- Email: [email protected]
Best antenna selection for coded SIMO–OFDM
ARTICLE IN PRESS Signal Processing 90 (2010) 391–394
Contents lists available at ScienceDirect
Signal Processing journal homepage: www.elsevier.com/locate/sigpro
Fast communication
Best antenna selection for coded SIMO–OFDM S. Nagaraj , J. Xiao San Diego State University, 5500 Campanile Drive, San Diego, CA 92182, USA
a r t i c l e in fo
abstract
Article history: Received 18 August 2008 Received in revised form 6 March 2009 Accepted 30 June 2009 Available online 4 July 2009
Multiple receive antennas with optimal combining have been known to improve error performance over fading multipath channels by providing spatial diversity. This benefit is obtained at the cost of greatly increased system complexity due to the need for multiple RF chains and signal combiners. Best antenna selection is a technique that can provide multiple antenna gains with only a single RF chain and no combiners. Best antenna selection is complicated by frequency selectivity in orthogonal frequency division multiplexing (OFDM) as the signal at any one antenna may not be the best at all subcarriers. In this paper, we propose a novel technique for best antenna selection in coded OFDM. To simplify the receiver, we assume a block fading model for the underlying frequency selective channel. The best antenna will then determined based on coding theorems known for block fading channels. Our simulations show significant improvement in coded OFDM performance over existing techniques. & 2009 Elsevier B.V. All rights reserved.
Keywords: Coded orthogonal frequency division multiplexing (COFDM) Single input multiple output (SIMO) Selection diversity (SD)
1. Introduction Orthogonal frequency division multiplexing (OFDM) is considered by many researchers as the most suitable modulation format for next generation wireless communication systems [1]. OFDM converts a frequency selective fading channel into several parallel flat fading subcarriers [2], removing the need for using complex equalizers. Bit interleaved coded modulation (BICM) [3] is a well-known coding technique for achieving diversity in OFDM systems. Performance of coded OFDM on fading channels can be further improved by employing multiple antennas at the transmitter or the receiver. With multiple antennas at the transmitter, space–time block codes [4] or space–time trellis codes [5] may be concatenated to BICM in order to achieve both space diversity and frequency diversity. With multiple antennas at the receiver, the signal at each antenna may be combined using maximum ratio
Corresponding author. Tel.: +1 619 594 7154; fax: +1 619 594 2654.
E-mail address: [email protected] (S. Nagaraj). 0165-1684/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2009.06.028
combining [6] techniques to achieve both space diversity and frequency diversity. Traditional combining techniques have a high receiver complexity since multiple RF chains are necessary at the receiver. Antenna selection diversity [7,8], on the other hand, can provide spatial diversity with only one RF chain at the price of a relatively small loss in performance. The receiver chooses the antenna with the highest instantaneous gain for reception. Antenna selection in OFDM [9] is complicated by frequency selectivity of the channel at each antenna. If the OFDM subcarriers experience independent fading, there may not be any advantage with antenna selection at all. With independent fading over a large number of subcarriers, the distribution of the instantaneous subcarrier gains will be near-identical for each antenna, resulting in minimal improvement with antenna selection. However, antenna selection may provide significant gains on indoor channels with correlated fading across the subcarriers. In this letter, we propose an antenna selection algorithm specifically for channels that offer small orders of diversity (indoor channels, for example). We use a block fading model for the underlying correlated frequency
ARTICLE IN PRESS 392
S. Nagaraj, J. Xiao / Signal Processing 90 (2010) 391–394
selective fading channel to simplify the algorithm greatly. We then use the rich available theory of coding for block fading channels to determine the best antenna for reception. Simulations show about 2–3 dB gain over existing antenna selection techniques when used on indoor channels. In Section 2, we present the system model of the proposed receive antenna selection COFDM system. In Section 3, we derive the criterion for best antenna selection in COFDM. In Section 4, we present simulation results supporting the claims made in this paper. We finally summarize our results in Section 5.
2. System model and receiver description Consider an N subcarrier OFDM system with N r receive antennas and a single transmit antenna on an L-tap (frequency diversity order is L) frequency selective, Rayleigh fading channel. The use of the cyclic prefix in OFDM allows each symbol to experience flat fading. Fig. 1 shows a diagram of the proposed OFDM transmitter. A rate r c ¼ kc =nc convolutional encoder C encodes a block of information bits and the resulting codebits of the codeword c are distributed over the N subcarriers using the channel allocator. The channel allocator is a rectangular interleaver with depth ¼ L. Groups of m interleaved code bits are modulated onto M-ary signal constellations X (where M ¼ 2m ). The signal set X has average energy S per symbol. The symbols are then input to the IFFT block of the OFDM transmitter. The coherence bandwidth measure allows us to divide the OFDM band into L independently fading blocks with N=L subcarriers in each. All subcarriers in the l-th block
c
Info Encoder Bits
then experience the same flat-fading channel gain g l;n at the nth receiver antenna, for l ¼ 1; . . . ; L and n ¼ 1; . . . ; N r . Note: Such a block fading approximation for OFDM system analysis is not new and has been used in [10] among others. Let xl;k be the k-th symbol (subcarrier) to be transmitted on the l-th block for k ¼ 1; . . . ; N=L. The symbol xl;k is received at the n-th receiver antenna as a faded and AWGN corrupted symbol yl;k;n ¼ g l;n xl;k þ nl;k;n , where nj;k;n are complex AWGN values with variance N 0 =2. The antenna selection algorithm determines the particular antenna n0 whose signal has to be processed further and connects that antenna to the decoder as shown in Fig. 2. b The receiver obtains the log-likelihoods ll;k;i of the i-th bit of the k-th symbol on the l-th block being 0 or 1 as
lbl;k;i ¼ min jyl;k g l;n0 xl;k j2 ,
where Xi;b is the set of signal points in X with the i-th bit of the label being equal to b (where b 2 f0; 1g). Finally, the receiver deinterleaves the code bits and applies the Viterbi algorithm to obtain the most likely transmitted codeword c˜ as c˜ ¼ arg min c
N=L X m X L X
lbl;k;i .
(2)
i¼1 k¼1 l¼1
3. Best antenna selection In this section, we first state a key property of error control codes on block fading channels—the singleton bound—and proceed to design our antenna selection algorithm based on that. The singleton bound is a very useful tool for analyzing
xl,k
Channel Allocator
(1)
xl;k 2Xi;b
Modulator
I F F T
Add CP
Fig. 1. Transmitter model for single transmit antenna coded OFDM.
Antenna 1
Switch
F Remove CP
Antenna Nr
F
Info
yl,k Decoder
Bits T
Fig. 2. Receiver model for multiple receive antenna coded OFDM; the switch connects only one of the N r antennas to the demodulator and decoder.
ARTICLE IN PRESS S. Nagaraj, J. Xiao / Signal Processing 90 (2010) 391–394
code performance on indoor channels with small orders of diversity.
393
2. Evaluate the smallest r-SNR at each antenna as P r-SNRmin;n ¼ rl¼1 jg l;n j2 3. Choose the antenna n0 with the largest r-SNRmin;n0
3.1. The singleton bound [11] Let L be the number of blocks in a block-fading channel. The maximum number of blocks r every error event can be spread over (equivalently, every pair of codewords can differ in) with a rate rc code is
r ¼ bLð1 rc Þc þ 1,
(3)
where bc is the greatest integer function. This result is valid for any coding approach (TCM, BICM, etc.) of any complexity. The total-SNR-maximizing criterion is valid only if rc 1=L (when r ¼ L). For higher rate codes typically used in practice, roL strictly. Maximizing the total SNR is not optimal for such scenarios. Since the diversity order achieved by the code is r (as a consequence of the singleton bound), two nearest-neighbor codewords c and c0 must differ in symbols over exactly r different blocks l1 ; . . . ; lr . The pairwise error probability (PEP) P 2 ðc; c0 Þ between c and c0 is ffi1 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pr 2 Es j¼1 wlj jg lj ;n0 j2 dmin 0 @ A P 2 ðc; c Þ ¼ Q (4) 2N 0 under maximum likelihood decoding and perfect channel knowledge at the receiver, where wlj is the number of symbols c and c0 differ in on the lj -th block and dmin is the minimum distance of the constellation X. Designing an antenna selection algorithm based on the above exact dependence of the PEP on jg lj ;n0 j for all pairs of codewords is very complicated. However, an extremely simple and intuitive figure of merit for code performance Pr 2 at moderate to high SNR is the sum j¼1 jg lj ;n0 j of the squared gains of the r blocks l1 ; . . . ; lr . We call this quantity the ‘‘r-SNR’’ of the considered set of r blocks and it will form the criterion for antenna selection in this paper. Note that with r ¼ L, the resulting r-SNR measure is simply the total SNR over all the L blocks and is identical to the total-SNR-maximizing criterion.
For many indoor channels, L is small. The maximum frequency diversity L achievable in OFDM is L ¼ Bs =Bc , where Bs is the system bandwidth (20 MHz in 802.11 g) and Bc is the channel coherence bandwidth (reciprocal of the channel r.m.s. delay spread). For the indoor model-C channel [12], the delay spread is 140 ns, resulting in a Bc of roughly 7 MHz and an equivalent L value of 3. An examination of the indoor wireless channel models in [12] shows that diversity orders L ¼ 224 are very common on indoor channels. For such channels, our simulations show a significant improvement in performance with the proposed technique. 4. Simulation results We performed simulations for L ¼ 426 Rayleigh fading channels and 256-subcarrier OFDM. These L values correspond to indoor channel models from [12]. We considered r c ¼ 12 convolutional codes with constraint length 7 and employed soft decision Viterbi decoding. Each OFDM symbol was encoded and decoded separately. We used 16-QAM signals in our simulations. Lastly, we assumed perfect channel knowledge at the receiver in our simulations. We compared the performance of the proposed r-SNR based antenna selection scheme with those of existing schemes like total-SNR based selection and instantaneous capacity based selection (suggested in [9]). Simulations were conducted for Nr ¼ 2 and 4 receivers and channels with L ¼ 4 and 6 independently fading blocks. Some results are shown in Figs. 3–6. In all the considered cases, the proposed scheme outperformed the existing alternatives by about 2–3 dB. Capacity maximizing selection is more suitable at the transmitting side rather than the receiving side as it requires power and bit adaptation also. The performance improvement with the proposed scheme 10−1 Capacity maximizing Total SNR maximizing Proposed
3.2. Antenna selection algorithm
1. Arrange the block gains g l;n at each antenna in the increasing order, i.e., jg 1;n j jg 2;n j jg L;n j.
10−2 Pb
There are L!=r!ðL rÞ! possible combinations of r blocks from L available blocks and as many r-SNR values. We will assume that the average codeword error performance is dominated by the smallest r-SNR measure (corresponding to the highest PEP) at moderate to high SNR. Approximating the code average error probability with the error probability of the most likely error event is a common tool in code analysis. The problem now reduces to selecting the antenna that maximizes the smallest r-SNR among all combinations of r blocks from L available blocks. The best antenna can be selected based on the following very simple algorithm:
10−3
10−4 5
10 SNR (dB)
15
Fig. 3. Comparison of antenna selection algorithms for N r ¼ 2 antennas on L ¼ 4 block fading channels.
ARTICLE IN PRESS 394
S. Nagaraj, J. Xiao / Signal Processing 90 (2010) 391–394
increased when the number of antennas was increased from 2 to 4. At the same time, performance improvement decreased when the channel order was increased from L ¼ 4 to 6 as expected. As the number of independently fading blocks increases, there is a smaller chance that any one antenna will be significantly better than the others. The performance with every antenna (and consequently with every selection algorithm) will achieve the same average performance on a Rayleigh fading channel asymptotically with increasing L. However, we can expect reasonable gains on most indoor channels where the available frequency diversity is limited as Figs. 3–6 show.
10−1 Capacity maximizing Total SNR maximizing Proposed
Pb
10−2
10−3
10−4
5. Conclusions
10−5 5
10 SNR (dB)
15
Fig. 4. Comparison of antenna selection algorithms for N r ¼ 2 antennas on L ¼ 6 block fading channels.
10−1 Capacity maximizing Total SNR maximizing Proposed
Pb
10−2
10−3
In this letter, we have proposed a novel way of identifying the best antenna for reception in SIMO–COFDM. Simulation results showed 2–3 dB improvement over existing techniques. We feel that this improvement is because the existing techniques such as SNR-maximizing or capacity-maximizing solutions are independent of the specific encoder C that is used. That would be optimal on channels with large diversity orders when the code performance on each OFDM frame approaches the average performance on a Rayleigh fading channel. However, on channels that offer small diversity orders, these approaches are suboptimal. The antenna selection algorithm we proposed is simple, yet, effective on channels that offer small orders of diversity. By limiting the SNR computation to only r (out of L) blocks, our analysis gives a more accurate estimate of the code performance than the total SNR. References
10−4 5
10 SNR (dB)
15
Fig. 5. Comparison of antenna selection algorithms for N r ¼ 4 antennas on L ¼ 4 block fading channels.
10−1 Capacity maximizing Total SNR maximizing Proposed
Pb
10−2
10−3
10−4
10−5 5
10 SNR (dB)
15
Fig. 6. Comparison of antenna selection algorithms for N r ¼ 4 antennas on L ¼ 6 block fading channels.
[1] R. Nee, R. Prasad, OFDM for Wireless Multimedia Communications, first ed., Artech House, 2000. [2] A. Kaye, D. George, Transmission of multiplexed PAM signals over multiple channel and diversity systems, IEEE Trans. Commun. Technol. (October 1970) 520–525. [3] G. Caire, G. Taricco, E. Biglieri, Bit-interleaved coded modulation, IEEE Trans. Inf. Theory (May 1998). [4] S. Alamouti, A simple transmit diversity technique for wireless communication, IEEE J. Sel. Areas Commun. (October 1998) 1451–1458. [5] V. Tarokh, N. Seshadri, A. Calderbank, Space time codes for high data rate wireless communication: performance criterion and code construction, IEEE Trans. Inf. Theory (March 1998) 744–765. [6] H. Hui, The performance of the maximum ratio combining method in correlated Rician fading channels for antenna diversity signal combining, IEEE Trans. Antennas Propag. (March 2005) 958–964. [7] A. Gorokhov, D. Gore, A. Paulraj, Performance bounds for antenna selection in MIMO systems, in: Proceedings of the IEEE International Conference on Communication, May 2003, pp. 3021–3025. [8] J. Li, M. Lin, A transmit antenna selection diversity scheme for wireless communications, in: Proceedings of the IEEE International Conference on Wireless Communications and Applied Electromagnetics, April 2004, pp. 490–494. [9] H. Zhang, A. Molisch, J. Zhang, Applying antenna selection in WLANs for achieving broadband multimedia communication, IEEE Trans. Broadcast. (December 2006) 475–482. [10] G. Fabregas, G. Caire, Coded modulation in the block fading channel: coding theorems and code construction, IEEE Trans. Inf. Theory (January 2006) 91–114. [11] R. Knopp, P. Humblet, On coding for block fading channels, IEEE Trans. Inf. Theory (January 2000) 189–205. [12] T. Rao, A. Giulietti, A performance study of the 802.11 g WLAN OFDM system, in: Proceedings of the EUROCON International Conference on Computer as a Tool, November 2005, pp. 21–24.
Contents lists available at ScienceDirect
Signal Processing journal homepage: www.elsevier.com/locate/sigpro
Fast communication
Best antenna selection for coded SIMO–OFDM S. Nagaraj , J. Xiao San Diego State University, 5500 Campanile Drive, San Diego, CA 92182, USA
a r t i c l e in fo
abstract
Article history: Received 18 August 2008 Received in revised form 6 March 2009 Accepted 30 June 2009 Available online 4 July 2009
Multiple receive antennas with optimal combining have been known to improve error performance over fading multipath channels by providing spatial diversity. This benefit is obtained at the cost of greatly increased system complexity due to the need for multiple RF chains and signal combiners. Best antenna selection is a technique that can provide multiple antenna gains with only a single RF chain and no combiners. Best antenna selection is complicated by frequency selectivity in orthogonal frequency division multiplexing (OFDM) as the signal at any one antenna may not be the best at all subcarriers. In this paper, we propose a novel technique for best antenna selection in coded OFDM. To simplify the receiver, we assume a block fading model for the underlying frequency selective channel. The best antenna will then determined based on coding theorems known for block fading channels. Our simulations show significant improvement in coded OFDM performance over existing techniques. & 2009 Elsevier B.V. All rights reserved.
Keywords: Coded orthogonal frequency division multiplexing (COFDM) Single input multiple output (SIMO) Selection diversity (SD)
1. Introduction Orthogonal frequency division multiplexing (OFDM) is considered by many researchers as the most suitable modulation format for next generation wireless communication systems [1]. OFDM converts a frequency selective fading channel into several parallel flat fading subcarriers [2], removing the need for using complex equalizers. Bit interleaved coded modulation (BICM) [3] is a well-known coding technique for achieving diversity in OFDM systems. Performance of coded OFDM on fading channels can be further improved by employing multiple antennas at the transmitter or the receiver. With multiple antennas at the transmitter, space–time block codes [4] or space–time trellis codes [5] may be concatenated to BICM in order to achieve both space diversity and frequency diversity. With multiple antennas at the receiver, the signal at each antenna may be combined using maximum ratio
Corresponding author. Tel.: +1 619 594 7154; fax: +1 619 594 2654.
E-mail address: [email protected] (S. Nagaraj). 0165-1684/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2009.06.028
combining [6] techniques to achieve both space diversity and frequency diversity. Traditional combining techniques have a high receiver complexity since multiple RF chains are necessary at the receiver. Antenna selection diversity [7,8], on the other hand, can provide spatial diversity with only one RF chain at the price of a relatively small loss in performance. The receiver chooses the antenna with the highest instantaneous gain for reception. Antenna selection in OFDM [9] is complicated by frequency selectivity of the channel at each antenna. If the OFDM subcarriers experience independent fading, there may not be any advantage with antenna selection at all. With independent fading over a large number of subcarriers, the distribution of the instantaneous subcarrier gains will be near-identical for each antenna, resulting in minimal improvement with antenna selection. However, antenna selection may provide significant gains on indoor channels with correlated fading across the subcarriers. In this letter, we propose an antenna selection algorithm specifically for channels that offer small orders of diversity (indoor channels, for example). We use a block fading model for the underlying correlated frequency
ARTICLE IN PRESS 392
S. Nagaraj, J. Xiao / Signal Processing 90 (2010) 391–394
selective fading channel to simplify the algorithm greatly. We then use the rich available theory of coding for block fading channels to determine the best antenna for reception. Simulations show about 2–3 dB gain over existing antenna selection techniques when used on indoor channels. In Section 2, we present the system model of the proposed receive antenna selection COFDM system. In Section 3, we derive the criterion for best antenna selection in COFDM. In Section 4, we present simulation results supporting the claims made in this paper. We finally summarize our results in Section 5.
2. System model and receiver description Consider an N subcarrier OFDM system with N r receive antennas and a single transmit antenna on an L-tap (frequency diversity order is L) frequency selective, Rayleigh fading channel. The use of the cyclic prefix in OFDM allows each symbol to experience flat fading. Fig. 1 shows a diagram of the proposed OFDM transmitter. A rate r c ¼ kc =nc convolutional encoder C encodes a block of information bits and the resulting codebits of the codeword c are distributed over the N subcarriers using the channel allocator. The channel allocator is a rectangular interleaver with depth ¼ L. Groups of m interleaved code bits are modulated onto M-ary signal constellations X (where M ¼ 2m ). The signal set X has average energy S per symbol. The symbols are then input to the IFFT block of the OFDM transmitter. The coherence bandwidth measure allows us to divide the OFDM band into L independently fading blocks with N=L subcarriers in each. All subcarriers in the l-th block
c
Info Encoder Bits
then experience the same flat-fading channel gain g l;n at the nth receiver antenna, for l ¼ 1; . . . ; L and n ¼ 1; . . . ; N r . Note: Such a block fading approximation for OFDM system analysis is not new and has been used in [10] among others. Let xl;k be the k-th symbol (subcarrier) to be transmitted on the l-th block for k ¼ 1; . . . ; N=L. The symbol xl;k is received at the n-th receiver antenna as a faded and AWGN corrupted symbol yl;k;n ¼ g l;n xl;k þ nl;k;n , where nj;k;n are complex AWGN values with variance N 0 =2. The antenna selection algorithm determines the particular antenna n0 whose signal has to be processed further and connects that antenna to the decoder as shown in Fig. 2. b The receiver obtains the log-likelihoods ll;k;i of the i-th bit of the k-th symbol on the l-th block being 0 or 1 as
lbl;k;i ¼ min jyl;k g l;n0 xl;k j2 ,
where Xi;b is the set of signal points in X with the i-th bit of the label being equal to b (where b 2 f0; 1g). Finally, the receiver deinterleaves the code bits and applies the Viterbi algorithm to obtain the most likely transmitted codeword c˜ as c˜ ¼ arg min c
N=L X m X L X
lbl;k;i .
(2)
i¼1 k¼1 l¼1
3. Best antenna selection In this section, we first state a key property of error control codes on block fading channels—the singleton bound—and proceed to design our antenna selection algorithm based on that. The singleton bound is a very useful tool for analyzing
xl,k
Channel Allocator
(1)
xl;k 2Xi;b
Modulator
I F F T
Add CP
Fig. 1. Transmitter model for single transmit antenna coded OFDM.
Antenna 1
Switch
F Remove CP
Antenna Nr
F
Info
yl,k Decoder
Bits T
Fig. 2. Receiver model for multiple receive antenna coded OFDM; the switch connects only one of the N r antennas to the demodulator and decoder.
ARTICLE IN PRESS S. Nagaraj, J. Xiao / Signal Processing 90 (2010) 391–394
code performance on indoor channels with small orders of diversity.
393
2. Evaluate the smallest r-SNR at each antenna as P r-SNRmin;n ¼ rl¼1 jg l;n j2 3. Choose the antenna n0 with the largest r-SNRmin;n0
3.1. The singleton bound [11] Let L be the number of blocks in a block-fading channel. The maximum number of blocks r every error event can be spread over (equivalently, every pair of codewords can differ in) with a rate rc code is
r ¼ bLð1 rc Þc þ 1,
(3)
where bc is the greatest integer function. This result is valid for any coding approach (TCM, BICM, etc.) of any complexity. The total-SNR-maximizing criterion is valid only if rc 1=L (when r ¼ L). For higher rate codes typically used in practice, roL strictly. Maximizing the total SNR is not optimal for such scenarios. Since the diversity order achieved by the code is r (as a consequence of the singleton bound), two nearest-neighbor codewords c and c0 must differ in symbols over exactly r different blocks l1 ; . . . ; lr . The pairwise error probability (PEP) P 2 ðc; c0 Þ between c and c0 is ffi1 0sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pr 2 Es j¼1 wlj jg lj ;n0 j2 dmin 0 @ A P 2 ðc; c Þ ¼ Q (4) 2N 0 under maximum likelihood decoding and perfect channel knowledge at the receiver, where wlj is the number of symbols c and c0 differ in on the lj -th block and dmin is the minimum distance of the constellation X. Designing an antenna selection algorithm based on the above exact dependence of the PEP on jg lj ;n0 j for all pairs of codewords is very complicated. However, an extremely simple and intuitive figure of merit for code performance Pr 2 at moderate to high SNR is the sum j¼1 jg lj ;n0 j of the squared gains of the r blocks l1 ; . . . ; lr . We call this quantity the ‘‘r-SNR’’ of the considered set of r blocks and it will form the criterion for antenna selection in this paper. Note that with r ¼ L, the resulting r-SNR measure is simply the total SNR over all the L blocks and is identical to the total-SNR-maximizing criterion.
For many indoor channels, L is small. The maximum frequency diversity L achievable in OFDM is L ¼ Bs =Bc , where Bs is the system bandwidth (20 MHz in 802.11 g) and Bc is the channel coherence bandwidth (reciprocal of the channel r.m.s. delay spread). For the indoor model-C channel [12], the delay spread is 140 ns, resulting in a Bc of roughly 7 MHz and an equivalent L value of 3. An examination of the indoor wireless channel models in [12] shows that diversity orders L ¼ 224 are very common on indoor channels. For such channels, our simulations show a significant improvement in performance with the proposed technique. 4. Simulation results We performed simulations for L ¼ 426 Rayleigh fading channels and 256-subcarrier OFDM. These L values correspond to indoor channel models from [12]. We considered r c ¼ 12 convolutional codes with constraint length 7 and employed soft decision Viterbi decoding. Each OFDM symbol was encoded and decoded separately. We used 16-QAM signals in our simulations. Lastly, we assumed perfect channel knowledge at the receiver in our simulations. We compared the performance of the proposed r-SNR based antenna selection scheme with those of existing schemes like total-SNR based selection and instantaneous capacity based selection (suggested in [9]). Simulations were conducted for Nr ¼ 2 and 4 receivers and channels with L ¼ 4 and 6 independently fading blocks. Some results are shown in Figs. 3–6. In all the considered cases, the proposed scheme outperformed the existing alternatives by about 2–3 dB. Capacity maximizing selection is more suitable at the transmitting side rather than the receiving side as it requires power and bit adaptation also. The performance improvement with the proposed scheme 10−1 Capacity maximizing Total SNR maximizing Proposed
3.2. Antenna selection algorithm
1. Arrange the block gains g l;n at each antenna in the increasing order, i.e., jg 1;n j jg 2;n j jg L;n j.
10−2 Pb
There are L!=r!ðL rÞ! possible combinations of r blocks from L available blocks and as many r-SNR values. We will assume that the average codeword error performance is dominated by the smallest r-SNR measure (corresponding to the highest PEP) at moderate to high SNR. Approximating the code average error probability with the error probability of the most likely error event is a common tool in code analysis. The problem now reduces to selecting the antenna that maximizes the smallest r-SNR among all combinations of r blocks from L available blocks. The best antenna can be selected based on the following very simple algorithm:
10−3
10−4 5
10 SNR (dB)
15
Fig. 3. Comparison of antenna selection algorithms for N r ¼ 2 antennas on L ¼ 4 block fading channels.
ARTICLE IN PRESS 394
S. Nagaraj, J. Xiao / Signal Processing 90 (2010) 391–394
increased when the number of antennas was increased from 2 to 4. At the same time, performance improvement decreased when the channel order was increased from L ¼ 4 to 6 as expected. As the number of independently fading blocks increases, there is a smaller chance that any one antenna will be significantly better than the others. The performance with every antenna (and consequently with every selection algorithm) will achieve the same average performance on a Rayleigh fading channel asymptotically with increasing L. However, we can expect reasonable gains on most indoor channels where the available frequency diversity is limited as Figs. 3–6 show.
10−1 Capacity maximizing Total SNR maximizing Proposed
Pb
10−2
10−3
10−4
5. Conclusions
10−5 5
10 SNR (dB)
15
Fig. 4. Comparison of antenna selection algorithms for N r ¼ 2 antennas on L ¼ 6 block fading channels.
10−1 Capacity maximizing Total SNR maximizing Proposed
Pb
10−2
10−3
In this letter, we have proposed a novel way of identifying the best antenna for reception in SIMO–COFDM. Simulation results showed 2–3 dB improvement over existing techniques. We feel that this improvement is because the existing techniques such as SNR-maximizing or capacity-maximizing solutions are independent of the specific encoder C that is used. That would be optimal on channels with large diversity orders when the code performance on each OFDM frame approaches the average performance on a Rayleigh fading channel. However, on channels that offer small diversity orders, these approaches are suboptimal. The antenna selection algorithm we proposed is simple, yet, effective on channels that offer small orders of diversity. By limiting the SNR computation to only r (out of L) blocks, our analysis gives a more accurate estimate of the code performance than the total SNR. References
10−4 5
10 SNR (dB)
15
Fig. 5. Comparison of antenna selection algorithms for N r ¼ 4 antennas on L ¼ 4 block fading channels.
10−1 Capacity maximizing Total SNR maximizing Proposed
Pb
10−2
10−3
10−4
10−5 5
10 SNR (dB)
15
Fig. 6. Comparison of antenna selection algorithms for N r ¼ 4 antennas on L ¼ 6 block fading channels.
[1] R. Nee, R. Prasad, OFDM for Wireless Multimedia Communications, first ed., Artech House, 2000. [2] A. Kaye, D. George, Transmission of multiplexed PAM signals over multiple channel and diversity systems, IEEE Trans. Commun. Technol. (October 1970) 520–525. [3] G. Caire, G. Taricco, E. Biglieri, Bit-interleaved coded modulation, IEEE Trans. Inf. Theory (May 1998). [4] S. Alamouti, A simple transmit diversity technique for wireless communication, IEEE J. Sel. Areas Commun. (October 1998) 1451–1458. [5] V. Tarokh, N. Seshadri, A. Calderbank, Space time codes for high data rate wireless communication: performance criterion and code construction, IEEE Trans. Inf. Theory (March 1998) 744–765. [6] H. Hui, The performance of the maximum ratio combining method in correlated Rician fading channels for antenna diversity signal combining, IEEE Trans. Antennas Propag. (March 2005) 958–964. [7] A. Gorokhov, D. Gore, A. Paulraj, Performance bounds for antenna selection in MIMO systems, in: Proceedings of the IEEE International Conference on Communication, May 2003, pp. 3021–3025. [8] J. Li, M. Lin, A transmit antenna selection diversity scheme for wireless communications, in: Proceedings of the IEEE International Conference on Wireless Communications and Applied Electromagnetics, April 2004, pp. 490–494. [9] H. Zhang, A. Molisch, J. Zhang, Applying antenna selection in WLANs for achieving broadband multimedia communication, IEEE Trans. Broadcast. (December 2006) 475–482. [10] G. Fabregas, G. Caire, Coded modulation in the block fading channel: coding theorems and code construction, IEEE Trans. Inf. Theory (January 2006) 91–114. [11] R. Knopp, P. Humblet, On coding for block fading channels, IEEE Trans. Inf. Theory (January 2000) 189–205. [12] T. Rao, A. Giulietti, A performance study of the 802.11 g WLAN OFDM system, in: Proceedings of the EUROCON International Conference on Computer as a Tool, November 2005, pp. 21–24.