Equations related to Spectral Efficiency in Hybrid Beamforming

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Equations related to Spectral Efficiency in Hybrid Beamforming

Fig 1: Hybrid Beamforming

In digital beamforming, each antenna element has its own radio frequency (RF) chain, consisting of analog components (such as amplifiers, filters, and mixers) and digital components (such as analog-to-digital converters (ADCs) and digital signal processors (DSPs)). On the other hand, Only a subset of antennas (or antenna elements) has their own RF chains, while the remaining antennas share a common RF chain.

In hybrid beamforming, the beamforming process is divided into analog (say, A) and digital (say, D) beamforming domains.

The goal is to optimise the overall throughput or sum rate R (A, D) obtained over Gaussian signalling on MMwave channels by designing (A, D).

The related sum rate optimization problem looks like this:

Here, set F consists all possible analog beamformers with constant-magnitude entries.
Now for hybrid architecture we will find singular value decomposition (SVD) of channel matrix to find the stronger eigen values and we will only allocate power accordingly to these paths to achieve low overhead in hybrid architecture.

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