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

Multilevel Coded Modulation for Unequal Error Protection and Multistage Decoding—Part II: Asymmetric Constellations

In this paper, multilevel coded asymmetric modulation with multistage decoding and unequal error protection (UEP) is discussed. These results further emphasize the fact that unconventional signal set partitionings are more promising than traditional (Ungerboeck-type) partitionings, to achieve UEP capabilities with multilevel coding and multistage decoding. Three types of unconventional partitionings are analyzed for asymmetric 8-PSK and 16-QAM constellations over the additive white Gaussian noise channel to introduce design guidelines. Generalizations to other PSK and QAM type constellations follow the same lines. Upper bounds on the bit-error probability based on union bound arguments are first derived. In some cases, these bounds become loose due to the large overlappings of decision regions associated with asymmetric constellations and unconventional partitionings. To overcome this problem, simpler and tighter approximated bounds are derived. Based on these bounds, it is shown that additional refinements can be achieved in the construction of multilevel UEP codes, by introducing asymmetries in PSK and QAM signal constellations

Permutation Trellis Coded Multi-level FSK Signaling to Mitigate Primary User Interference in Cognitive Radio Networks

We employ Permutation Trellis Code (PTC) based multi-level Frequency Shift Keying signaling to mitigate the impact of Primary Users (PUs) on the performance of Secondary Users (SUs) in Cognitive Radio Networks (CRNs). The PUs are assumed to be dynamic in that they appear intermittently and stay active for an unknown duration. Our approach is based on the use of PTC combined with multi-level FSK modulation so that an SU can improve its data rate by increasing its transmission bandwidth while operating at low power and not creating destructive interference for PUs. We evaluate system performance by obtaining an approximation for the actual Bit Error Rate (BER) using properties of the Viterbi decoder and carry out a thorough performance analysis in terms of BER and throughput. The results show that the proposed coded system achieves i) robustness by ensuring that SUs have stable throughput in the presence of heavy PU interference and ii) improved resiliency of SU links to interference in the presence of multiple dynamic PUs.Comment: 30 pages, 12 figure

A Unified Exact BER Performance Analysis of Asynchronous DS-CDMA Systems Using BPSK Modulation over Fading Channels

Abstract—An asynchronous binary DS-CDMA system using random spreading sequences is considered when communicating over various fading channels. New closed-form expressions are derived for the conditional Characteristic Function (CF) of the multiple access interference. A unified analysis is provided for calculating the exact average Bit Error Rate (BER) expressed in the form of a single numerical integration based on the CF approach. The numerical results obtained from our exact BER analysis are verified by our simulation results and are also compared to those obtained by the Standard Gaussian Approximation (SGA), confirming the accuracy of the SGA for most practical conditions, except for high Signal-to-Noise Ratios (SNR) and for a low number of interferers. Index Terms—BER analysis, CDMA, fading, Rayleigh, Ricean, Hoyt, Nakagami-m, random spreading sequence