A channel time variation suppression scheme based on beamforming is proposed for high-mobility orthogonal frequency division multiplexing (OFDM) downlink transmissions. The residual channel time variation after Doppler shift compensation by finite resolution receive beamforming can be measured by the Doppler spread. The interchannel interference (ICI) due to the time-varying channel is then analyzed and the relation between the signal-to-interference ratio (SIR) and Doppler spread is given. Based on the derived Doppler spread and ICI, a beamforming network optimization scheme is proposed to reduce the channel time variation. A closed-form solution is first obtained to minimize the average ICI, which exploits the structure of a tridiagonal Toeplitz matrix. Next, an optimization problem is formulated to minimize the maximum Doppler spread to further verify the impact of average ICI on channel time variation. The sequential parametric convex approximation (SPCA) algorithm is exploited to solve the non-convex min-max problem. Numerical results verify the theoretical analysis.

In high-mobility massive multiple-input multiple-output (MIMO) systems, Doppler shifts compensation can be combined with beamforming network to effectively suppress the channel time variation. The key of the beamforming network lies in the optimization of the common configurable amplitudes and phases (CCAP) parameter. In this paper, we reveal more insights of this approach by conducting the in-depth analysis. First, we demonstrate that the CCAP parameter optimizes the beamforming network to reduce channel time variation and approximates in a semi-sinusoidal form. Then, a scaling law between the asymptotic Doppler spread and the number of antennas M is derived, revealing that the asymptotic Doppler spread decreases at a rate of 1/M. We further prove that the optimal CCAP parameter obtained from Jakes' channel model can be directly applied to more general cases, while the inverse proportionality between the resulting asymptotic Doppler spread and the number of antennas remains valid. Numerical results confirm the correctness of the theoretical analysis.

In this paper, we consider the frequency synchronization issue in orthogonal frequency division multiplexing distributed antenna systems. There may exist multiple carrier frequency offsets (CFOs) between the transmitter and distributed receive antennas. To solve the multi-CFO estimation problem, we first derive the blind maximum likelihood estimator, which has superior estimation performance, but exhibits high computational complexity. Furthermore, we develop a blind pairing-based efficient estimator (PBEE), which divides the multiple antennas into pairs of two. The two CFOs in each pair are jointly estimated with a carefully designed cost function, which proves to be exactly a cosine function parameterized by the two CFOs even with the effect of noise. Consequently, the joint estimation of the two CFOs can be simplified to the one-dimensional search optimization problem. The PBEE can achieve better CFO estimation performance than the existing competitors. From the theoretical mean square error (MSE) analysis of PBEE, we further derive the optimal antenna pairing scheme by minimizing the signal-to-noise ratio degradation caused by the uncompensated residual CFOs. Finally, the Cramér-Rao bound of CFO estimation is derived and numerical results are provided to corroborate the proposed studies.

Communications in high-mobility environments have received a lot of attention 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 the 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 the 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 the beamforming network optimization technique.

In this paper, we consider a downlink orthogonal frequency division multiplexing system from a base station to a high-speed train equipped with fully/partly calibrated massive uniform linear antenna-array (ULA) in wireless environments with abundant scatterers. Multiple Doppler frequency off- sets (DFOs) stemming from intensive propagation paths together with transceiver oscillator frequency offset (OFO) result in a fast time-varying frequency-selective channel. We develop an angle domain carrier frequency offset (CFO, a general designation for DFO and OFO) estimation approach. A high-resolution beamforming network is designed to separate different DFOs into a set of parallel branches in angle domain such that each branch is mainly affected by a single dominant DFO. Then, a joint estimation algorithm for both maximum DFO and OFO is developed for fully calibrated ULA. Next, its estimation mean square error performance is analyzed under inter-subarray mismatches. To mitigate the detrimental effects of inter-subarray mismatches, we introduce a calibration-oriented beamforming parameter and develop the corresponding modified joint estimation algorithm for partly calibrated ULA. Moreover, the Cramér-Rao lower bound of CFO estimation is derived. Both theoretical and numerical results are provided to corroborate the proposed method.

In this paper, we design a novel angle-domain adaptive filtering (ADAF)-based frequency synchronization method for massive multiple-input multiple-output (MIMO) multiuser uplink, which is suitable for users with either separate or overlapped angle-of-arrival (AoA) regions. We first introduce the angle-constraining matrix (ACM), which consists of a set of selected match-filter (MF) beamformers pointing to the AoAs of the interested user. Then, the adaptive beamformer can be acquired by appropriately designing the ADAF vector. Such beamformer can achieve a two-stage adaptive multiuser interference (MUI) suppression, i.e., inherently suppressing the MUI from distant users by ACM in the first stage and substantially mitigating the MUI from adjacent overlapping users by ADAF vector in the second stage. For both separate and mutually overlapping users, the carrier frequency offset (CFO) estimation and subsequent data detection can be performed individually for each user, which reduces the computational complexity. Moreover, ADAF is rather insensitive to imperfect AoA knowledge, making itself promising for multiuser uplink transmission. Numerical results are provided to show the effectiveness of the proposed method, as well as its superiority over existing competitors.

In this letter, we take the initiative in adaptively determining the optimal temporal filter (TF) length for space-time equalization (STE) schemes, where overfitting may occur under too large TF length. We specifically consider the system without employing cyclic-prefix such that the spectral efficiency could be maintained. Based on the delicately derived connection between the mean square error (MSE) of equalized training symbols and unknown data symbols, the MSE of the latter can be predicated and serves as the decision metric for determining the optimal TF length. Numerical results demonstrate that the proposed STE scheme with TF of adaptively optimized length can work properly, even in the presence of cochannel interference.

In this paper, two blind carrier frequency offset (CFO) estimators for orthogonal frequency division multiplexing (OFDM) with distributed multi-antenna receiver are designed. We first propose a pairing based efficient estimator (PBEE), where multiple CFOs are divided and then estimated in pairs of two with a carefully designed cost function. This cost function is proven to be exactly a cosine function parameterized by the two CFOs even with the effect of noise. Consequently, the CFOs estimate can be obtained in closed-form after a one-dimensional search. Moreover, in order to improve the estimation performance, we further develop the maximum likelihood (ML) estimator. The computationally inefficient multi-dimensional search of ML estimator can be solved by introducing an extra one-step adjustment to the PBEE. Both the two estimators support fully loaded transmissions, which can save the spectral efficiency. Numerical results are provided to corroborate the proposed studies.

In this paper, we address the orthogonal frequency division multiplexing (OFDM) downlink transmission in scenarios abundant of scatters when the high- speed rail (HSR), equipped with partly calibrated massive uniform linear array (ULA), is in high- speed motion relative to the base station. A high- resolution beamforming network is designed to separate multiple Doppler frequency offsets (DFOs) in spatial domain into a series of parallel beamforming branches, such that each branch is mainly affected by single dominant DFO, wherein the conventional carrier frequency offset (CFO) compensation and subsequent data detection could be carried out individually. In view of this, a joint- estimation algorithm is proposed to jointly estimate the CFO and equivalent channel of each beamforming branch. Moreover, the calibration- oriented beamforming parameter (COBP) is introduced to mitigate the detrimental effects in presence of inter-subarray uncertainties. Both numerical and theoretical results are provided to corroborate the effectiveness of the proposed method.