Beamforming Network Optimization for Reducing Channel Time Variation in High-Mobility Massive MIMO

Abstract

Communications in high-mobility environments have caught a lot of attentions recently. In this paper, fast time-varying channels for massive multiple-input multiple-output (MIMO) systems are addressed. We derive the exact channel power spectrum density (PSD) for the uplink from a high-speed railway (HSR) to a base station (BS) and propose to further reduce the channel time variation via beamforming network optimization. A large-scale uniform linear array (ULA) is equipped at the HSR to separate multiple Doppler shifts in angle domain through high-resolution transmit beamforming. Each branch comprises a dominant Doppler shift, which can be compensated to suppress the channel time variation, and we derive the channel PSD and the Doppler spread to assess the residual channel time variation. Interestingly, the channel PSD can be exactly expressed as the product of a pattern function and a beam-distortion function. The former reflects the impact of array aperture and is the converted radiation pattern of ULA, while the latter depends on the configuration of beamforming directions. Inspired by the PSD analysis, we introduce a common configurable amplitudes and phases (CCAP) parameter to optimize the beamforming network, by partly removing the constant modulus quantized phase constraints of matched filter (MF) beamformers. In this way, the residual Doppler shifts can be ulteriorly suppressed, further reducing the residual channel time variation. The optimal CCAP parameter minimizing the Doppler spread is derived in a closed form. Numerical results are provided to corroborate both the channel PSD analysis and the superiority of beamforming network optimization technique.Index Terms-High-mobility communication, time-varying channel, power spectrum density (PSD), Doppler spread, angledomain massive MIMO, beamforming network optimization.

Radiation Efficiency Aware High-Mobility Massive MIMO With Antenna Selection

“…Denote s = [s(0), s(1), ..., s(N − 1)] T as the length-N transmitted time domain symbols in one orthogonal frequency division multiplexing (OFDM) block. We consider the antenna weighting technique [9] is adopted, where the mth antenna is weighted by a complex weight w m . The multi-branch transmit matched filtering (MF) beamforming is performed towards a set of Q selected directions ϑ q ∈ (θ L , θ R ), q = 1, 2, ..., Q.…”

“…w = [w 1 , w 2 , · · · , w M ] T denotes the weighting vector. Then, according to [9], the received signal at BS can be expressed in the form of…”

“…In the scheme in [9] (labelled as 'AW-Mini-DS'), the antenna weighting is designed to only minimize the Doppler spread, which may lead to severe loss of transmission efficiency. Let us consider the following example.…”

“…For high-mobility downlink, the work in [7] separated the Doppler shifts by beamforming network with a large-scale antenna array and proposed a joint oscillator frequency offset and Doppler shift estimation scheme. For uplink transmissions, it has been demonstrated that the harmful effect of Doppler shift can be also mitigated by massive MIMO technique [8], [9]. For example, the authors in [8] proposed a transmit multi-branch beamforming scheme where the angle domain Doppler shifts compensation is exploited to suppress the uplink channel variation.…”

High-Mobility CoMP Massive MIMO Uplink Transmissions: Channel PSD Analysis and Doppler Spread Suppression

“…Moreover, the high spatial resolution characteristics of massive MIMO transmissions could combat Doppler spread [7], [13]. Besides, the exact power spectrum density (PSD) of uplink equivalent channel is derived in [11], and an antenna weighting technique is further proposed to reduce the channel time variation. However, the scheme in [11] suffers from severe loss of energy radiation efficiency (ERE) when channel has small angular spread [12].…”