Optimal Detector Randomization for Multiuser Communications Systems

Abstract

Abstract-Optimal detector randomization is studied for the downlink of a multiuser communications system, in which users can perform time-sharing among multiple detectors. A formulation is provided to obtain optimal signal amplitudes, detectors, and detector randomization factors. It is shown that the solution of this joint optimization problem can be calculated in two steps, resulting in significant reduction in computational complexity. It is proved that the optimal solution is achieved via randomization among at most min{K, N d } detector sets, where K is the number of users and N d is the number of detectors at each receiver. Lower and upper bounds are derived on the performance of optimal detector randomization, and it is proved that the optimal detector randomization approach can reduce the worst-case average probability of error of the optimal approach that employs a single detector for each user by up to K times. Various sufficient conditions are obtained for the improvability and nonimprovability via detector randomization. In the special case of equal crosscorrelations and noise powers, a simple solution is developed for the optimal detector randomization problem, and necessary and sufficient conditions are presented for the uniqueness of that solution. Numerical examples are provided to illustrate the improvements achieved via detector randomization.

Maximization of average number of correctly received symbols over multiple channels in the presence of idle periods

“…The expression in (8) corresponds to the average number of symbols that are correctly received during the communication interval of length λ i T . Extending (8) to all the channels yields the average number of correctly received symbols during an interval of T seconds over all channels:…”

“…Time sharing (randomization) has attracted a significant deal of interest in the literature due to its capability to provide performance improvements for communication systems [1][2][3][4][5][6][7][8][9][10][11]. In [2], it is demonstrated that the average probability of error over additive noise channels with arbitrary noise probability density functions (PDFs) can be reduced via optimal stochastic signaling, which performs time sharing among at most three different signal levels for each information symbol.…”

“…The study in [5] investigates performance gains that can be achieved by detector randomization and stochastic signaling, and proves that the optimal receiver design is realized by time sharing (randomization) between at most two maximum a-posteriori probability (MAP) detectors corresponding to two deterministic signal vectors. For the downlink of a multiuser communications system, [8] performs joint optimization of signal amplitudes, detectors, and detector randomization factors in order to reduce the worst-case average probability of error. Similarly, jamming performance of average power constrained jammers can be enhanced by performing time sharing among different power levels [3,6,7].…”

Average Capacity Maximization via Channel Switching in the Presence of Additive White Gaussian Noise Channels and Switching Delays

“…In addition to the capacity, other metrics such as probability of error, probability of detection, and outage probability are considered in various resource allocation problems; e.g., [7]- [15]. For example, in the detector randomization problem, the aim is to minimize the average probability of error of a communication system by optimizing time sharing factors and transmit power (signal) levels corresponding to different detectors at the receiver [7]- [9]. Also, a jammer can maximize the average probability of error or minimize the detection probability of a victim receiver by performing optimal time sharing among multiple power levels [12]- [14].…”

Optimal Channel Switching Strategy for Average Capacity Maximization

“…It is obtained that the joint optimization of the transmitted signals and the detectors at the receiver leads to time sharing between at most two MAP detectors corresponding to two deterministic signal constellations. In [13], the benefits of time sharing among multiple detectors are investigated for the downlink of a multiuser communication system and the optimal time sharing strategy is characterized.…”