12 research outputs found
On Optimum Power Allocation for the V-BLAST
A unified analytical framework for optimum power allocation in the unordered
V-BLAST algorithm and its comparative performance analysis are presented.
Compact closed-form approximations for the optimum power allocation are
derived, based on average total and block error rates. The choice of the
criterion has little impact on the power allocation and, overall, the optimum
strategy is to allocate more power to lower step transmitters and less to
higher ones. High-SNR approximations for optimized average block and total
error rates are given. The SNR gain of optimization is rigorously defined and
studied using analytical tools, including lower and upper bounds, high and low
SNR approximations. The gain is upper bounded by the number of transmitters,
for any modulation format and type of fading channel. While the average
optimization is less complex than the instantaneous one, its performance is
almost as good at high SNR. A measure of robustness of the optimized algorithm
is introduced and evaluated. The optimized algorithm is shown to be robust to
perturbations in individual and total transmit powers. Based on the algorithm
robustness, a pre-set power allocation is suggested as a low-complexity
alternative to the other optimization strategies, which exhibits only a minor
loss in performance over the practical SNR range.Comment: Accepted by IEEE Transactions on Communications, Apr. 200
Bit Error Rate is Convex at High SNR
Motivated by a wide-spread use of convex optimization techniques, convexity
properties of bit error rate of the maximum likelihood detector operating in
the AWGN channel are studied for arbitrary constellations and bit mappings,
which may also include coding under maximum-likelihood decoding. Under this
generic setting, the pairwise probability of error and bit error rate are shown
to be convex functions of the SNR in the high SNR regime with
explicitly-determined boundary. The bit error rate is also shown to be a convex
function of the noise power in the low noise/high SNR regime.Comment: to be presented at IZS-10, March 201
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
Optimum Power and Rate Allocation for Coded V-BLAST: Average Optimization
An analytical framework for performance analysis and optimization of coded V-BLAST is developed. Average power and/or rate allocations to minimize the outage probability as well as their robustness and dual problems are investigated. Compact, closed-form expressions for the optimum allocations and corresponding system performance are given. The uniform power allocation is shown to be near optimum in the low outage regime in combination with the optimum rate allocation. The average rate allocation provides the largest performance improvement (extra diversity gain), and the average power allocation offers a modest SNR gain limited by the number of transmit antennas but does not increase the diversity gain. The dual problems are shown to have the same solutions as the primal ones. All these allocation strategies are shown to be robust. The reported results also apply to coded multiuser detection and channel equalization systems relying on successive interference cancellation
Error Rates of Capacity-Achieving Codes Are Convex
Motivated by a wide-spread use of convex optimization techniques, convexity properties of bit error rate of the maximum likelihood detector operating in the AWGN channel are studied for arbitrary constellations and bit mappings, which also includes coding under maximum-likelihood decoding. Under this generic setting, the pairwise probability of error and bit error rate are shown to be convex functions of the SNR and noise power in the high SNR/low noise regime with explicitly-determined boundary. Any code, including capacity-achieving ones, whose decision regions include the hardened noise spheres (from the noise sphere hardening argument in the channel coding theorem) satisfies this high SNR requirement and thus has convex error rates in both SNR and noise power. We conjecture that all capacity-achieving codes have convex error rates
Convexity of error rates in digital communications under non-Gaussian noise
Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations. Earlier results obtained for the AWGN channel are extended to a wide class of (non-Gaussian) noise densities, including unimodal and spherically-invariant noise. Under these broad conditions, symbol error rates are shown to be convex functions of the SNR in the high-SNR regime with an explicitly-determined threshold, which depends only on the constellation dimensionality and minimum distance, thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way. It is the decreasing nature of the noise power density around the decision region boundaries that insures the convexity of symbol error rates in the general case. The known high/low SNR bounds of the convexity/concavity regions are tightened and no further improvement is shown to be possible in general
On Convexity of Error Rates in Digital Communications
Convexity properties of error rates of a class of decoders, including the maximum-likelihood/min-distance one as a special case, are studied for arbitrary constellations, bit mapping, and coding. Earlier results obtained for the additive white Gaussian noise channel are extended to a wide class of noise densities, including unimodal and spherically invariant noise. Under these broad conditions, symbol and bit error rates are shown to be convex functions of the signal-to-noise ratio (SNR) in the high-SNR regime with an explicitly determined threshold, which depends only on the constellation dimensionality and minimum distance, thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way. It is the decreasing nature of the noise power density around the decision region boundaries that ensures the convexity of symbol error rates in the general case. The known high/low-SNR bounds of the convexity/concavity regions are tightened and no further improvement is shown to be possible in general. The high-SNR bound fits closely into the channel coding theorem: all codes, including capacity-achieving ones, whose decision regions include the hardened noise spheres (from the noise sphere hardening argument in the channel coding theorem), satisfy this high-SNR requirement and thus has convex error rates in both SNR and noise power. We conjecture that all capacity-achieving codes have convex error rates. Convexity properties in signal amplitude and noise power are also investigated. Some applications of the results are discussed. In particular, it is shown that fading is convexity-preserving and is never good in low dimensions under spherically invariant noise, which may also include any linear diversity combining
Convexity of error rates in digital communications under non-Gaussian noise
Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations. Earlier results obtained for the AWGN channel are extended to a wide class of (non-Gaussian) noise densities, including unimodal and spherically-invariant noise. Under these broad conditions, symbol error rates are shown to be convex functions of the SNR in the high-SNR regime with an explicitly-determined threshold, which depends only on the constellation dimensionality and minimum distance, thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way. It is the decreasing nature of the noise power density around the decision region boundaries that insures the convexity of symbol error rates in the general case. The known high/low SNR bounds of the convexity/concavity regions are tightened and no further improvement is shown to be possible in general
Performance Analysis of V-BLAST with Optimum Power Allocation
Comprehensive performance analysis of the unordered V-BLAST algorithm with various power allocation strategies is presented, which makes use of analytical tools and resorts to Monte-Carlo simulations for validation purposes only. High-SNR approximations for the optimized average block and total error rates are given. The SNR gain of optimization is rigorously defined and studied using analytical tools, including lower and upper bounds, high and low SNR approximations. The gain is upper bounded by the number of transmitters, for any modulation format and any type of fading This upper bound is achieved at high SNR by the considered optimization strategies. While the average optimization is less complex than the instantaneous one, its performance is almost as good at high SNR. A measure of robustness of the optimized algorithm is introduced and evaluated, including compact closed-form approximations. The optimized algorithm is shown to be robust to perturbations in individual and total transmit powers. Based on the algorithm robustness, a pre-set power allocation is suggested as a low-complexity alternative to the other optimization strategies, which exhibits only a minor loss in performance over the practical SNR range