Towards Fully Optimized BICM Transceivers

Bit-interleaved coded modulation (BICM) transceivers often use equally spaced constellations and a random interleaver. In this paper, we propose a new BICM design, which considers hierarchical (nonequally spaced) constellations, a bit-level multiplexer, and multiple interleavers. It is shown that this new scheme increases the degrees of freedom that can be exploited in order to improve its performance. Analytical bounds on the bit error rate (BER) of the system in terms of the constellation parameters and the multiplexing rules are developed for the additive white Gaussian Noise (AWGN) and Nakagami-$m$ fading channels. These bounds are then used to design the BICM transceiver. Numerical results show that, compared to conventional BICM designs, and for a target BER of $10^{-6}$, gains up to 3 dB in the AWGN channel are obtained. For fading channels, the gains depend on the fading parameter, and reach 2 dB for a target BER of $10^{-7}$ and $m=5$.Comment: Submitted to the IEEE Transactions on Communication

BER of MRC for M-QAM with imperfect channel estimation over correlated Nakagami-m fading

In this contribution, we provide an exact BER analysis for M-QAM transmission over arbitrarily correlated Nakagami-m fading channels with maximal-ratio combining (MRC) and imperfect channel estimation at the receiver. Assuming an arbitrary joint fading distribution and a generic pilot-based channel estimation method, we derive an exact BER expression that involves an expectation over (at most) 4 variables, irrespective of the number of receive antennas. The resulting BER expression includes well-known PDFs and the PDF of only the norm of the channel vector. In order to obtain the latter PDF for arbitrarily correlated Nakagami-m fading, several approaches from the literature are discussed. For identically distributed and arbitrarily correlated Nakagami-m channels with integer m, we present several BER performance results, which are obtained from numerical evaluation and confirmed by straightforward computer simulations. The numerical evaluation of the exact BER expression turns out to be much less time-consuming than the computer simulations

Bit Error Probability of Spatial Modulation (SM-) MIMO over Generalized Fading Channels

International audienceIn this paper, we study the performance of Spatial Modulation (SM-) Multiple-Input-Multiple-Output (MIMO) wireless systems over generic fading channels. More precisely, a comprehensive analytical framework to compute the Average Bit Error Probability (ABEP) is introduced, which can be used for any MIMO setups, for arbitrary correlated fading channels, and for generic modulation schemes. It is shown that, when compared to state-of-the-art literature, our framework: i) has more general applicability over generalized fading channels; ii) is, in general, more accurate as it exploits an improved union-bound method; and, iii) more importantly, clearly highlights interesting fundamental trends about the performance of SM, which are difficult to capture with available frameworks. For example, by focusing on the canonical reference scenario with independent and identically distributed (i.i.d.) Rayleigh fading, we introduce very simple formulas which yield insightful design information on the optimal modulation scheme to be used for the signal- constellation diagram, as well as highlight the different role played by the bit mapping on the signal- and spatial-constellation diagrams. Numerical results show that, for many MIMO setups, SM with Phase Shift Keying (PSK) modulation outperforms SM with Quadrature Amplitude Modulation (QAM), which is a result never reported in the literature. Also, by exploiting asymptotic analysis, closed-form formulas of the performance gain of SM over other single-antenna transmission technologies are provided. Numerical results show that SM can outperform many single-antenna systems, and that for any transmission rate there is an optimal allocation of the information bits onto spatial- and signal-constellation diagrams. Furthermore, by focusing on the Nakagami-m fading scenario with generically correlated fading, we show that the fading severity plays a very important role in determining the diversity gain of SM. In particular, the performance gain over single-antenna systems increases for fading channels less severe than Rayleigh fading, while it gets smaller for more severe fading channels. Also, it is shown that the impact of fading correlation at the transmitter is reduced for less severe fading. Finally, analytical frameworks and claims are substantiated through extensive Monte Carlo simulations

On the BICM Capacity

Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor

Error performance analysis of cross QAM and space-time labeling diversity for cross QAM.

Doctoral Degrees. University of KwaZulu-Natal, Durban.Abstract available in the PD