A partial coherent detector for orthogonal modulations in two-way relay communications with physical network coding and fading

We present in this paper a partial coherent receiver for detecting (at the relay) the modulo-2 sum bit of the uplink orthogonal modulations in a two-way relay communication system with physical network coding and fading. The detector exploits the availability of implicit pilot symbols in every signaling interval of an orthogonal modulation and is able to provide reasonably accurate data recovery without the need of sending pilot symbols. Using the characteristic function approach, we were able to derive a tight analytical upper bound on the bit-error-rate (BER) of the detector. The first component in the upper bound tells us that when the uplink symbols from the two users are identical, the BER approaches that of conventional point-to-point coherent detection, i.e. the multiple-access interference arising from physical network coding has no effect on the BER when the two data bits are identical. On the other hand, the second component in the upper bound shows that when the data from the two users are different, the BER increases dramatically. In essence, the BER of the proposed partial coherent detector is the average of those of the coherent and non-coherent detectors. We also outline in the paper a simple technique for achieving full coherent detection at the relay without resorting to transmitting any pilot symbols.