Single-symbol ML decodable distributed STBCs for partially-coherent cooperative networks

Abstract

Abstract-Space-time block codes (STBCs) that are single-symbol decodable (SSD) in a co-located multiple antenna setting need not be SSD in a distributed cooperative communication setting. A relay network with N relays and a single source-destination pair is called a partially-coherent relay channel (PCRC) if the destination has perfect channel state information (CSI) of all the channels and the relays have only the phase information of the sourceto-relay channels. In this paper, first, a new set of necessary and sufficient conditions for a STBC to be SSD for co-located multiple antenna communication is obtained. Then, this is extended to a set of necessary and sufficient conditions for a distributed STBC (DSTBC) to be SSD for a PCRC, by identifying the additional conditions. Using this, several SSD DSTBCs for PCRC are identified among the known classes of STBCs. It is proved that even if a SSD STBC for a co-located MIMO channel does not satisfy the additional conditions for the code to be SSD for a PCRC, single-symbol decoding of it in a PCRC gives full-diversity and only coding gain is lost.

Performance analysis of randomised space–time block codes for amplify‐and‐forward cooperative relaying

“…As a last step, let r i [ C L be a random vector containing the linear combination coefficients for the ith node, the code x i [ C P transmitted by the ith relay is given by x i = C(z i )r i . For the time being, we do not make any specific assumption on the statistical model of the randomisation matrix L×N , which collects the randomisation vectors used by the relays; we highlight only that, unlike [36][37][38][39][40][41], the R-DSTBC A&F coding rule is completely decentralised since the ith relay chooses r i locally from a given distribution, which does not depend on i.…”

“…An alternative way is that each relay transmits to the destination the random seed used to generate the random matrices; nevertheless, this option requires a finite-rate feedback channel from the relays to the destination that, besides demanding dedicated communication resources, introduces further distortions. The relaying matrices can be designed such that to optimise the average pairwise error probability (PEP) [36], the outage probability [37], the diversity-multiplexing trade-off [38], or such that to lower the computational complexity of the ML decoder at the destination [39][40][41]. However, in such cases, as an inevitable result, a preliminary code allocation is also necessary with an additional consequence waste of resources.…”

Training-Embedded, Single-Symbol ML-Decodable, Distributed STBCs for Relay Networks

“…From the results of Theorem 1, the covariance matrix R given in (6) will not be a scaled identity matrix but a diagonal matrix such that [R] i,i = [R] j,j for 1 ≤ i, j ≤ 2 a−1 and [R] i,i = [R] j,j for 2 a−1 + 1 ≤ i, j ≤ 2 a . It can be verified that such a structure on R along with the block diagonal structure of the design ensures that every complex-symbol can be ML decoded independent of others.…”

“…Since the work of [1], [2], significant efforts have been made to design SSD DSTBCs. Towards that direction, SSD DSTBCs have been proposed for cooperative networks in [3], [4], [5] and [6].…”

“…The constructed codes include the training symbols in the structure of the code which has been shown to be the key point to obtain high rate along with the SSD property. The authors of [11] show that non-square TE-CODs provide higher rates (in symbols per channel use) compared to the known SSD DSTBCs [5], [6] for relay networks when the number of relays is less than 10. Note that, the known codes in [5], [6] and [11] (non-square TE-CODs) have exponential decoding delay and hence, in this paper, we focus on constructing SSD DSTBCs with low delay only.…”