Survey of RF Communications and Sensing Convergence Research <s> J. JOINT CODING TECHNIQUES <s> We investigate the theory of the finite Heisenberg-Weyl group in relation to the development of adaptive radar and to the construction of spreading sequences and error-correcting codes in communications. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of error-correcting codes, that the finite Heisenberg-Weyl groups provide a unified basis for the construction of useful waveforms/sequences for radar, communications, and the theory of error-correcting codes. <s> BIB001 </s> Survey of RF Communications and Sensing Convergence Research <s> J. JOINT CODING TECHNIQUES <s> We describe a method of constructing a sequence (pulse train) of phase-coded waveforms, for which the ambiguity function is free of range sidelobes along modest Doppler shifts. The constituent waveforms are Golay complementary waveforms which have ideal ambiguity along the zero Doppler axis but are sensitive to nonzero Doppler shifts. We extend this construction to multiple dimensions, in particular to radar polarimetry, where the two dimensions are realized by orthogonal polarizations. Here we determine a sequence of two-by-two Alamouti matrices where the entries involve Golay pairs and for which the range sidelobes associated with a matrix-valued ambiguity function vanish at modest Doppler shifts. The Prouhet-Thue-Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay complementary waveforms. <s> BIB002 </s> Survey of RF Communications and Sensing Convergence Research <s> J. JOINT CODING TECHNIQUES <s> In this paper, we consider the design of integrated radar and communication systems that utilize weighted pulse trains with the elements of Oppermann sequences serving as complex-valued weights. An analytical expression of the ambiguity function for weighted pulse trains with Oppermann sequences is derived. Given a family of Oppermann sequences, it is shown that the related ambiguity function depends only on one sequence parameter. This property simplifies the design of the associated weighted pulse trains as it constrains the degrees of freedom. In contrast to the single polyphase pulse compression sequences that are typically deployed in radar applications, the families considered in this paper form sets of sequences. As such, they readily facilitate also multiple-access in communication systems. Numerical examples are provided that show the wide range of options offered by Oppermann sequences in the design of integrated radar and communication systems. <s> BIB003 </s> Survey of RF Communications and Sensing Convergence Research <s> J. JOINT CODING TECHNIQUES <s> A scenario involving a source, a channel, and a destination, where the destination is interested in both reliably reconstructing the message transmitted by the source and estimating with a fidelity criterion the state of the channel, is considered. The source knows the channel statistics but is oblivious to the actual channel state realization. Herein, it is established that a distortion constraint for channel state estimation can be reduced to an additional cost constraint on the source input distribution, in the limit of large coding block length. A newly defined capacity-distortion function thus characterizes the fundamental tradeoff between transmission rate and state estimation distortion. It is also shown that noncoherent communication coupled with channel state estimation conditioned on treating the decoded message as training symbols achieves the capacity-distortion function. Among the various examples considered, the capacity-distortion function for a memoryless Rayleigh fading channel is characterized to within 1.443 bits at high signal-to-noise ratio. The constrained channel coding approach is also extended to multiple access channels, leading to a coupled cost constraint on the input distributions for the transmitting sources. <s> BIB004 </s> Survey of RF Communications and Sensing Convergence Research <s> J. JOINT CODING TECHNIQUES <s> We address the co-existence of MIMO radars and a MIMO communication system. Unlike previous works, we consider a scenario in which the radar system operates in the presence of clutter. Both the radar and the communication system use transmit precoding. Initially, spectrum sharing is formulated as a problem that maximizes the radar SINR subject to the communication system meeting certain rate and power constraints. Due to the dependence of the clutter on the radar precoding matrix, the optimization with respect to the radar precoder is a maximization of a nonconvex function over a nonconvex feasible set. Since solving such problem is computationally intractable, we propose to maximize a lower bound of the SINR. In the resulting alternating maximization problem, the alternating iteration of the communication TX covariance matrix reduces to one SDP problem, while the iteration of the radar precoder is solved by a sequence of SOCP problems, which are more efficient and tractable than SDP. Simulation results validate the effectiveness of the proposed spectrum sharing method for scenarios with clutter. <s> BIB005
Joint coding techniques, such as codes attractive from a communications and radar ambiguity standpoint, as well as codes that trade data rate and channel estimation error have been investigated as a solution at the symbol level. Some research has looked at direct relationships between radar estimation sidelobe ambiguity and communications channel coding  , while others have suggested specific coding techniques that have favorable properties, such as finite Heisenberg-Weyl groups BIB001 , Golay waveforms with Doppler resilient properties BIB002 , and complementary sequences  . Complementary Golay sequences have attractive correlation properties when their autocorrelations are summed, and also bound the PAPR for OFDM communications waveforms to less than 3 dB. An example of the autocorrelation property from Reference BIB002 is shown in Figure 18 . We used an example of the codes provided in the source paper to demonstrate the zero-sidelobe behavior of the sum. The individual autocorrelations for the two complementary sequences are shown in the solid blue line and the dashed red line. Their sum is shown in the thick, solid green line, and has no observable sidelobes to within the quantization noise of our system. By themselves, they exhibit significant sidelobe activity. However, when the autocorrelations are summed, their complementary nature cancel all sidelobes, making them attractive for using radar ranging. This sum is shown in the solid, thick green line. For communications users, use of these codes has the benefit of bounding the potential peak-to-average power ratio. Recent work has looked at trading communications with channel state estimation BIB004 . However, in this case, the channel state estimation is a nuisance parameter to increasing communications throughput, not a desired radar or sensing modality. Some research has looked into coding as a means to sharing bandwidth between an OFDM radar and Global Positioning System (GPS) signal  to complement both operations. Oppermann sequences have also been proposed as a natural framework for developing radar waveforms with good ambiguity properties and multi-user communications access schemes BIB003 . Others have applied precoding to both a MIMO communications user and an in-band MIMO radar user operating in clutter, optimizing the radar precoding to maximize joint performance BIB005 .