Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications

Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multi-dimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels ("fading is never good in low dimensions") and optimization of a unitary-precoded OFDM system. For example, the error rate bounds of a unitary-precoded OFDM system with QPSK modulation, which reveal the best and worst precoding, are extended to arbitrary constellations, which may also include coding. The reported results also apply to the interference channel under Gaussian approximation, to the bit error rate when it can be expressed or approximated as a non-negative linear combination of individual symbol error rates, and to coded systems.Comment: accepted by IEEE IT Transaction

Multiple symbol differential detection of uncoded and trellis coded MPSK

A differential detection for MPSK, which uses a multiple symbol observation interval, is presented and its performance analyzed and simulated. The technique makes use of maximum-likelihood sequence estimation of the transmitted phases rather than symbol-by-symbol detection as in conventional differential detection. As such the performance of this multiple symbol detection scheme fills the gap between conventional (two-symbol observation) differentially coherent detection of MPSK and ideal coherent of MPSK with differential encoding. The amount of improvement gained over conventional differential detection depends on the number of phases, M, and the number of additional symbol intervals added to the observation. What is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation. The analysis and simulation results presented are for uncoded and trellis coded MPSK

Performance evaluation of communication systems with transmit diversity

Transmit diversity is a key technique to combat fading with multiple transmit antennae for next-generation wireless communication systems. Space-time block code (STBC) is a main component of this technique. This dissertation consists of four parts: the first three discuss performance evaluation of STBCs in various circumstances, the fourth outlines a novel differential scheme with full transmit diversity. In the first part, closed-form expressions for the bit error rate (BER) are derived for STBC based on Alamouti\u27s scheme and utilizing M-ary phase shift keying (MPSK) modulation. The analysis is carried out for a slow, flat Rayleigh fading channel with coherent detection and with non-coherent differential encoding/decoding. The BER expression for coherent detection is exact. But for differential detection it is an approximation appropriate for a high signal-to-noise ratio. Numerical results are provided for analysis and simulations for BPSK and QPSK modulations. A signal-to-noise ratio loss of approximately 3 dB always occurs with conventional differential detection for STBC compared to coherent detection. In the second part of this dissertation, a multiple-symbol differential detection (MSDD) technique is proposed for MPSK STBCs, which greatly reduces this performance loss by extending the observation interval for decoding. The technique uses maximum likelihood block sequence detection instead of traditional block-by-block detection and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric for an observation interval of N blocks is derived. It is shown that for a moderate number of blocks, MSDD provides more than 1.0 dB performance improvement corresponding to conventional differential detection. In addition, a closed-form pairwise error probability for differential BPSI( STBC is derived for an observation interval of N blocks, and an approximate BER is obtained to evaluate the performance. In the third part, the BER performance of STBC over a spatio-temporal correlated channel with coherent and noncoherent detection is illustrated, where a general space-time correlation model is utilized. The simulation results demonstrate that spatial correlation negatively effects the performance of the STBC scheme with differential detection but temporal correlation positively impacts it. However, with coherent detection, spatial correlation still has negative effect on the performance but temporal correlation has no impact on it. In the final part of this dissertation, a differential detection scheme for DS/CDMA MIMO link is presented. The transmission provides for full transmit and receive diversity gain using a simple detection scheme, which is a natural extension of differential detection combined with an orthogonal transmit diversity (OTD) approach. A capacity analysis for this scheme is illustrated