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We investigate methods of co-existence between radar and communications systems. Each system typically considers the other system a source of interference. Consequently, the traditional solution is to isolate the two systems spectrally or spatially. By considering a cooperative radar and communications signaling scheme, we derive achievable bounds on performance for a receiver that observes communications and radar return in the same frequency allocation. We assume the radar and communications operations to be a single joint system. Bounds on performance of the joint system are measured in terms of data information rate for communications and a novel radar estimation information rate for the radar.Index Terms-Performance bounds, radar-communications co-existence. I. INTRODUCTIONT HERE is an ever increasing demand for spectrum and given the limit on resources, communications and radar systems are increasingly encouraged to share bandwidth. This can cause inter-system interference that degrades the performance of both systems. The standard solution is to separate (temporally, spatially or spectrally) the radar and communications systems. In this paper, we do not require this separation, and we explore the fundamental radar and communications co-existence performance bounds. An important contribution that enables this exploration is the novel parameterization of estimation information rate. The estimation information rate incorporates the insights of rate distortion theory but emphasizes the symmetry with the communications bound. In this paper, we refine and extend the performance bounds introduced in [1], as well as the additional bounds discussed in [2]. We also expand the results in [1] in greater detail. The two new inner bounds on performance discussed in this paper are the isolated sub-band inner bound and the optimal Fisher information inner bound.

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We develop and present a novel minimum estimation error variance waveform design method. The method optimizes the spectral shape of a unimodular radar waveform such that the performance of a joint radar-communications system that shares spectrum is maximized. We also develop the novel spectral water-filling successive interference cancelation data rate, which employs the continuous spectral water-filling algorithm to obtain the optimal communications power spectrum. We perform a numerical study to compare the performance of the new technique with the previously derived spectral mask shaping method. The global estimation rate and the data rate capture the radar and the communications performance, respectively.