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We investigate the special case of diamond relay comprising a Gaussianchannel with identical frequency response from the user to the relays andfronthaul links with limited rate from the relays to the destination. We usethe oblivious compress and forward (CF) with distributed compression and decodeand forward (DF) where each relay decodes the whole message and sends half ofits bits to the destination. We derive achievable rate by using time-sharingbetween DF and CF. It is proved that optimal CF-DF time sharing is advantageousover superposition of CF and DF. The optimal time sharing proportion between DFand CF and power and rate allocations are different at each frequency and arefully determined.

The Filtered Gaussian Primitive Diamond Channel