We examine the frequency-selective Gaussian primitive diamond relay channel, where the signal received at both relays is described by identical frequency-selective Gaussian channels, and where the relays are connected to the destination via noiseless fronthaul links of a given capacity. The frequency response of the filters are available to all system components. We characterize analytically the Gaussian input frequency power distribution that maximizes the optimal information rate of the oblivious (code independent) relay operation achieved by joint decompression-decoding (or optimized Wyner-Ziv) procedure.

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.

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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.