Optimal Randomization of Signal Constellations on the Downlink of a Multiuser DS-CDMA System

Abstract

Abstract-In this study, the jointly optimal power control with signal constellation randomization is proposed for the downlink of a multiuser communications system. Unlike a conventional system in which a fixed signal constellation is employed for all the bits of a user (for given channel conditions and noise power), power control with signal constellation randomization involves randomization/time-sharing among different signal constellations for each user. A formulation is obtained for the problem of optimal power control with signal constellation randomization, and it is shown that the optimal solution can be represented by a randomization among (K + 1) or fewer distinct signal constellations for each user, where K denotes the number of users. In addition to the original nonconvex formulation, an approximate solution based on convex relaxation is derived. Then, detailed performance analysis is presented when the receivers employ symmetric signaling and sign detectors. Specifically, the maximum asymptotical improvement ratio is shown to be equal to the number of users, and the conditions under which the maximum and minimum asymptotical improvement ratios are achieved are derived. Numerical examples are presented to investigate the theoretical results, and to illustrate performance improvements achieved via the proposed approach.

Optimal Stochastic Signaling Under Average Power and Bit Rate Constraints

“…Optimization problems in the form of (7) have been studied in the literature [14], [16]- [20]. If F (x) is continuous and the components of x belong to finite closed intervals, then the optimal solution of (7) can be expressed as a randomization among at most three points, which follows from Carethéodory's theorem [13], [28].…”

“…In certain scenarios, employing randomization (i.e., stochastic signaling) instead of deterministic signals/constellation points can improve the average probability of error performance [4], [13]- [20]. Stochastic signaling relies on the idea of modeling signal S i corresponding to the ith information symbol as a random variable instead of a deterministic quantity for each i.…”

“…the deterministic signaling scheme given in [3] via stochastic signaling are derived. In [20], the stochastic signaling idea is applied in a downlink multiuser communication system. In particular, the optimal power control scheme is developed such that each user is allowed to randomize among multiple signal constellations instead of employing a fixed signal constellation, and it is shown that randomization can improve error performance in some scenarios.…”

“…In [25]- [27], random rotations and phase shifts are employed to increase the transmission diversity. Also, in [20], the optimal randomization of constellations is investigated for each user in a multiuser setting under power constraints. However, these studies do not take into account the prior probability distribution in their formulation (i.e., assume that it is fixed), and only utilize randomization in signal levels to achieve improvement according to a certain performance criterion.…”

Gauss karışım gürültüsü varlığında tek eşik sezici ile maksimum olabilirlik sezici arasında performans karşılaştırması

“…Tek eşikli sezici ve işaret sezici basit yapısından dolayı avantajlı görülmekle birlikte, gürültünün unimodal dağılıma sahip olmadığı durumlarda oldukça kötü performanslar gösterebilmektedir [11]- [13]. Literatürde, gürültünün simetrik Gauss karışımı olarak modellendiği çalışmalar mevcuttur [14]- [15].…”