Abstract
In this study, we consider the downlink beamforming problem in millimeter wave (mmWave) systems subjected to both path blockages and imperfect channel state information (CSI), and propose a new robust hybrid sum-outage minimizing design as a solution. We first formulate the problem as an empirical risk minimization (ERM) stochastic learning problem, whose solution can be obtained by the alternate iteration of a baseband digital and a radio frequency (RF) analog Riemann manifold-constrained beamforming updates through a mini-batch stochastic gradient descent (MSGD) approach, with gradient minimizing update rules given in closed-form, and learning rates optimized based on the lower-bounds of the corresponding Lipschitz constants. Unlike existing solutions to the path blockage-robust mmWave beamforming problem, wherein out-of-band side information is required or perfect CSI is assumed, our method relies only on the estimates and statistical knowledge of the channel's angles of departure (AoD) and complex gains, which are simultaneously captured in a Bernoulli-Gaussian model and used to generate the training data for the MSGD-based optimizer. Further, unlike preceding fully-digital or fully-connected hybrid contributions, the proposed scheme assumes a virtually-configured partially-connected setup; therefore, it is compatible with coordinated multipoint (CoMP) architectures, which are known to be crucial in terms of exploiting the full potential of mmWave systems. Simulation results confirm the effectiveness of our MSGD-based robust hybrid CoMP mmWave beamformer in mitigating the effects of path blockage and CSI error, demonstrating its superiority to state-of-the-art (SotA) alternatives.
Highlights
The ever-growing demands for data-rate and massive wireless connectivity have driven the fifth generation (5G) standard to incorporate technologies that exploit the mmWave spectrum available in the 24–30 [GHz] bands [1]–[3]
An interesting and final conclusion that can be drawn from the comparison of the results shown in Figures 3 through 6 is that among the considered methods, the maximum ratio transmission (MRT), OutMin, and new hybrid techniques are all somewhat robust to channel state information (CSI) imperfections, whereas the sum-rate maximization (SRM) schemes seems to be the most sensitive to the quality of channel estimates
Aiming at the minimization of sum-outage in mmWave systems subjected to both path blockages and imperfect CSI, we proposed a new hybrid coordinated multipoint (CoMP) beamforming algorithm
Summary
The ever-growing demands for data-rate and massive wireless connectivity have driven the fifth generation (5G) standard to incorporate technologies that exploit the mmWave spectrum available in the 24–30 [GHz] bands [1]–[3]. Contributions concentrated on mitigating the path loss issue by exploiting the high directivity of mmWave antenna arrays [11], [12] and aimed at taking advantage of the sparsity of the mmWave channel To this end, novel sparse signal processing methods were developed, albeit under the assumption of perfect CSI and for a singleuser single-carrier setup. The LoS-only path blockage assumption adopted in [27] can be further extended to match empirical evidence on the behavior of mmWave channels [7], [8], [10] This generalization has been made by the stochastic gradient descent (SGD) approach employed in [28], where a digital CoMP beamforming scheme was proposed to minimize outage in mmWave systems subjected to Bernoulli-distributed blockages of both LoS and non-line-of-sight (NLoS) paths. We propose a novel SGD-based hybrid-beamforming scheme for mmWave systems that is robust to both CSI imperfection and incoherent random path-blockage under the limited partiallyconnected CoMP paradigm
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