In this paper, we first consider a channel that is contaminated by two independent Gaussian noises @math and @math . The capacity of this channel is computed when independent noisy versions of @math are known to the transmitter and or receiver. It is shown that the channel capacity is greater then the capacity when @math is completely unknown, but is less then the capacity when @math is perfectly known at the transmitter or receiver. For example, if there is one noisy version of @math known at the transmitter only, the capacity is @math , where @math is the input power constraint and @math is the power of the noise corrupting @math . We then consider a Gaussian cognitive interference channel (IC) and propose a causal noisy dirty paper coding (DPC) strategy. We compute the achievable region using this noisy DPC strategy and quantify the regions when it achieves the upper bound on the rate.
Following Costa's work, several extensions of DPC have been studied, , colored Gaussian noise @cite_2 , arbitrary distributions of @math @cite_8 and deterministic sequences @cite_5 . The case when @math is perfectly known to the encoder and a noisy version is known to the decoder is considered in @cite_9 , mainly focusing on discrete memoryless channels. The only result in @cite_9 for Gaussian channel reveals no additional gain due to the presence of the noisy estimate at the decoder, since perfect knowledge is available at the encoder and DPC can be used. In contrast, in this paper we study the case when only noisy knowledge of @math is available at both transmitter and receiver.
@cite_8 @cite_5 @cite_9 @cite_2
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The sum capacity of a Gaussian broadcast MIMO channel can be achieved with dirty paper coding (DPC). However, algorithms that approach the DPC sum capacity do not appear viable in the forseeable future, which motivates lower complexity interference suppression techniques. Block diagonalization (BD) is a linear preceding technique for downlink multiuser MIMO systems. With perfect channel knowledge at the transmitter, BD can eliminate other users' interference at each receiver. In this paper, we study the sum capacity of BD with and without receive antenna selection. We analytically compare BD without receive antenna selection to DPC for a set of given channels. It is shown that (1) if the user channels are orthogonal to each other, then BD achieves the same sum capacity as DPC; (2) if the user channels lie in the same subspace, then the gain of DPC over BD can be upper bounded by the minimum of the number of transmit and receive antennas. These observations also hold for BD with receive antenna selection. Further, we study the ergodic sum capacity of BD with and without receive antenna selection in a Rayleigh fading channel. Simulations show that BD can achieve a significant part of the total throughput of DPC. An upper bound on the ergodic sum capacity gain of DPC over BD is proposed for easy estimation of the gap between the sum capacity of DPC and BD without receive antenna selection. We consider a state-dependent three-terminal full-duplex relay channel with the channel states noncausally available at only the source, that is, neither at the relay nor at the destination. This model has application to cooperation over certain wireless channels with asymmetric cognition capabilities and cognitive interference relay channels. We establish lower bounds on the channel capacity for both discrete memoryless (DM) and Gaussian cases. For the DM case, the coding scheme for the lower bound uses techniques of rate-splitting at the source, decode-and-forward (DF) relaying, and a Gel'fand-Pinsker-like binning scheme. In this coding scheme, the relay decodes only partially the information sent by the source. Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF. For the Gaussian case, we consider channel models in which each of the relay node and the destination node experiences on its link an additive Gaussian outside interference. We first focus on the case in which the links to the relay and to the destination are corrupted by the same interference; and then we focus on the case of independent interferences. We also discuss a model with correlated interferences. For each of the first two models, we establish a lower bound on the channel capacity. The coding schemes for the lower bounds use techniques of dirty paper coding or carbon copying onto dirty paper, interference reduction at the source and decode-and-forward relaying. The results reveal that, by opposition to carbon copying onto dirty paper and its root Costa's initial dirty paper coding (DPC), it may be benef 1Consider an additive Gaussian noise channel affected by an additive interference sequence, taken from a given codebook, which is known non-causally at the transmitter (e.g., via prior decoding). It is known that in this case optimal performance is attained by Dirty Paper Coding, which treats the interference signal as unstructured. In other words, for this example, the knowledge of the specific interferer's codebook at the decoder is not useful in terms of capacity. In this paper, two variations of this basic scenario are presented in which treating interference as unstructured is instead generally suboptimal. In the first case, a second encoder of the source message is present in the system that is not aware of the interferer's sequence, and source and interference messages are uncorrelated; In the second case, the sources encoded by the informed transmitter and interferer are correlated (and an uninformed encoder may or may not be present). Results are given in terms of conditions for achievability for both discrete and Gaussian models of the scenarios discussed above, and corroborated by numerical results. Optimal strategies are also identified in special cases. The conclusions herein point to the importance of exploiting the interfererence structure in multiterminal and source-channel coding scenarios. Over discrete memoryless channels (DMC), linear decoders (maximizing additive metrics) afford several nice properties. In particular, if suitable encoders are employed, the use of decoding algorithms with manageable complexities is permitted. For a compound DMC, decoders that perform well without the channel's knowledge are required in order to achieve capacity. Several such decoders have been studied in the literature, however, there is no such known decoder which is linear. Hence, the problem of finding linear decoders achieving capacity for compound DMC is addressed, and it is shown that under minor concessions, such decoders exist and can be constructed. A geometric method based on the very noisy transformation is developed and used to solve this problem.