Multiuser cognitive radio networks an information

Authors: K G Nagananda Parthajit Mohapatra Chandra R Murthy Shalinee Kishore

Publish Date: 2013/03/26

Volume: 5, Issue: 1, Pages: 43-65

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Abstract

Achievable rate regions and outer bounds are derived for threeuser interference channels where the transmitters cooperate in a unidirectional manner via a noncausal messagesharing mechanism The threeuser channel facilitates different ways of messagesharing between the primary and secondary or cognitive transmitters Three natural extensions of unidirectional messagesharing from two users to three users are introduced i Cumulative message sharing ii primaryonly message sharing and iii cognitiveonly message sharing To emphasize the notion of interference management channels are classified based on different ratesplitting strategies at the transmitters The techniques of superposition coding and Gel’fand–Pinsker’s binning are employed to derive an achievable rate region for each of the cognitive interference channels The results are specialized to the Gaussian channel which enables a visual comparison of the achievable rate regions through simulations and help us achieve some additional rate points under extreme assumptions We also provide key insights into the role of ratesplitting at the transmitters as an aid to better interference management at the receiversThe work of K G Nagananda and Shalinee Kishore at Lehigh University was partly supported by the National Science Foundation under Grant CNS 0721433/0721445 The work of Parthajit Mohapatra Chandra R Murthy and the initial work of K G Nagananda at the Indian Institute of Science was partly supported by a research grant from the Aerospace Network Research ConsortiumHere we present the proof of achievability for the channel mathcalC rm CuMS2 The proof is presented in four parts namely codebook generation encoding decoding and analysis of probabilities of decoding errors at the three receivers We start with the codebook generation schemeLet us fix p in mathcalP rm CuMS2 Generate a random time sharing codeword mathbf q of length n according to the distribution prodnolimits i=1npq i Generate 2nR 11 independent codewords Wj according to prodnolimits i=1npw iq i For every wj generate one codeword X 1j according to prodnolimits i=1npx 1iw ijq iFor τ = 12 generate 2nR 2tau+IWU tauQ+4epsilon independent codewords U τl τ according to prodnolimits i=1npu tau iq i For every codeword  triple leftbf u 1l 1 bf u 2l 2 bf wjright generate one codeword X 2l 1 l 2 j according to prodnolimits i=1npx 2iu 1il 1 u 2il 2 w ij q i Uniformly distribute the 2nR 2tau+IWU tauQ+4epsilon codewords U τl τ into 2nR 2tau bins indexed by k tau in left1ldots2nR 2tauright such that each bin contains 2nIWU tauQ+4epsilon codewordsFor ρ = 13 generate 2nR 3rho+ IWU 1U 2V rhoQ+4epsilon independent codewords V ρt ρ according to prodnolimits i=1npv rho iq i For every codeword quadruple leftbf v 1t 1 bf v 3t 3 bf u 1l 1 bf u 2l 2 bf wjright generate one codeword X 3t 1 t 3 l 1 l 2 j according to prodnolimits i=1np x 3iv 1it 1 v 3it 3 u 1il 1 u 2il 2 w ij q i Distribute 2nR 3rho+ IWU 1U 2V rhoQ+4epsilon codewords V ρt ρ uniformly into 2nR 3rho bins indexed by r rho in left1ldots2nR 3rhoright such that each bin contains 2nIWU 1U 2V rhoQ+4epsilon codewords The indices are given by j in left1ldots2nR 11right l tau in left1ldots2nR 2tau+IWU tauQ+4epsilonright and t rho in1ldots 2nR 3rho+IWU 1U 2V rhoQ+4epsilonLet us suppose that the source message vector generated at the three senders is m 11 m 21 m 22 m 31 m 33 = j k 1 k 2 r 1 r 3 At the encoders the first component is treated as the message index and the last four components are treated as the bin indices mathcalS 2 looks for a codeword u 1l 1 in bin k 1 and a codeword u 2l 2 in bin k 2 such that bf u 1l 1 bf wj bf q in A epsilonn and bf u 2l 2 bf wj bf q in A epsilonn respectively mathcalS 3 looks for a codeword v 1t 1 in bin r 1 and a codeword v 3t 3 in bin r 3 such that bf v 1t 1 bf u 1l 1 bf u 2l 2 bf wj bf q in A epsilonn and bf v 3t 3 bf u 1l 1 bf u 2l 2 bf wj bf q in A epsilonn respectively mathcalS 1 mathcalS 2 and mathcalS 3 then transmit codewords x 1j x 2l 1 l 2 j and x 3t 1 t 3 l 1 l 2 j respectively through n channel uses The transmissions are assumed to be synchronized

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