WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 2011; 11:1226–1238 Published online 30 October 2009 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.881 SCLDGM coded modulation for MIMO systems with spatial multiplexing and space-time block codes Miguel Gonz ´ alez-L ´ opez 1 , Francisco J. V ´ azquez-Ara ´ ujo 1∗,† , Luis Castedo 1 and Javier Garcia-Frias 2 1 Department of Electronics and Systems, University of A Coru˜ na, 15071 A Coru˜ na, Spain 2 Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19711, U.S.A. ABSTRACT We analyze Multiple-Input Multiple-Output (MIMO) coded modulation systems where either Bit-Interleaved Coded Mod- ulation (BICM) with spatial multiplexing or concatenation of channel coding and Space-Time Block Codes (STBCs) is used at transmission, assuming iterative Turbo-like decoding at reception. We optimize Serially-Concatenated Low-Density Generator Matrix (SCLDGM) codes (a subclass of LDPC codes) for each system configuration, with the goal of assessing its ability to approach the capacity limits in either ergodic or quasi-static channels. Our focus is on three relevant STBCs: the Orthogonal Space-Time Block Codes (OSTBCs) for two transmit antennas (i.e., the Alamouti code), which enables optimum detection with low complexity; the Golden code, which provides a capacity increase with respect to the input constellation; and Linear Dispersion (LD) codes, which enable practical detection in asymmetrical antenna configurations (i.e., more transmit than receive antennas) for cases in which optimum detection is infeasible. We conclude that BICM without concatenation with STBCs is in general the best option, except for Alamouti-coded 2 × 1 and Golden-coded 2 × 2 MIMO systems. Copyright © 2009 John Wiley & Sons, Ltd. KEYWORDS LDGM codes; SCLDGM codes; STBC; linear dispersion codes; Alamouti; MIMO * Correspondence Francisco J. V´ azquez-Ara ´ ujo, Facultad de Inform´ atica, Campus de Elvi ˜ na, s/n, 15071 A Coru˜ na, Spain. E-mail: fjvazquez@udc.es 1. INTRODUCTION The use of multiple transmit and/or receive antennas, referred to as Multiple-Input Multiple-Output (MIMO) sys- tems, is one of the most promising transmission techniques for achieving the high data rates demanded by the future wireless communication systems. This assertion relies on the theoretical and experimental evidence that the capacity of a MIMO system is considerably higher than that of a conventional single antenna system [1]. Approaching the ultimate limits of MIMO channels (either ergodic or quasi-static) requires specific coding techniques that take into account both the spatial and tem- poral dimensions of the MIMO channel. These techniques are collectively known as Space-Time Coding (STC). Orthogonal Space-Time Block Codes (OSTBCs) [2] are one of the most widely used STC methods because they are easy to encode and decode. In addition, OSTBCs are capable of achieving the maximum transmit diversity provided by the MIMO channel. The basic idea of OSTBCs is the encoding of the transmitting symbols into a unitary matrix to spatially decouple their Maximum Likelihood (ML) detection. For the case of two transmit antennas (i.e., n T = 2) the OSTBC is known as the Alamouti code [3] and has been adopted by the recently approved IEEE 802.16e standard (WiMAX) for wireless local and metropolitan area networks [4,5], as well as in the current draft specification of the IEEE 802.11n next-generation wireless standard for Local Area Networks [6]. OSTBCs, however, need an outer channel code to approach the theoretical capacity limits. Indeed, although OSTBCs simplify detection and provide maximum diver- sity, little (or no) coding gain can be expected from them. Remarkable coding gains can be obtained if a capacity-approaching binary encoder, such as Turbo [7] or Low-Density Parity Check (LDPC) [8,9], is employed. In this work, we focus on a particular subclass of LDPC codes known as Serially-Concatenated Low-Density Gen- erator Matrix (SCLDGM) codes [10] whose performance is similar to that of general LDPC codes but with very 1226 Copyright © 2009 John Wiley & Sons, Ltd.