are randomly interleaved and QPSK modulated. The channel model is the international telecommunicational union (ITU) “vehicular A” (VA) and mobile velocity is 30 km/h. Perfect channel state information is available at the receiver. We define the signal-tonoise ratio (SNR) per receive antenna and per subcarrier to be 10 log10 (Nt Es /2 ), where Es is the symbol energy.We first show the EXIT charts of the channel decoder under different in Fig. 2, where = 1.0 corresponds to the conventional channel decoder. It can be observed that = 2.5 is an approximately optimal solution. At the low input mutual information region, it maximizes the output mutual information Ie (Le ; C), which could reduce the SNR threshold requiring for the turbo cliff region. Further increase of would not improve the output mutual information at that region. However, the output mutual information Ie (Le ; C) is nearly the same at the high input mutual information region under different . If is set too small, more iterations are needed for the iterative receiver to converge, which would be computationally inefficient.
70
W. Lin, C. He / Int. J. Electron. Commun. (AEÜ) 62 (2008) 68 – 71 1 0.9 0.8 0.7
Ie(Ia)
0.6 0.5 0.4 PIC-MRC MMSE Channel Decoder α=1.0 Channel Decoder α=2.0 Channel Decoder α=2.5 Channel Decoder α=3.0
0.3 0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
Ia(Ie)
Fig. 2. Receiver EXIT charts, at SNR = 5 dB.
5. Conclusions
100
In this letter, we have proposed a novel low-complexity iterative receiver for coded MIMO–OFDM systems. The SISO detector is simply a PIC–MRC operation. After channel decoding, the LLRs of encoded bits are multiplied by a constant factor to achieve a performance gain. Simulation results show that the proposed iterative receiver can obtain significant performance gain and converge to the MFB with low computational complexity at high SNRs.
10-1
BER
10-2 10-3
10
The matched filter bound (MFB) is also presented as a lower bound of BER of the iterative receiver. For the conventional PIC–MRC detector, an error floor can be observed. The BER performance of the proposed PIC–MRC detector is much better than that of the conventional one after two iterations and converges to the MFB at high SNRs. Five iterations is needed for the MMSE [1] detector to converge and then the simulation result is also shown in Fig. 3. Comparing the propose PIC–MRC detector with the MMSE detector at the fifth iteration, the performance loss is only 0.5 dB at BER of 10−4 . But our scheme is much simpler than the MMSE [1] detector since the matrix inversion is avoided. Though the constant factor is optimized under the VA channel, we find that = 2.5 is also effective for other channels, such as “vehicular A” (VB), “pedestrian A” (PA) and “pedestrian B” (PB). We don’t give the simulation results due to the page limit.
Iteration=1 Iteration=2 Iteration=3 Iteration=4 Iteration=5 Iteration=6 MMSE [1] MFB
-4
10-5 10-6 2
3
Acknowledgements 4
5
6
7
SNR(dB)
Fig. 3. BER performance comparison of iterative receiver for 8×8 MIMO–OFDM systems (VA).
If → ∞, it reduces the SISO decoder to a hard-decision decoder, resulting in performance loss. The EXIT charts of the PIC–MRC detector and the MMSE detector at SNR = 5 dB are also given in Fig. 2. For the MMSE detector, the mutual information input to the channel decoder is already high enough at the first iteration. At that region, the LLRs multiplication by a constant factor would not improve mutual information of channel decoder output. Thus no optimization of is needed for the MMSE detector. However, for the PIC–MRC detector, the mutual information input to the channel decoder is still low at the first iteration. Thus our scheme would improve the system performance of the PIC–MRC detector. The bit error rate (BER) performance of the conventional PIC–MRC detector (=1.0, dashed line) is compared with that of the proposed one ( = 2.5, solid line) in Fig. 3. Six iterations are implemented in both schemes.
This research was supported by the Science and Technology Committee of Shanghai Municipality (under Grant nos. 06DZ15013 and 03DZ15010) and Shanghai Research Center for Wireless Communications.
References [1] Sellathurai M, Haykin S. Turbo-blast for wireless communications: theory and experiments. IEEE Trans Signal Process 2002;50:2538–46. [2] Abe T, Matsumoto T. Space–time turbo equalization in frequency selective mimo channels. IEEE Trans Vehicular Technol 2003;52:469–75. [3] Tuchler M, Singer AC, Koetter R. Minimum mean squared error equalization using a prior information. IEEE Trans Signal Process 2002;50:673–83. [4] Brink ST. Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Trans Commun 2001;40:1727–37. [5] Tuchler M, Hagenauer J. Exit charts of irregular codes, Conference on Information Sciences and Systems, 2002.
W. Lin, C. He / Int. J. Electron. Commun. (AEÜ) 62 (2008) 68 – 71
Wenfeng Lin was born in Quanzhou, China, 1978. He received his M.S. degree in Circuit and System from XiDian University, Xi’an, China, in 2004. He is currently pursuiting his Ph.D. degree in the Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai. His research interests include wireless communications and signal processing, primarily on the iterative algorithms and adaptive modulation and coding. Chen He graduated from Southeast University of China and obtained his B.E. degree and his M.E. degree in electronic engineering in 1982 and 1985, respectively, and then, he joined the Department of Electronic Engineering in Southeast University of China from 1985. He visited Tokushima University of Japan as a foreign researcher from October 1990 to September 1991 and obtained his Ph.D. degree from
71
Tokushima University of Japan in electronics system in 1994. He jointed the Department of Electronic Engineering in Shanghai Jiao Tong University of China from 1996. He visited the Communication Research Laboratory of Japan from December 1999 to December 2000 as a research fellow. Now, he is a professor of Shanghai Jiao Tong University of China. His current research interests are wireless communication systems and intelligent information processing.