The Filtered Gaussian Primitive Diamond Channel

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