How do you exploit the sparsity and angular diversity of mmWave channel for beamforming and precoding?

2 How to model mmWave channels?

Unlike sub-6 GHz channels, which are usually modeled as wide-sense stationary and uncorrelated, mmWave channels are characterized by sparsity and angular diversity. Sparsity means that only a few propagation paths contribute to the channel, while angular diversity means that these paths have distinct directions of arrival (DoA) and departure (DoD). Therefore, a common way to model mmWave channels is to use the geometric channel model, which represents the channel as a sum of complex gains multiplied by steering vectors that depend on the DoA and DoD of each path.

3 How to estimate mmWave channels?

Estimating mmWave channels is challenging because of the high dimensionality of the channel matrix, the limited feedback resources, and the dynamic channel conditions. A popular approach to overcome these challenges is to use compressed sensing (CS) techniques, which leverage the sparsity of the channel to reduce the number of measurements and feedback bits required. CS techniques usually involve two steps: (1) designing a sensing matrix that probes the channel with different beam patterns, and (2) applying a reconstruction algorithm that recovers the channel from the noisy and quantized measurements.

4 How to exploit sparsity for beamforming?

Beamforming is a technique that uses multiple antennas to form a beam that focuses the signal power towards the desired direction and suppresses the interference from other directions. Beamforming can improve the signal-to-noise ratio (SNR), the spectral efficiency, and the coverage of mmWave systems. However, beamforming also requires accurate knowledge of the channel state information (CSI), which is hard to obtain in mmWave systems. Therefore, exploiting the sparsity of the channel can help to design efficient beamforming strategies that only rely on partial or imperfect CSI. For example, one can use sparse recovery algorithms to identify the dominant paths of the channel and then align the beam with their directions.

5 How to exploit angular diversity for precoding?

Precoding is a technique that uses multiple antennas to pre-process the transmitted signal in order to optimize the received signal quality and mitigate the inter-user interference. Precoding can enhance the data rate, the fairness, and the robustness of mmWave systems. However, precoding also requires accurate knowledge of the channel state information (CSI), which is hard to obtain in mmWave systems. Therefore, exploiting the angular diversity of the channel can help to design effective precoding schemes that only rely on partial or imperfect CSI. For example, one can use hybrid precoding architectures that combine analog and digital precoding to approximate the optimal precoding matrix with fewer RF chains and lower complexity.