Asymptotic Coded BER Analysis for MIMO BICM-ID with Quantized Extrinsic LLR

In this paper, we derive a closed-form expression for the probability density/mass function (PDF/PMF) and the moment generating function (MGF) of the quantized detector soft output, i.e., extrinsic log-likelihood ratio (LLR), for multiple-input multiple-output (MIMO) bit-interleaved coded modulation with iterative decoding (BICM-ID) systems. The effect of either LLR clipping or LLR clipping with rounding, often applied in practical implementations, are considered. Using the derived expression, we analyze the asymptotic coded bit error rate (BER) for MIMO BICM-ID systems with the two quantization operations under a flat Rayleigh fading channel. The error rate degradation caused by quantizing the extrinsic LLR is then interpreted as an additional signal-to-noise ratio (SNR) loss. Rather than Monte Carlo simulations, this theoretical treatment provides a more convenient alternative to determining the clipping level and optimal word-length (the number of bits needed to represent signals) for LLR in a BICM-ID implementation. Finally, several other applications of this proposed theoretical analysis are also demonstrated.

[1]  James A. Ritcey,et al.  Design, analysis, and performance evaluation for BICM-ID with square QAM constellations in Rayleigh fading channels , 2001, IEEE J. Sel. Areas Commun..

[2]  Stefan H. Müller-Weinfurtner.  Coding approaches for multiple antenna transmission in fast fading and OFDM , 2002, IEEE Trans. Signal Process..

[3]  Leszek Szczecinski,et al.  Distribution of max-log metrics for QAM-based BICM in fading channels , 2009, IEEE Transactions on Communications.

[4]  Helmut Bölcskei,et al.  Soft-output sphere decoding: algorithms and VLSI implementation , 2008, IEEE Journal on Selected Areas in Communications.

[5]  Leszek Szczecinski,et al.  Distribution of L-values in gray-mapped M2-QAM: closed-form approximations and applications , 2009, IEEE Transactions on Communications.

[6]  Gerald Matz,et al.  Quantization for soft-output demodulators in bit-interleaved coded modulation systems , 2009, 2009 IEEE International Symposium on Information Theory.

[7]  Lutz H.-J. Lampe,et al.  An analytical approach for performance evaluation of BICM transmission over Nakagami-m fading channels , 2010, IEEE Transactions on Communications.

[8]  Rainer Leupers,et al.  A Scalable VLSI Architecture for Soft-Input Soft-Output Single Tree-Search Sphere Decoding , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Stephan ten Brink,et al.  Achieving near-capacity on a multiple-antenna channel , 2003, IEEE Trans. Commun..

[10]  Helmut Bölcskei,et al.  Soft–Input Soft–Output Single Tree-Search Sphere Decoding , 2009, IEEE Transactions on Information Theory.

[11]  Gerald Matz,et al.  Log-likelihood ratio clipping in MIMO-BICM systems: Information geometric analysis and impact on system capacity , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  Wolfgang Rave.  Quantization of Log-Likelihood Ratios to Maximize Mutual Information , 2009, IEEE Signal Processing Letters.

[13]  Gerald Matz,et al.  Performance Assessment of MIMO-BICM Demodulators based on System Capacity , 2009, ArXiv.

[14]  Giuseppe Caire,et al.  Error probability analysis of bit-interleaved coded modulation , 2006, IEEE Transactions on Information Theory.

[15]  Leszek Szczecinski,et al.  On the distribution of extrinsic L-values in gray-mapped 16-QAM , 2007, IWCMC.

[16]  M. Juntti,et al.  The effect of LLR clipping to the complexity of list sphere detector algorithms , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[17]  Giuseppe Caire,et al.  Bit-Interleaved Coded Modulation , 2008, Found. Trends Commun. Inf. Theory.

[18]  Heinrich Meyr,et al.  Digital communication receivers - synchronization, channel estimation, and signal processing , 1997, Wiley series in telecommunications and signal processing.

[19]  Ephraim Zehavi,et al.  8-PSK trellis codes for a Rayleigh channel , 1992, IEEE Trans. Commun..

[20]  Heinrich Meyr,et al.  A Systematic Framework for Iterative Maximum Likelihood Receiver Design , 2010, IEEE Transactions on Communications.

[21]  Gerd Ascheid,et al.  Tight Approximation of the Bit Error Rate for BICM(-ID) Assuming Imperfect CSI , 2008, IEEE Transactions on Wireless Communications.

[22]  X. Li.  Bit-interleaved coded modulation with iterative decoding using soft feedback , 1998 .

[23]  M. Simon.  Probability distributions involving Gaussian random variables : a handbook for engineers and scientists , 2002 .