[Paper Review] High-Mobility Wideband Massive MIMO Communications: Doppler Compensation, Analysis and Scaling Law

Guo Wei, Weile Zhang+3 more|arXiv (Cornell University)|Jul 18, 2018

Advanced MIMO Systems Optimization4 citations

TL;DR

This paper proposes angle-domain Doppler compensation in high-mobility wideband massive MIMO uplink systems using a large uniform linear array (ULA) at the transmitter. By forming parallel beamforming branches, each subject to a single dominant Doppler frequency offset (DFO), the system enables pre-transmission DFO compensation. The key result is a scaling law showing Doppler spread decreases as $1/ar{M}$, with asymptotic suppression of channel time-variation when the number of transmit antennas $M$ is sufficiently large.

ABSTRACT

In this paper, we apply angle-domain Doppler compensation for high-mobility wideband massive multi-input multi-output (MIMO) uplink transmission. The time-varying multipath channel is considered between high-speed terminal and static base station (BS), where multiple Doppler frequency offsets (DFOs) are associated with distinct angle of departures (AoDs). With the aid of the large-scale uniform linear array (ULA) at the transmitter, we design a beamforming network to generate multiple parallel beamforming branches, each transmitting signal pointing to one particular angle. Then, the transmitted signal in each branch will experience only one dominant DFO when passing over the time-varying channel, which can be easily compensated before transmission starts. We theoretically analyze the Doppler spread of the equivalent uplink channel after angle-domain Doppler compensation, which takes into account both the mainlobe and sidelobes of the transmit beam in each branch. It is seen that the channel time-variation can be effectively suppressed if the number of transmit antennas is sufficiently large. Interestingly, the asymptotic scaling law of channel variation is obtained, which shows that the Doppler spread is proportional to the maximum DFO and decreases approximately as $1/\sqrt{M}$ ($M$ is the number of transmit antennas) when $M$ is sufficiently large. Numerical results are provided to corroborate the proposed scheme.

Motivation & Objective

• Address the challenge of time-varying channels in high-mobility wideband massive MIMO uplink due to multiple Doppler frequency offsets (DFOs).
• Overcome limitations of conventional methods that fail under dense multipath conditions with limited spatial resolution.
• Leverage the high spatial resolution of large-scale uniform linear arrays (ULAs) to enable per-beam DFO compensation at the transmitter.
• Theoretically analyze the residual Doppler spread in the equivalent uplink channel after compensation, including mainlobe and sidelobe effects.
• Derive and validate an asymptotic scaling law for channel time-variation, showing suppression proportional to $1/\sqrt{M}$.

Proposed method

• Employ matched filter beamforming at the transmitter to generate multiple parallel beamforming branches, each steered toward a distinct angle of departure (AoD).
• Each beamforming branch experiences only one dominant DFO, enabling pre-transmission Doppler compensation at the transmitter.
• Model the time-varying multipath channel between a high-speed terminal and a static base station, with DFOs linked to distinct AoDs.
• Theoretical analysis accounts for both mainlobe and sidelobe contributions in each beam, using integral expressions involving complete elliptic integrals.
• Derive asymptotic bounds on Doppler spread by approximating integrals over beam response functions, leveraging large-$M$ asymptotics.
• Use integral approximations and bounds (e.g., via Equation (6.153) in [33]) to show that $\Lambda_{1,1}$ grows as $\frac{2}{\pi}\ln(2M)$, while $\Lambda_{1,2}$ and $\Lambda_{1,3}$ decay as $1/M$, justifying their neglect for large $M$.

Experimental results

Research questions

• RQ1 Can angle-domain beamforming at the transmitter enable effective Doppler compensation in high-mobility wideband massive MIMO uplink?
• RQ2 How does the residual Doppler spread in the equivalent uplink channel scale with the number of transmit antennas $M$?
• RQ3 What is the impact of mainlobe and sidelobe responses on the effective Doppler spread after beamforming and DFO compensation?
• RQ4 Can a theoretical scaling law be derived for the time-variation of the uplink channel under angle-domain Doppler compensation?
• RQ5 How do beamforming sidelobes and beam response lobes affect the asymptotic behavior of channel variation?

Key findings

• The Doppler spread of the equivalent uplink channel after angle-domain Doppler compensation scales asymptotically as $1/\sqrt{M}$, where $M$ is the number of transmit antennas.
• The mainlobe contribution $\Lambda_{1,1}$ grows logarithmically with $M$, approximately as $\frac{2}{\pi}\ln(2M)$, while sidelobe contributions $\Lambda_{1,2}$ and $\Lambda_{1,3}$ decay as $1/M$.
• For sufficiently large $M$, the sidelobe contributions become negligible, and the dominant term $\Lambda_{1,1}$ governs the asymptotic behavior of channel time-variation.
• The beamforming network effectively isolates each DFO per beam, enabling pre-compensation and significantly reducing inter-carrier interference (ICI).
• Theoretical analysis confirms that channel time-variation is effectively suppressed when $M$ is large, validating the feasibility of high-mobility massive MIMO in dynamic environments.
• Numerical results corroborate the theoretical analysis, demonstrating that the scaling law accurately predicts performance gains with increasing $M$.