Capacity Bounds for Relay Channels With Intersymbol Interference and Colored Gaussian Noise

Abstract

The capacity of a relay channel with inter-symbol interference (ISI) and additive colored Gaussian noise is examined under an input power constraint. Prior results are used to show that the capacity of this channel can be computed by examining the circular degraded relay channel in the limit of infinite block length. The current work provides single letter expressions for the achievable rates with decodeand-forward (DF) and compress-and-forward (CF) processing employed at the relay. Additionally, the cut-set bound for the relay channel is generalized for the ISI/colored Gaussian noise scenario. All results hinge on showing the optimality of the decomposition of the relay channel with ISI/colored Gaussian noise into an equivalent collection of coupled parallel, scalar, memoryless relay channels. The region of optimality of the DF and CF achievable rates are also discussed. Optimal power allocation strategies are also discussed for the two lower bounds and the cut-set upper bound. As the maximizing power allocations for DF and CF appear to be intractable, the desired cost functions are modified and then optimized. The resulting rates are illustrated through the computation of numerical examples.Chiranjib Choudhuri (cchoudhu@usc.edu) and Urbashi Mitra (ubli@usc.edu) are with the Ming Hsieh

Análise Estatística da Capacidade de Canais PLC Residenciais Cooperativos Baseada no Modelo Single Relay Channel

“…Para demonstrar tais expressões, assim como foi feito em [5], considera-se o número de subcanais N → ∞. Desta forma, o single relay channel pode ser modelado como um Linear Gaussian Relay Channel (LGRC) [6].…”

Compound Multiple Access Channel with common message and intersymbol interference

“…We use notations and formulations similar to [3] and [4]. We use * and ⊛ to denote the linear and circular convolution, respectively.…”

“…Goldsmith and Effros [3] obtained the capacity region of a finite-memory broadcast channel (BC) with ISI and colored Gaussian noise and showed that this capacity region is equal to the capacity region of an n-circular Gaussian BC as n grows to infinity. Recently, Choudhuri and Mitra [4] derived single-letter expressions for the achievable rates and an upper bound on the capacity of a relay channel with ISI and additive colored Gaussian noise.…”

Interference mitigation techniques in modern wireless communication systems

“…The problem of ISI arose with the early attempts at telegraph transmission in the mid-nineteenth century. Since that time, the problem has been considered from many viewpoints [20,21,[139][140][141][142][143][144][145][146][147][148][149][150]. For example, in [139], a method for specifying an optimum linear, time invariant receiving filter for a digital data transmission system was derived, assuming that the transmission medium introduces intersymbol interference and additive Gaussian noise, while, in [140], the impact of ISI on the error performance in binary differentially-coherent phase-shift-keying (PSK) systems was evaluated.…”

“…The influence of ISI in the capacity region of broadcast channels in the presence of colored Gaussian noise was studied in [146], whereas the impact of ISI on the capacity of frequency-selective channels in training-based transmission schemes was presented in [144]. Furthermore, the impact of ISI and additive colored Gaussian noise on the capacity of relay channels was examined in [147]. In [148], the authors presented the impact of ISI on the performance of diversity systems with multiple branches, in the presence of multipath Rayleigh, Nakagami-m and Rician fading.…”