A Tutorial on Near-Field XL-MIMO Communications Towards 6G

Extremely large-scale multiple-input multiple-output (XL-MIMO) is a promising technology for the sixth-generation (6G) mobile communication networks. By significantly boosting the antenna number or size to at least an order of magnitude beyond current massive MIMO systems, XL-MIMO is expected to unprecedentedly enhance the spectral efficiency and spatial resolution for wireless communication. The evolution from massive MIMO to XL-MIMO is not simply an increase in the array size, but faces new design challenges, in terms of near-field channel modelling, performance analysis, channel estimation, and practical implementation. In this article, we give a comprehensive tutorial overview on near-field XL-MIMO communications, aiming to provide useful guidance for tackling the above challenges. First, the basic near-field modelling for XL-MIMO is established, by considering the new characteristics of non-uniform spherical wave (NUSW) and spatial non-stationarity. Next, based on the near-field modelling, the performance analysis of XL-MIMO is presented, including the near-field signal-to-noise ratio (SNR) scaling laws, beam focusing pattern, achievable rate, and degrees-of-freedom (DoF). Furthermore, various XL-MIMO design issues such as near-field beam codebook, beam training, channel estimation, and delay alignment modulation (DAM) transmission are elaborated. Finally, we point out promising directions to inspire future research on near-field XL-MIMO communications.

Delay-Doppler Alignment Modulation for Spatially Sparse Massive MIMO Communication

Delay alignment modulation (DAM) is an emerging technique for achieving inter-symbol interference (ISI)-free wideband communications using spatial-delay processing, without relying on channel equalization or multi-carrier transmission. However, existing works on DAM only consider multiple-input single-output (MISO) communication systems and assume time-invariant channels. In this paper, by extending DAM to time-variant frequency-selective multiple-input multiple-output (MIMO) channels, we propose a novel technique termed \emph{delay-Doppler alignment modulation} (DDAM). Specifically, by leveraging \emph{delay-Doppler compensation} and \emph{path-based beamforming}, the Doppler effect of each multi-path can be eliminated and all multi-path signal components may reach the receiver concurrently and constructively. We first show that by applying path-based zero-forcing (ZF) precoding and receive combining, DDAM can transform the original time-variant frequency-selective channels into time-invariant ISI-free channels. The necessary and/or sufficient conditions to achieve such a transformation are derived. Then an asymptotic analysis is provided by showing that when the number of base station (BS) antennas is much larger than that of channel paths, DDAM enables time-invariant ISI-free channels with the simple delay-Doppler compensation and path-based maximal-ratio transmission (MRT) beamforming. Furthermore, for the general DDAM design with some tolerable ISI, the path-based transmit precoding and receive combining matrices are optimized to maximize the spectral efficiency. Numerical results are provided to compare the proposed DDAM technique with various benchmarking schemes, including MIMO-orthogonal time frequency space (OTFS), MIMO-orthogonal frequency-division multiplexing (OFDM) without or with carrier frequency offset (CFO) compensation, and beam alignment along the dominant path.

Achievable Rate Region and Path-Based Beamforming for Multi-User Single-Carrier Delay Alignment Modulation

Delay alignment modulation (DAM) is a novel wideband transmission technique for mmWave massive MIMO systems, which exploits the high spatial resolution and multi-path sparsity to mitigate ISI, without relying on channel equalization or multi-carrier transmission. In particular, DAM leverages the delay pre-compensation and path-based beamforming to effectively align the multi-path components, thus achieving the constructive multi-path combination for eliminating the ISI while preserving the multi-path power gain. Different from the existing works only considering single-user DAM, this paper investigates the DAM technique for multi-user mmWave massive MIMO communication. First, we consider the asymptotic regime when the number of antennas Mt at BS is sufficiently large. It is shown that by employing the simple delay pre-compensation and per-path-based MRT beamforming, the single-carrier DAM is able to perfectly eliminate both ISI and IUI. Next, we consider the general scenario with Mt being finite. In this scenario, we characterize the achievable rate region of the multi-user DAM system by finding its Pareto boundary. Specifically, we formulate a rate-profile-constrained sum rate maximization problem by optimizing the per-path-based beamforming. Furthermore, we present three low-complexity per-path-based beamforming strategies based on the MRT, zero-forcing, and regularized zero-forcing principles, respectively, based on which the achievable sum rates are studied. Finally, we provide simulation results to demonstrate the performance of our proposed strategies as compared to two benchmark schemes based on the strongest-path-based beamforming and the prevalent OFDM, respectively. It is shown that DAM achieves higher spectral efficiency and/or lower peak-to-average-ratio, for systems with high spatial resolution and multi-path diversity.

Multi-User Delay Alignment Modulation for Millimeter Wave Massive MIMO

Delay alignment modulation (DAM) is a novel wideband communication technique, which exploits the high spatial resolution and multi-path sparsity of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems to mitigate inter-symbol interference (ISI), without relying on conventional techniques like channel equalization or multi-carrier transmission. In this paper, we extend the DAM technique to multi-user mmWave massive MIMO communication systems. We first provide asymptotic analysis by showing that when the number of base station (BS) antennas is much larger than the total number of channel paths, DAM is able to eliminate both ISI and inter-user interference (IUI) with the simple delay pre-compensation and per-path-based maximal ratio transmission (MRT) beamforming. We then study the general multi-user DAM design by considering the three classical transmit beamforming strategies in a per-path basis, namely MRT, zero-forcing (ZF) and regularized zero-forcing (RZF). Simulation results demonstrate that multi-user DAM can significantly outperform the benchmarking single-carrier ISI mitigation technique that only uses the strongest channel path of each user.

Delay Alignment Modulation: Manipulating Channel Delay Spread for Efficient Single- and Multi-Carrier Communication

The evolution of mobile communication networks has always been accompanied by the advancement of inter-symbol interference (ISI) mitigation techniques, from equalization in 2G, spread spectrum and RAKE receiver in 3G, to OFDM in 4G and 5G. Looking forward towards 6G, by exploiting the extremely large spatial dimension brought by large antenna arrays and multi-path sparsity of millimeter wave (mmWave)/Terahertz channels, we propose a novel ISI mitigation technique, termed delay alignment modulation (DAM). The key ideas of DAM are path delay pre-compensation and path-based beamforming, i.e., by deliberately introducing symbol delays to compensate respective multi-path delays of the channel, so that with appropriate per-path-based beamforming, the multi-path signal components will arrive at the receiver simultaneously and constructively. To gain some insights, we first show that perfect delay alignment can be achieved to transform the time-dispersive channel to time non-dispersive channel, without sophisticated channel equalization or multi-carrier processing. This thus enables efficient equalization-free single-carrier transmission or CP-free OFDM transmission. When perfect DAM is infeasible or undesirable, we propose the generic DAM technique to significantly reduce the channel delay spread. This thus provides a new DoF to combat channel time dispersion for more efficient single- or multi-carrier signal transmissions. As an illustration, we propose the novel DAM-OFDM technique, which may save the CP overhead or mitigate the PAPR and CFO issues suffered by conventional OFDM. We show that DAM-OFDM involves joint frequency-domain and time-domain beamforming optimization, for which a closed-form solution is derived. Simulation results show that the proposed DAM-OFDM achieves significant performance gains over the conventional OFDM, in terms of spectral efficiency, BER and PAPR.

Delay Alignment Modulation: Enabling Equalization-Free Single-Carrier Communication

This paper proposes a novel broadband transmission technology, termed delay alignment modulation (DAM), which enables the low-complexity equalization-free single-carrier communication, yet without suffering from inter-symbol interference (ISI). The key idea of DAM is to deliberately introduce appropriate delays for information-bearing symbols at the transmitter side, so that after propagating over the time-dispersive channel, all multi-path signal components will arrive at the receiver simultaneously and constructively. We first show that by applying DAM for the basic multiple-input single-output (MISO) communication system, an ISI-free additive white Gaussian noise (AWGN) system can be obtained with the simple zero-forcing (ZF) beamforming. Furthermore, the more general DAM scheme is studied with the ISI-maximal-ratio transmission (MRT) and the ISI-minimum mean-square error (MMSE) beamforming. Simulation results are provided to show that when the channel is sparse and/or the antenna dimension is large, DAM not only resolves the notorious practical issues suffered by orthogonal frequency-division multiplexing (OFDM) such as high peak-to-average-power ratio (PAPR), severe out-of-band (OOB) emission, and vulnerability to carrier frequency offset (CFO), with low complexity, but also achieves higher spectral efficiency due to the saving of guard interval overhead.