In this paper, we investigate the hybrid beamforming design for the full-duplex (FD) millimeter-wave (mmWave) multiple-input multiple-output (MIMO) system, aiming to maximize the overall spectral efficiency (SE) and cancel the self-interference (SI) simultaneously. The coupling transmit power constraints, unit-modulus constraints, and strong SI make the problem under study highly nonconvex. To solve the complicated problem, we first transform it into an equivalent yet more tractable weighted minimum mean square error minimization problem and then propose an effective two-stage hybrid beam-forming design. In the first stage, we propose to extend the known matrix approximation method to the FD scenario to obtain the initial hybrid beamforming design. In the second stage, we propose to use the block coordinate descent method to update the digital beamformers and combiners while retaining the obtained analog solutions, which sufficiently exploits the easily adjustable property of digital solutions to cancel the residual SI and compensate for the SE loss. We further analyze the computational complexity of the proposed design. Numerical results demonstrate that our proposed two-stage hybrid beamforming design is superior to conventional related methods.

Compressive subspace learning (CSL) with the exploitation of space diversity has found a potential performance improvement for wideband spectrum sensing (WBSS). However, previous works mainly focus on either exploiting antenna auto-correlations or adopting a multiple-input multiple-output (MIMO) channel without considering the spatial correlations, which will degrade their performances. In this paper, we consider a spatially correlated MIMO channel and propose two CSL algorithms (i.e., mCSLSACC and vCSLACC) which exploit antenna cross-correlations, where the mCSLSACC utilizes an antenna averaging temporal decomposition, and the vCSLACC uses a spatial-temporal joint decomposition. For both algorithms, the conditions of statistical covariance matrices (SCMs) without noise corruption are derived. Through establishing the singular value relation of SCMs in statistical sense between the proposed and traditional CSL algorithms, we show the superiority of the proposed CSL algorithms. By further depicting the receiving correlation matrix of MIMO channel with the exponential correlation model, we give important closed-form expressions for the proposed CSL algorithms in terms of the amplification of singular values over traditional CSL algorithms. Such expressions provide a possibility to determine optimal algorithm parameters for high system performances in an analytical way. Simulations validate the correctness of this work and its performance improvement over existing works in terms of WBSS performance.