The Filtered Gaussian Primitive Diamond Channel

We investigate a special case of diamond relay comprising Gaussian channels with an identical frequency response from the user to the relays, and with lossless fronthaul links with limited rate from the relays to the destination. We use the oblivious compress and forward (CF) scheme with with distributed compression, and a decode and forward (DF) scheme, where each relay decodes the whole message and sends half of the bits to the destination. It is proved that optimal CF-DF time-sharing scheme is advantageous over the CF-DF superposition scheme. We derive an achievable rate by using time-sharing between CF and DF. The optimal time-sharing proportion between CF and DF, and the power and rate allocations are different for each frequency and are fully determined.