Optimal and suboptimal receivers for code-multiplexed transmitted-reference ultra-wideband systems

In this study, optimal and suboptimal receivers are investigated for code-multiplexed transmitted-reference (CM-TR) ultra-wideband systems. First, a single-user scenario is considered, and a CM-TR system is modeled as a generalized noncoherent pulse-position modulated system. Based on that model, the optimal receiver that minimizes the bit error probability is derived. Then, it is shown that the conventional CM-TR receiver converges to the optimal receiver under certain conditions and achieves close-to-optimal performance in practical cases. Next, multi-user systems are considered, and the conventional receiver, blinking receiver, and chip discriminator are investigated. Also, the linear minimum mean-squared error (MMSE) receiver is derived for the downlink of a multi-user CM-TR system. In addition, the maximum likelihood receiver is obtained as a performance benchmark. The practicality and the computational complexity of the receivers are discussed, and their performance is evaluated via simulations. The linear MMSE receiver is observed to provide the best trade-off between performance and complexity/practicality. © 2012 John Wiley & Sons, Ltd

Stochastic signal design on the downlink of a multiuser communications system

Stochastic signal design is studied for the downlink of a multiuser communications system. First, a formulation is proposed for the joint design of optimal stochastic signals. Then, an approximate formulation, which can get arbitrarily close to the optimal solution, is obtained based on convex relaxation. In addition, when the receivers employ symmetric signaling and sign detectors, it is shown that the maximum asymptotical improvement ratio is equal to the number of users, and the conditions under which that maximum asymptotical improvement ratio is achieved are presented. Numerical examples are provided to explain the theoretical results. © 2012 IEEE

Performance analysis of code-multiplexed transmitted-reference ultra-wideband systems

In code-multiplexed transmitted-reference (CM-TR) ultra-wideband (UWB) systems, data signals and reference signals are transmitted using two distinct orthogonal codes. In this way, performance improvements and/or implementation advantages are obtained compared to transmitted-reference (TR) and frequency-shifted reference (FSR) ultra-wideband (UWB) systems. In this study, performance of CM-TR systems is investigated, and probability of error expressions are obtained. For the single user case, a closed-form expression for the exact probability of error is derived, whereas a Gaussian approximation, the accuracy of which depends on the number of frames per symbol, is considered for the multiuser case. Also, the maximum likelihood detector is derived, and numerical examples are presented. © 2011 IEEE

Optimal channel switching in the presence of stochastic signaling

Optimal channel switching and detector design is studied for M-ary communication systems in the presence of stochastic signaling, which facilitates randomization of signal values transmitted for each information symbol. Considering the presence of multiple additive noise channels (which can have non-Gaussian distributions in general) between a transmitter and a receiver, the joint optimization of the channel switching (timesharing) strategy, stochastic signals, and detectors is performed in order to achieve the minimum average probability of error. It is proved that the optimal solution to this problem corresponds to either (i) switching between at most two channels with deterministic signaling over each channel, or (ii) time-sharing between at most two different signals over a single channel (i.e., stochastic signaling over a single channel). For both cases, the optimal solutions are shown to employ corresponding maximum a posteriori probability (MAP) detectors at the receiver. Numerical results are presented to investigate the proposed approach. © 2013 IEEE

Optimal signaling and detector design for M-ary communication systems in the presence of multiple additive noise channels

An M-ary communication system is considered in which the transmitter and the receiver are connected via multiple additive (possibly non-Gaussian) noise channels, any one of which can be utilized for the transmission of a given symbol. Contrary to deterministic signaling (i.e., employing a fixed constellation), a stochastic signaling approach is adopted by treating the signal values transmitted for each information symbol over each channel as random variables. In particular, the joint optimization of the channel switching (i.e., time sharing among different channels) strategy, stochastic signals, and decision rules at the receiver is performed in order to minimize the average probability of error under an average transmit power constraint. It is proved that the solution to this problem involves either one of the following: (i) deterministic signaling over a single channel, (ii) randomizing (time sharing) between two different signal constellations over a single channel, or (iii) switching (time sharing) between two channels with deterministic signaling over each channel. For all cases, the optimal strategies are shown to employ corresponding maximum a posteriori probability (MAP) decision rules at the receiver. In addition, sufficient conditions are derived in order to specify whether the proposed strategy can or cannot improve the error performance over the conventional approach, in which a single channel is employed with deterministic signaling at the average power limit. Finally, numerical examples are presented to illustrate the theoretical results. © 2013 Elsevier Inc

Maximization of correct decision probability via channel switching over Rayleigh fading channels

In this study, optimal channel switching (time sharing) strategies are investigated under average power and cost constraints in order to maximize the average number of correctly received symbols between a transmitter and a receiver that are connected via multiple additive Gaussian noise channels. The optimal strategy is shown to perform channel switching either among at most three channels with full channel utilization (i.e., no idle periods), or between at most two channels with partial channel utilization. In addition, it is stated that the optimal solution must operate at the maximum average power and the maximum average cost, which facilitates low-complexity approaches for calculating the optimal strategy. For two-channel strategies, an upper bound in terms of the noise standard deviations of the employed channels is provided for the ratio between the optimal power levels. Furthermore, a simple condition depending solely on the systems parameters is derived, under which partial channel utilization cannot be optimal. Numerical examples are presented to demonstrate the validity of the theoretical results. © 2016 IEEE

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

In this study, optimal channel switching (time sharing) strategies are investigated under average power and cost constraints for maximizing the average number of correctly received symbols between a transmitter and a receiver that are connected via multiple flat-fading channels with additive Gaussian noise. The optimal strategy is shown to correspond to channel switching either among at most three different channels with full channel utilization (i.e., no idle periods), or between at most two different channels with partial channel utilization. Also, it is stated that the optimal solution must operate at the maximum average power and the maximum average cost, which facilitates low-complexity approaches for obtaining the optimal strategy. For two-channel strategies, an upper bound is derived, in terms of the parameters of the employed channels, on the ratio between the optimal power levels. In addition, theoretical results are derived for characterizing the optimal solution for channel switching between two channels, and for comparing performance of single channel strategies. Sufficient conditions that depend solely on the systems parameters are obtained for specifying when partial channel utilization cannot be optimal. Furthermore, the proposed optimal channel switching problem is investigated for logarithmic cost functions, and various theoretical results are obtained related to the optimal strategy. Numerical examples are presented to illustrate the validity of the theoretical results. © 2016 Elsevier Inc. All rights reserved

Maximization of correct decision probability via channel switching over Rayleigh fading channels

In this study, optimal channel switching (time sharing) strategies are investigated under average power and cost constraints in order to maximize the average number of correctly received symbols between a transmitter and a receiver that are connected via multiple additive Gaussian noise channels. The optimal strategy is shown to perform channel switching either among at most three channels with full channel utilization (i.e., no idle periods), or between at most two channels with partial channel utilization. In addition, it is stated that the optimal solution must operate at the maximum average power and the maximum average cost, which facilitates low-complexity approaches for calculating the optimal strategy. For two-channel strategies, an upper bound in terms of the noise standard deviations of the employed channels is provided for the ratio between the optimal power levels. Furthermore, a simple condition depending solely on the systems parameters is derived, under which partial channel utilization cannot be optimal. Numerical examples are presented to demonstrate the validity of the theoretical results. © 2016 IEEE