The Gaussian Primitive Discrete Time and Filtered Diamond Channel: Correlated Noise and Dirty-Paper Coding

We investigate the primitive diamond relay channel model comprising Gaussian channels with identical frequency responses from the user to the relays and with lossless fronthaul links with a limited rate from the relays to the destination. The model is further extended by addressing correlated noise at the relays, which can be present in the uplink system, for example, due to interference or a jammer. We use the oblivious compress and forward (CF) scheme with distributed compression, and the decode and forward (DF) scheme. The CF system rate is calculated for the correlated noise case and a closed-form formula is derived. The effect of positive and negative correlation on the system rate is shown. It is proved that CF-DF time-sharing scheme is advantageous over a CF-DF superposition coding (SPC) scheme for the correlated noise case. We also analyze another scheme to combine CF and DF, which is based on dirty paper coding (DPC). This scheme's analysis relies on the correlated noise CF results, providing another motivation for examining this case. It is proved that also in this setting, the CF-DF time-sharing scheme is advantageous over the CF-DF DPC scheme. The optimal time-sharing proportion between CF and DF, and each frequency's power and rate allocations are determined for positive noise correlation.