Reduced-Dimension Multiuser Detection

We present a new framework for reduced-dimension multiuser detection (RD-MUD) that trades off complexity for bit-error-rate (BER) performance. This approach can significantly reduce the number of matched filter branches required by classic multiuser detection designs. We show that the RD-MUD can perform similarly to the linear MUD detector when M is sufficiently large relative to N and K, where N and K are the number of total and active users, respectively. We also study the inherent RD-MUD tradeoff between complexity (the number of correlating signals) and BER performance. This leads to a new notion of approximate sufficient statistics, whereby sufficient statistics are approximated to reduce complexity at the expense of some BER performance loss.1

[1]  A. Calderbank,et al.  Z4‐Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line‐Sets , 1997 .

[2]  Robert D. Nowak,et al.  Signal Reconstruction From Noisy Random Projections , 2006, IEEE Transactions on Information Theory.

[3]  Yonina C. Eldar,et al.  Coherence-Based Performance Guarantees for Estimating a Sparse Vector Under Random Noise , 2009, IEEE Transactions on Signal Processing.

[4]  Robert W. Heath,et al.  Finite-step algorithms for constructing optimal CDMA signature sequences , 2004, IEEE Transactions on Information Theory.

[5]  Waheed U. Bajwa,et al.  Multiuser detection in asynchronous on-off random access channels using lasso , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[6]  Sundeep Rangan,et al.  On-Off Random Access Channels: A Compressed Sensing Framework , 2009, ArXiv.

[7]  Sergio Verdú,et al.  Linear multiuser detectors for synchronous code-division multiple-access channels , 1989, IEEE Trans. Inf. Theory.

[8]  Antonia Maria Tulino,et al.  Random Matrix Theory and Wireless Communications , 2004, Found. Trends Commun. Inf. Theory.

[9]  Sergio Verdú,et al.  Near-far resistance of multiuser detectors in asynchronous channels , 1990, IEEE Trans. Commun..

[10]  Roy D. Yates,et al.  Iterative construction of optimum signature sequence sets in synchronous CDMA systems , 2001, IEEE Trans. Inf. Theory.

[11]  Kwang-Cheng Chen,et al.  Identification of active users in synchronous CDMA multiuser detection , 1998, IEEE J. Sel. Areas Commun..

[12]  Behnaam Aazhang,et al.  Multistage detection in asynchronous code-division multiple-access communications , 1990, IEEE Trans. Commun..

[13]  Robert D. Nowak,et al.  Compressive Sampling for Signal Detection , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[14]  Yonina C. Eldar,et al.  Xampling--Part I: Practice , 2009, ArXiv.

[15]  Shlomo Shamai,et al.  Spectral Efficiency of CDMA with Random Spreading , 1999, IEEE Trans. Inf. Theory.

[16]  Robert W. Heath,et al.  On quasi-orthogonal signatures for CDMA systems , 2006, IEEE Transactions on Information Theory.

[17]  Giuseppe Ricci,et al.  Blind multiuser detection of L out of K active users of an N user synchronous CDMA system , 1999, 1999 IEEE 49th Vehicular Technology Conference (Cat. No.99CH36363).

[18]  S. Moshavi,et al.  Multi-user detection for DS-CDMA communications , 1996, IEEE Commun. Mag..

[19]  Sergio Verdú,et al.  Minimum probability of error for asynchronous Gaussian multiple-access channels , 1986, IEEE Trans. Inf. Theory.

[20]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[21]  Craig K. Rushforth,et al.  A Family of Suboptimum Detectors for Coherent Multiuser Communications , 1990, IEEE J. Sel. Areas Commun..

[22]  Georgios B. Giannakis,et al.  Exploiting Sparse User Activity in Multiuser Detection , 2011 .

[23]  S. Verdú,et al.  Asymptotic efficiency of linear multiuser detectors , 1986, 1986 25th IEEE Conference on Decision and Control.

[24]  Abbas Jamalipour,et al.  Wireless communications , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[25]  N. Fisher,et al.  Probability Inequalities for Sums of Bounded Random Variables , 1994 .

[26]  Michele Morelli,et al.  Timing and frequency synchronization for the uplink of an OFDMA system , 2004, IEEE Transactions on Communications.

[27]  H. Vincent Poor,et al.  Transmitter Waveform and Widely Linear Receiver Design: Noncooperative Games for Wireless Multiple-Access Networks , 2010, IEEE Transactions on Information Theory.

[28]  Sergio Verdu,et al.  Multiuser Detection , 1998 .

[29]  Jian Yang,et al.  On joint transmitter and receiver optimization for multiple-input-multiple-output (MIMO) transmission systems , 1994, IEEE Trans. Commun..

[30]  Marco Lops,et al.  Multiuser Detection in a Dynamic Environment– Part I: User Identification and Data Detection , 2007, IEEE Transactions on Information Theory.

[31]  Paul D. Alexander,et al.  Random Sequence Multisets for Synchronous Code-Division Multiple-Access Channels , 1998, IEEE Trans. Inf. Theory.

[32]  Marco Lops,et al.  Multiuser Detection in a Dynamic Environment— Part II: Joint User Identification and Parameter Estimation , 2009, IEEE Transactions on Information Theory.

[33]  Zoran Zvonar,et al.  Multiuser detection for CDMA systems , 1995, IEEE Wirel. Commun..

[34]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[35]  Yonina C. Eldar,et al.  Time-Delay Estimation From Low-Rate Samples: A Union of Subspaces Approach , 2009, IEEE Transactions on Signal Processing.

[36]  A. Robert Calderbank,et al.  Asynchronous code-division random access using convex optimization , 2011, Phys. Commun..

[37]  O. Christensen An introduction to frames and Riesz bases , 2002 .

[38]  Chih-Chun Wang,et al.  Multiuser Detection of Sparsely Spread CDMA , 2008, IEEE Journal on Selected Areas in Communications.

[39]  Andrew J. Viterbi,et al.  Very Low Rate Convolutional Codes for Maximum Theoretical Performance of Spread-Spectrum Multiple-Access Channels , 1990, IEEE J. Sel. Areas Commun..

[40]  Bhaskar D. Rao,et al.  Support Recovery of Sparse Signals , 2010, ArXiv.

[41]  Venkat Anantharam,et al.  Optimal sequences and sum capacity of synchronous CDMA systems , 1999, IEEE Trans. Inf. Theory.

[42]  Yonina C. Eldar Uncertainty Relations for Shift-Invariant Analog Signals , 2008, IEEE Transactions on Information Theory.

[43]  A. Viterbi CDMA: Principles of Spread Spectrum Communication , 1995 .

[44]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[45]  Z. Šidák Rectangular Confidence Regions for the Means of Multivariate Normal Distributions , 1967 .

[46]  Venkat Anantharam,et al.  Optimal sequences for CDMA under colored noise: A Schur-saddle function property , 2002, IEEE Trans. Inf. Theory.

[47]  Yonina C. Eldar,et al.  Block-Sparse Signals: Uncertainty Relations and Efficient Recovery , 2009, IEEE Transactions on Signal Processing.

[48]  Christian Schlegel,et al.  Coordinated Multiuser Communications , 2006 .

[49]  Yonina C. Eldar,et al.  Robust Recovery of Signals From a Structured Union of Subspaces , 2008, IEEE Transactions on Information Theory.

[50]  A. Robert Calderbank,et al.  Finding needles in compressed haystacks , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[51]  Gongguo Tang,et al.  Performance Analysis for Sparse Support Recovery , 2009, IEEE Transactions on Information Theory.

[52]  Mahesh K. Varanasi,et al.  Group detection for synchronous Gaussian code-division multiple-access channels , 1995, IEEE Trans. Inf. Theory.

[53]  Yonina C. Eldar Compressed Sensing of Analog Signals in Shift-Invariant Spaces , 2008, IEEE Transactions on Signal Processing.

[54]  Yonina C. Eldar,et al.  From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals , 2009, IEEE Journal of Selected Topics in Signal Processing.

[55]  Tommy Guess CDMA with power control and sequence design: the capacity region with and without multidimensional signaling , 2004, IEEE Transactions on Information Theory.

[56]  S. Verdú Near/Far Resistant Receivers for DS/SSMA Communications , 1990 .

[57]  Alexandra Duel-Hallen,et al.  Decorrelating decision-feedback multiuser detector for synchronous code-division multiple-access channel , 1993, IEEE Trans. Commun..

[58]  J. G. Andrews,et al.  Interference cancellation for cellular systems: a contemporary overview , 2005, IEEE Wireless Communications.

[59]  H. Vincent Poor,et al.  Online activity detection in a multiuser environment using the matrix CUSUM Algorithm , 2002, IEEE Trans. Inf. Theory.

[60]  Richard G. Baraniuk,et al.  Signal Processing With Compressive Measurements , 2010, IEEE Journal of Selected Topics in Signal Processing.

[61]  Sundeep Rangan,et al.  Necessary and Sufficient Conditions for Sparsity Pattern Recovery , 2008, IEEE Transactions on Information Theory.

[62]  Lie Wang,et al.  Stable Recovery of Sparse Signals and an Oracle Inequality , 2010, IEEE Transactions on Information Theory.

[63]  Marco Lops,et al.  Low-complexity receivers for multiuser detection with an unknown number of active users , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[64]  J. Haupt,et al.  A Generalized Restricted Isometry Property , 2008 .

[65]  Mahesh K. Varanasi,et al.  Decision Feedback Multiuser Detection: A Systematic Approach , 1999, IEEE Trans. Inf. Theory.

[66]  Michael L. Honig,et al.  Advances in Multiuser Detection , 2009 .

[67]  Anthony Ephremides,et al.  Optimal sequences and sum capacity of symbol asynchronous CDMA systems , 2005, IEEE Transactions on Information Theory.

[68]  Yonina C. Eldar,et al.  Structured Compressed Sensing: From Theory to Applications , 2011, IEEE Transactions on Signal Processing.

[69]  H. Vincent Poor,et al.  Probability of error in MMSE multiuser detection , 1997, IEEE Trans. Inf. Theory.

[70]  Pierre Vandergheynst,et al.  Average Case Analysis of Multichannel Thresholding , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[71]  Per Ödling,et al.  A time and frequency synchronization scheme for multiuser OFDM , 1999, IEEE J. Sel. Areas Commun..

[72]  Yonina C. Eldar,et al.  Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals , 2007, IEEE Transactions on Signal Processing.

[73]  Marvin K. Simon,et al.  Spread Spectrum Communications Handbook , 1994 .

[74]  A. Robert Calderbank,et al.  Why Gabor frames? Two fundamental measures of coherence and their role in model selection , 2010, Journal of Communications and Networks.

[75]  Sergio Verdú,et al.  Computational complexity of optimum multiuser detection , 1989, Algorithmica.

[76]  Yonina C. Eldar,et al.  Xampling: Signal Acquisition and Processing in Union of Subspaces , 2009, IEEE Transactions on Signal Processing.

[77]  Richard G. Baraniuk,et al.  Detection and estimation with compressive measurements , 2006 .

[78]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[79]  Ezio Biglieri,et al.  Large-System Analysis of Multiuser Detection With an Unknown Number of Users: A High-SNR Approach , 2010, IEEE Transactions on Information Theory.

[80]  Hongya Ge,et al.  Spreading Codes Enabling Warp Converging Wiener Filters for Multiuser Detection in CDMA Systems , 2008, 2008 IEEE International Conference on Communications.

[81]  W. Hoeffding Probability Inequalities for sums of Bounded Random Variables , 1963 .

[82]  G. Reeves,et al.  A note on optimal support recovery in compressed sensing , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[83]  Mike E. Davies,et al.  Iterative Hard Thresholding for Compressed Sensing , 2008, ArXiv.

[84]  Yonina C. Eldar,et al.  Noise Folding in Compressed Sensing , 2011, IEEE Signal Processing Letters.

[85]  Marco Lops,et al.  Multiuser Detection in a Dynamic Environment: Joint User Identification and Parameter Estimation , 2007, 2007 IEEE International Symposium on Information Theory.