Increased amounts of bandwidth are required to guarantee both high-quality/high-rate wireless services (4G and 5G) and reliable sensing capabilities, such as for automotive radar, air traffic control, earth geophysical monitoring, and security applications. Therefore, coexistence between radar and communication systems using overlapping bandwidths has come to be a primary investigation field in recent years. Various signal processing techniques, such as interference mitigation, precoding or spatial separation, and waveform design, allow both radar and communications to share the spectrum.

Radar and communications (R&C) as key utilities of electromagnetic (EM) waves have fundamentally shaped human society and triggered the modern information age. Although R&C had been historically progressing separately, in recent decades, they have been converging toward integration, forming integrated sensing and communication (ISAC) systems, giving rise to new highly desirable capabilities in next-generation wireless networks and future radars. To better understand the essence of ISAC, this article provides a systematic overview of the historical development of R&C from a signal processing (SP) perspective. We first interpret the duality between R&C as signals and systems, followed by an introduction of their fundamental principles. We then elaborate on the two main trends in their technological evolution, namely, the increase of frequencies and bandwidths and the expansion of antenna arrays. We then show how the intertwined narratives of R&C evolved into ISAC and discuss the resultant SP framework. Finally, we overview future research directions in this field.

This paper considers the joint design of a MIMO radar with co-located antennas and a MIMO communication system. The degrees of freedom under the designer's control are the waveforms transmitted by the radar transmit array, the filter at the radar array and the code-book employed by the communication system to form its spacetime code matrix. Two formulations of the spectrum sharing problem are proposed. Firstly, the design problem is stated as the constrained maximization of the Signal-to-Interference-plus-Noise Ratio (SINR) at the radar receiver, where interference is due to both clutter and the co-existence structure, and the constraints concern both the similarity with a standard radar waveform and the rate achievable by the communication system, on top of those on the transmit energy. The resulting problem is non-convex, but a reduced-complexity iterative algorithm, based on iterative alternating maximization of three suitably designed sub-problems, is proposed and analyzed. In addition, the constrained maximization of the communication rate is also investigated. The convergence of all the devised algorithms is guaranteed. Finally, a thorough performance assessment is presented, aimed at showing the merits of the proposed approach.

The focus of this paper is on coexistence between a communication system and a pulsed radar sharing the same bandwidth. Based on the fact that the interference generated by the radar onto the communication receiver is intermittent and depends on the density of scattering objects (such as, e.g., targets), we first show that the communication system is equivalent to a set of independent parallel channels, whereby precoding on each channel can be introduced as a new degree of freedom. We introduce a new figure of merit, named the compound rate, which is a convex combination of rates with and without interference, to be optimized under constraints concerning the signal-to-interference-plus-noise ratio (including signal-dependent interference due to clutter) experienced by the radar and obviously the powers emitted by the two systems: the degrees of freedom are the radar waveform and the aforementioned encoding matrix for the communication symbols. We provide closed-form solutions for the optimum transmit policies for both systems under two basic models for the scattering produced by the radar onto the communication receiver, and account for possible correlation of the signal-independent fraction of the interference impinging on the radar. We also discuss the region of the achievable communication rates with and without interference. A thorough performance assessment shows the potentials and the limitations of the proposed co-existing architecture.

Most existing approaches to co-existing communication/ radar systems assume that the radar and communication systems are coordinated, i.e., they share information, such as relative position, transmitted waveforms and channel state. In this paper, we consider an un-coordinated scenario where a communication receiver is to operate in the presence of a number of radars, of which only a sub-set may be active, which poses the problem of estimating the active waveforms and the relevant parameters thereof, so as to cancel them prior to demodulation. Two algorithms are proposed for such a joint waveform estimation/data demodulation problem, both exploiting sparsity of a proper representation of the interference and of the vector containing the errors of the data block, so as to implement an iterative joint interference removal/data demodulation process. The former algorithm is based on classical on-grid compressed sensing (CS), while the latter forces an atomic norm (AN) constraint: in both cases the radar parameters and the communication demodulation errors can be estimated by solving a convex problem. We also propose a way to improve the efficiency of the AN-based algorithm. The performance of these algorithms are demonstrated through extensive simulations, taking into account a variety of conditions concerning both the interferers and the respective channel states.

The millimeter-wave (mmWave) full-dimensional (FD) MIMO system employs planar arrays at both the base station and user equipment and can simultaneously support both azimuth and elevation beamforming. In this paper, we propose atomic-norm-based methods for mmWave FD-MIMO channel estimation under both uniform planar arrays (UPA) and nonuniform planar arrays (NUPA). Unlike existing algorithms such as compressive sensing (CS) or subspace methods, the atomicnorm- based algorithms do not require to discretize the angle spaces of the angle of arrival (AoA) and angle of departure (AoD) into grids, thus provide much better accuracy in estimation. In the UPA case, to reduce the computational complexity, the original large-scale atomic norm minimization problem is approximately reformulated as a semi-definite program (SDP) containing two decoupled two-level Toeplitz matrices. The SDP is then solved via the alternating direction method of multipliers (ADMM) where each iteration involves only closed-form computations. In the NUPA case, the atomic-norm-based formulation for channel estimation becomes nonconvex and a gradient-decentbased algorithm is proposed to solve the problem. Simulation results show that the proposed algorithms achieve better performance than the CS-based and subspace-based algorithms.