4. Hybrid Precoding/Combining for Massive MIMO with Hybrid ARQ

In this work, we consider hybrid precoding and combining in the azimuth plane, and therefore restrict our attention to the use of ULAs at the transmitter and receiver. Nonetheless, we note that the proposed design techniques directly carry over to the case of full-dimensional beamforming where both azimuth and elevation beamforming are enabled by arranging the antenna elements in a uniform rectangular configuration or a cylindrical configuration.

For the channel reciprocity to be useful, it is required that the sample duration allocated for uplink channel training T _u and that for downlink data transmission T _d should not exceed the channel coherence time T _coh. Suppose that the channel remains invariant before the user moves a quarter of the wavelength λ. Accordingly, the channel coherence time is calculated as \(T_{\mathrm {coh}}=\frac {1}{4}\frac {\lambda }{v}\) with v as the mobile speed of the terminal. Furthermore, let T _s denote the sample duration of an orthogonal frequency-division multiplexing (OFDM) symbol, which consists of a guard interval T _cp and an effective symbol interval T _eff. To avoid inter-symbol interference, it can be assumed for simplicity that the guard interval is set equal to the channel delay spread τ, i.e., T _cp = τ. Accordingly, the channel coherence time in terms of the number of channel uses is expressed by \(T_{\mathrm {coh}}^{\mathrm {cu}}=\frac {T_{\mathrm {coh}}T_{\mathrm {eff}}}{T_{s}T_{\mathrm {cp}}}\). To estimate the frequency response, the N _r transceivers at the user terminal transmit orthogonal pilot sequences on the uplink, each of length no less than N _r channel uses. In general, it is required that \(T_{\mathrm {coh}}^{\mathrm {cu}}\geq 2N_{\mathrm {r}}\) such that the ensuing data transmission could take place [5].

In an ARQ-based system with a single-channel (and a single processing unit), multiple copies of the same signal are received independently at different time instances. However, in a multi-channel system, performing combining across the independently received signals from parallel channels can take place as each channel will have a separate processing unit.