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This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M -ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on a modified Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.INDEX TERMS Joint communications and radar, maximum likelihood, ambiguity function, Fisher information matrix.

This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using 𝑀-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on the Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM.

In this work, we implemented line-of-sight (LoS) ray tracing functionality to investigate problems in millimetre-wave propagation modelling and network planning in 3D city model environments. First, we validated an existing LoS propagation probability model expressed as an exponential rule with the link distance. By fitting ray tracing simulation results under different scenarios to the model, the relationships between key parameters in the model and factors including the building density and the transmitter height were qualitatively analysed. Next, we developed a network planning framework for a multi-hop outdoor urban network by formulating a mixed-integer linear programming problem which minimises the overall deployment cost through optimal site selection. Taking the sets of potential site locations and potential links as inputs, we selected a subset of the sites that comprise a tree-structured network that satisfies all the user demands at a minimum deployment cost. We also analysed the time required for solving this optimisation problem in order to provide a prediction of the execution time for larger-sized problems.