Outage probability analysis of distributed reception with hard decision exchanges

This paper considers the problem of jointly decoding binary messages from a single distant transmitter to a cooperative receive cluster. The nodes in the receive cluster exchange information to decode messages from the transmitter. The outage probability of distributed reception with binary hard decision exchanges is compared with the outage probability of ideal receive beamforming with unquantized observation exchanges. Low-dimensional analysis and numerical results show, via two simple but surprisingly good approximations, that the outage probability performance of distributed reception with hard decision exchanges is well-predicted by the SNR of ideal receive beamforming after subtracting a hard decision penalty of slightly less than 2 dB. These results, developed in non-asymptotic regimes, are consistent with prior asymptotic results (for a large number of nodes and low per-node SNR) on hard decisions in binary communication systems.