1 Introduction
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We propose a double-pilot-based time-varying hybrid precoding system based on the analysis that analog precoding and digital precoding vary in different speeds and the size of them is totally distinct, which determines the separate methods for them.
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We leverage a beamforming index prediction net (BIP-Net) based on convolution 2D (Conv2D) LSTM, which is pretty efficient because we just predict the index of the beamforming from a codebook, which allows the fast training of net.
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To the best of our knowledge, besides the different rate designs of the double-pilot hybrid precoding system, this is the first paper corresponding to the combination of beamforming prediction and deep learning in a UAV-enabled or time-varying system as well. In addition, the method proposed is flexible and feasible since it can be adopted in any beamforming methods based on a codebook.
2 System model and problem definition
2.1 System model
2.1.1 Physical model
2.1.2 Time-varying geometry channel
2.2 Problem definition and time-varying influence
2.2.1 Hybrid precoding problem definition
2.2.2 Time-varying influence
2.3 Analysis of analog precoding in time-varying channel
2.3.1 Solution space of analog precoding
2.3.2 Robustness of analog precoding
3 Methods
3.1 Analog precoding sampling and prediction
3.1.1 Beam sampling step
3.1.2 Beam prediction step
3.2 Low complexity digital precoding
4 Beamforming index prediction-net in beam prediction step
5 Results and discussion
Pilots required | ||
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Method | Period | |
A period of the beam sampling step | A period of prediction period | |
Proposed | \({N_t}^2+N_{RF}^2(R_{\mathrm{smpl}}-1)\) | \(N_{RF}^2\) |
Taylor expansion | \({N_t}^2R_{\mathrm{smpl}}\) | \({N_t}^2\) |