Exact Capacity Analysis of Rate Adaptive Power Nonadaptive Multibranch Multihop Decode-and-Forward Relaying Networks

The capacity of rate adaptive, power nonadaptive, multibranch, multihop, decode-and-forward relaying networks is analyzed for ergodically fading channels. Different cases of superimposed, selection, and orthogonal relaying are investigated. Parallel channel coding and repetition coding are considered for each case. Closed-form expressions for the maximum instantaneous achievable rates are obtained for each case. The distribution functions of the maximum instantaneous achievable rates for a source-relay-symmetric (S-R-sym.), relay-destination-symmetric (R-D-sym.) case are evaluated. The ergodic capacity of rate adaptive, power nonadaptive, multibranch, dual-hop networks in the S-R-sym., R-D-sym. case with no-source-destination-link assumption is derived for Rayleigh fading. It is observed that parallel channel coding gain can attain as much as 1 bit improvement for the examples considered. Increasing the number of branches deteriorates the performance of the orthogonal relaying scheme, but improves the performances of the other schemes albeit with diminishing returns. The performances of all schemes degrade rapidly as the number of hops per branch increases, such that no scheme is more energy efficient than direct transmission for more than three hops per branch.