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An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems

Robert W. Heath, Nuria Gonzalez-Prelcic, Sundeep Rangan, Wonil Roh, Akbar Sayeed

arXiv:1512.03007v1cs.IT

TL;DR

This article surveys signal processing for mmWave wireless communication systems, including MIMO architectures and algorithms. It covers beam training, hybrid precoding, beamspace representations, and low-dimensional transceivers, while noting beam squint degradation and feedback requirements as constraints.

  • Problem

    MmWave wireless systems require suitable signal processing and MIMO architectures for diverse networks, while beam squint can significantly degrade performance.

  • Method

    The article provides an overview of state-of-the-art mmWave signal processing, covering channel characteristics, MIMO architectures, signal processing algorithms, beamspace masks, and low-dimensional communication subspaces.

  • Results

    The survey describes how an extra digital processing layer enables better beam patterns and more flexibility, and how low-dimensional transceiver performance can be made arbitrarily close to that of full-dimensional systems.

  • Takeaways & Limitations

    Beamspace channel sparsity supports low-dimensional transceivers, while hybrid and digital processing provide flexibility for mmWave beam design.

  • Takeaways & Limitations

    Adaptive beam training can require feedback, and beam squint can significantly degrade performance.

Abstract

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Communication at millimeter wave (mmWave) frequencies is defining a new era of wireless communication. The mmWave band offers higher bandwidth communication channels versus those presently used in commercial wireless systems. The applications of mmWave are immense: wireless local and personal area networks in the unlicensed band, 5G cellular systems, not to mention vehicular area networks, ad hoc networks, and wearables. Signal processing is critical for enabling the next generation of mmWave communication. Due to the use of large antenna arrays at the transmitter and receiver, combined with radio frequency and mixed signal power constraints, new multiple-input multiple-output (MIMO) communication signal processing techniques are needed. Because of the wide bandwidths, low complexity transceiver algorithms become important. There are opportunities to exploit techniques like compressed sensing for channel estimation and beamforming. This article provides an overview of signal processing challenges in mmWave wireless systems, with an emphasis on those faced by using MIMO communication at higher carrier frequencies.

I. INTRODUCTION

mmWave offers broad application opportunities and higher-bandwidth channels, but its hardware constraints, distinct propagation, and large arrays require specialized MIMO signal processing. The article surveys architectures, beamforming, channel estimation, and related algorithms.

  • Motivation: mmWave spans 30–300 GHz and provides larger spectral channels than most commercial wireless systems operating below 6 GHz.The 60 GHz unlicensed band supports approximately 2 GHz channels and data rates up to 6 Gbps.
  • Motivation: Sub-6 GHz spectrum is limited, and cognitive-radio approaches remain insufficient when gigabit-per-second data rates are required.This motivates interest in mmWave cellular systems.
  • Signal processing challenges: mmWave signal processing differs because of hardware constraints, different channel models, and large antenna arrays at transmitters and receivers.These differences form the foundations of the survey.
  • Signal processing challenges: Power and circuit limitations motivate analog–digital partitioning, hybrid beamforming, beamspace processing, lens-based antennas, and low-rate ADC methods.Imperfect phase shifters also require impairment models and algorithms that maintain performance under quantization and insertion loss.
  • Article scope: The article overviews channel characteristics, mmWave MIMO architectures, precoding and combining, beam training, and channel estimation.Reviewed architectures include analog beamforming, hybrid precoding and combining, and one-bit architectures; estimation approaches include codebook, compressed sensing, and threshold-based methods.

II. MILLIMETER WAVE PROPAGATION AND CHANNEL MODELS

mmWave propagation has distinctive channel characteristics, including higher penetration loss and environment-dependent path loss, while directional antenna gains can offset increased free-space loss. These properties support short-range cellular deployments but make directional MIMO techniques central.

  • Propagation characteristics: MmWave propagation is shaped by small wavelengths, producing lower diffraction, higher scattering, and potentially much larger penetration losses.Channel models retain familiar multipath, angle-spread, and Doppler concepts but use different parameters.
  • Distance-based path loss: Without directional antenna gains, mmWave free-space propagation has higher path loss because isotropic loss increases as λ^-2.Friis’ law captures this wavelength dependence for free-space propagation.
  • Directional gain: For a fixed physical aperture, directional antenna gains generally scale as λ^-2 because more antenna elements fit into the same area.The resulting gain scaling can more than compensate for increased free-space path loss.
  • Distance-based path loss: Statistical path-loss models represent average loss with distance using linear parameters and a lognormal shadowing term.The model uses PL(d) [dB] = α + 10β log10(d) + ξ, with ξ ∼ N(0, σ^2).
  • Distance-based path loss: For distances up to 200 m, mmWave distance-based path loss can be no worse than conventional cellular frequencies after additional beamforming gain.These findings supported mmWave picocellular deployments and increased interest in mmWave cellular systems.
  • Implications: If mmWave is used in cellular networks, directional transmissions, adaptive beamforming, and other MIMO techniques will be central.The conclusion follows from the need to compensate propagation loss through directional gains.

B. Blocking and outage

mmWave links are highly vulnerable to blockage, with material-dependent attenuation and limited diffraction, while reflections can support non-line-of-sight coverage. Blocking and outage probabilities are modeled as distance-dependent link states, but joint inter-cell outage remains unresolved.

  • Directional mmWave transmissions face severe blockage vulnerability because common materials strongly attenuate signals.
  • Brick can attenuate mmWave signals by 40 to 80 dB, while the human body can cause a 20 to 35 dB loss.
  • Building materials and the human body can reflect signals, enabling coverage through non-line-of-sight paths.
  • Coverage models represent links with two states, LOS and NLOS, or three states that additionally include signal outage.
  • The probability of each link state is modeled as a function of distance, using measurement-based, analytical, geographic, or stochastic-geometry approaches.
  • A major open issue is characterizing joint outage probabilities across links from different cells for evaluating macro-diversity.

D. Beamspace (virtual) system representation

Beamspace representation expresses mmWave MIMO channels in angular and, for selective channels, delay-Doppler Fourier coordinates, exploiting their sparse or low-rank structure. Wideband operation introduces beam squint, whose frequency-dependent steering angles can degrade performance.

  • The highly directional, high-dimensional mmWave MIMO channel has a sparse or low-rank beamspace channel matrix.
  • Beamspace is related to antenna-space representation through a spatial Fourier transform using uniformly spaced spatial angles and an orthonormal basis.
  • Time- and frequency-selective channels extend beamspace sampling to uniformly spaced delay and Doppler coordinates.
  • Beam squint makes the steering angles frequency-dependent in wideband systems and can significantly degrade performance.
  • Beam squint is a significant problem when the dispersion factor Nαθℓ is at least 0.2 on the transmit or receive side.
  • A simple multi-beam solution has been proposed when beam-squint effects are relevant, while sufficiently small dispersion can make frequency dependence negligible.

E. Beamspace channel sparsity: Low-dimensional communication subspace

Sparse mmWave beamspace channels concentrate communication power in a low-dimensional subspace that can be accessed with selected transmit and receive beams. This enables low-complexity beamspace transceivers, while grid mismatch remains a modeling limitation.

  • Beamspace channel sparsity: The effective channel rank p_eff counts singular values capturing most channel power, and optimal communication uses the corresponding singular vectors.The supported subspace dimension is defined by a threshold η close to 1, such as 0.8 or 0.9.
  • Beamspace channel sparsity: Sparse beamspace MIMO channels concentrate channel power in a low-dimensional sub-matrix of the beamspace channel.Fourier basis vectors serve as approximate singular vectors for the spatial signal space.
  • Beamspace channel sparsity: Beamspace transceivers select |M_t| ≪ N_t transmit beams and |M_r| ≪ N_r receive beams to access the low-dimensional communication subspace.The transmit and receive masks index dominant beams, and the reduced channel is formed from the corresponding sub-matrix.
  • Beamspace channel sparsity: min(|M_t|, |M_r|) ≈ p_eff, and sufficiently small γ can make low-dimensional transceiver performance arbitrarily close to an optimal SVD-based receiver.The threshold is reduced so that the masked channel captures most of the channel power; random multipath channels use expected beam power to define the masks.
  • Extended virtual representation: The extended virtual representation replaces DFT basis functions with more general dictionaries, but grid error occurs when DoAs or DoDs do not lie on the uniform grid.The error is usually neglected when the grid size is large enough.
  • MIMO architectures: Hardware constraints motivate mmWave MIMO architectures that divide processing between analog and digital domains and trade off antenna count or converter resolution.Separate RF chains and per-antenna data converters are difficult because of packing, power, and high-rate digital-processing demands.

A. Analog beamforming

Analog beamforming provides a simple mmWave MIMO implementation by connecting antenna elements to RF chains through phase-shifting networks. Its hardware simplicity limits flexibility, motivating hybrid, switching, and lens-based alternatives.

  • Analog beamforming: Analog beamforming connects several antenna elements to a single RF chain through digitally controlled phase shifters that steer beams.The phase-shifter weights are adaptively adjusted to meet objectives such as maximizing received signal.
  • Analog beamforming: Quantized phase shifts and absent amplitude adjustment limit phased-array performance and make fine beam tuning more difficult.Active phase shifters add loss, noise, and nonlinearity, while passive phase shifters occupy more area and incur greater insertion loss.
  • Analog beamforming: A single analog beamformer supports only single-user, single-stream transmission, preventing multi-stream and multi-user MIMO benefits.Beam steering also requires training and channel-estimation techniques when a link has not yet been established.
  • Hybrid architectures: Hybrid architectures divide precoding and combining between analog and digital domains to provide a compromise between MIMO performance and hardware complexity.Digital processing can correct analog imprecision, including residual multi-stream interference, while subarrays reduce hardware complexity at the expense of array flexibility.
  • Alternative hybrid realizations: Switching networks exploit channel sparsity through compressed spatial sampling and antenna selection instead of optimization over quantized phase values.Switches can connect each RF chain to all antennas in small arrays or to subsets in larger arrays.
  • Lens-based architectures: CAP-MIMO uses a lens-based front-end to access beamspace directly, mapping data streams to feed antennas and reducing hardware complexity relative to conventional digital beamforming.The number of conversion modules and transceiver chains tracks the number of data streams rather than the number of antennas.

C. Low resolution receivers

Low-resolution receivers reduce ADC and baseband power consumption, but they alter communication fundamentals and create new channel-estimation and capacity-design challenges.

  • Low-resolution ADCs: Reducing ADC resolution lowers power consumption in both the MIMO receiver front-end and baseband circuitry.The receiver trades more RF chains against fewer power-hungry ADCs.
  • Low-resolution ADCs: A one-bit ADC can have negligible front-end power consumption; at 240 GS/s, one example consumes around 10 mW.High-speed data-interface circuits also consume substantial power at mmWave frequencies.
  • Communication limits: With one-bit ADCs, the optimum signal constellation is discrete and constrained by receiver resolution.The low-SNR capacity gap between one-bit and infinite-resolution ADCs is 1.96 dB in MIMO systems.
  • Communication limits: At high SNR, one-bit systems achieve at most 2^Nr bps/Hz when the channel rank is no less than Nr.Capacity characterization with low-resolution ADCs remains an ongoing research challenge.
  • Signal processing implications: One-bit ADCs change channel-state-information processing, making channel inversion potentially preferable to eigenbeamforming and channel acquisition more difficult.Channel-estimation error decreases at best quadratically per measurement bit, but also decreases with channel sparsity, motivating one-bit compressive sensing.
  • Open challenges: mmWave-specific channel-estimation algorithms remain needed, particularly algorithms designed jointly with transmit and receive signal processing.

IV. PRECODING AND COMBINING

MmWave precoding and combining must address architecture-dependent parameters, analog–channel coupling, and exploitable channel sparsity. The paper surveys beam training strategies that configure beams with or without explicit channel knowledge.

  • IV. PRECODING AND COMBINING: MmWave precoding and combining differ because architectures add configurable parameters, analog processing intertwines with channel estimation, and channels exhibit exploitable sparsity.These properties make algorithms architecture-dependent while providing structure for signal processing.
  • Beam training: Beam training discovers strong angular directions without explicit channel estimation by iteratively measuring angular power over a beam codebook.Codebook beams use progressively narrower beamwidths to identify favorable angle-of-arrival and angle-of-departure directions.
  • Beam training protocols: IEEE 802.11ad beam training uses sector-level sweep for coarse adaptation, beam refinement for fine training, and periodic beam tracking.The protocol organizes these phases within a Beam Training Interval.
  • Hybrid beam training: Hybrid beam-training schemes use multiresolution measurements, bisection, and iterative path subtraction to estimate angular parameters and path gains.Adaptive searches begin with wide beams and narrow toward promising directions using a specially constructed codebook.
  • Hybrid beam training: Hybrid beamforming codebooks provide more design degrees of freedom than analog-only codebooks, yielding better beam patterns and greater flexibility under phase-shifter limitations.The adaptive scheme requires a feedback link between transmitter and receiver.

B. Hybrid precoding

Hybrid precoding divides processing between analog RF hardware and digital baseband hardware, using fewer RF chains than antennas. Reviewed algorithms exploit channel structure and hardware constraints to approach digital performance while reducing complexity or power.

  • Hybrid precoding: Hybrid precoding divides processing between analog and digital domains and uses far fewer RF chains than antennas.The analog and digital precoders and combiners are constrained by the selected hardware architecture.
  • Open challenges: Hybrid precoding remains challenging because of receiver constraints, combinatorial switch-based designs, computationally costly local searches, and unresolved wideband extensions.Frequency-selective extensions remain difficult because adaptive frequency-selective filtering is hard to implement in the analog domain.
  • Algorithmic designs: OMP-based designs approximate the unconstrained SVD precoder using feasible constant-magnitude RF precoders and steering-vector dictionaries derived from channel AoDs.The resulting solution is close to the unconstrained digital solution and substantially improves over single-stream analog beamforming.
  • Performance conditions: If Lr, Lt ≥ 2Ns, a phase-shifter-based hybrid system performs as the all-digital precoding and combining scheme.
  • Partial channel knowledge: With only local AoD or AoA knowledge at the respective transmitter or receiver, two-stage hybrid precoding can approach perfect-channel-knowledge performance.
  • Architecture trade-offs: Subarray architectures incur a small loss relative to fully connected architectures while reducing power consumption.Subarrays reduce hardware complexity at the expense of overall array flexibility.

D. Single-user hybrid precoding and combining with lens-based front-end

Lens-based beamspace processing exploits sparse mmWave channels to reduce transceiver complexity while retaining near-optimal performance under suitable thresholding and channel conditions.

  • SVD-based processing uses the right singular vectors for transmitter precoding and the left singular vectors for receiver post-processing, creating p_eff = min(|M_r|, |M_t|) orthogonal channels.A simpler Fourier-basis approach can instead use approximate eigenvectors of sparse beamspace channels.
  • MIMO precoding removes the gap between unquantized and quantized achievable rates at low and medium SNRs and substantially outperforms no precoding.These gains are stated for the considered setting; when full row rank does not hold, a different method is required.
  • Multiuser beamspace processing assigns dominant beams to users and can apply baseband processing to reduce inter-user interference.Lens- or phase-shifter-based front ends further reduce hardware complexity, while integrated beam selection and channel estimation remain important.
  • Beamspace channel representations are sparse, with each user associated with a set of dominant beams.The representation uses hb,k = U*hk, and dominant beams capture users’ channel directions.
  • Selecting p = |M| ≪ N dominant beams reduces the precoding problem from an N-dimensional system to a lower-dimensional p × K system.The resulting precoding matrix is computationally less intensive because p is much smaller than N.
  • Thresholding captures most channel power, enabling reduced-complexity linear beamspace precoders and combiners with near-optimal performance.The thresholds determine the retained beamspace submatrix used for processing.

2) Multiuser precoding in the hybird precoding framework:

Multiuser hybrid precoding combines analog beam selection with digital interference suppression, while sparse channel estimation reduces measurement and computational demands. The framework remains limited by quantization, broadband operation, and unresolved multiuser settings.

  • Multiuser hybrid precoding: A two-stage hybrid precoding algorithm achieves near-optimal performance compared with a certain fully digital approach.The analog stage maximizes received power through single-user beam training, while the baseband stage uses channel estimates to reduce inter-user interference.
  • Multiuser hybrid precoding: Quantizing baseband precoders is especially critical for preserving hybrid precoding gains over analog-only beamsteering.The cited work considers quantization of both analog and digital precoders.
  • Open problems: Hybrid precoding for uplink and downlink, different combining strategies, and frequency-selective channels remains an open research direction.The stated need spans both transmission directions and broadband settings.
  • Sparse channel estimation: Compressed sensing formulates channel estimation as sparse recovery and uses adaptive or greedy algorithms such as OMP to reconstruct channel paths.Measurement design aims for a low-coherence sensing matrix to support recovery guarantees.
  • Hardware constraints: Switch-based analog combining can match or improve coherence relative to phase-shifter measurements while providing similar channel-estimation performance and lower power consumption.The comparison concerns analog-only binary pseudorandom combining matrices based on switches.

B. Beam training and sparse channel estimation in lens-based CAP-MIMO transceivers

CAP-MIMO beam training first identifies dominant transmit and receive beams, then estimates the reduced beamspace channel by sequentially exciting and measuring those beams.

  • CAP-MIMO channel estimation has two steps: determining beam masks and estimating the entries of the resulting low-dimensional beamspace channel.The masks define the retained transmit and receive beam sets.
  • The reduced beamspace channel is estimated columnwise by sequentially exciting selected transmit beams and measuring corresponding receive beams.Each excited transmit beam produces measurements across the selected receive beams.
  • Beam-mask determination sequentially transmits different beams and retains receive beams whose measured power exceeds the threshold.The threshold determines which channel entries are considered dominant.
  • The procedure generally requires between O(N) and O(N^2) transmissions, depending on the number of relevant beams.

C. Channel estimation with 1-bit architectures

One-bit and compressive-sensing approaches exploit mmWave channel sparsity to estimate channels with constrained hardware and fewer measurements, but broadband and multiuser extensions remain active problems.

  • One-bit compressive sensing reconstructs sparse mmWave channel vectors from quantized measurements using the virtual channel representation.The formulation estimates hb = vec(Hb) from the training and received-signal model.
  • GAMP can solve the sparse channel-estimation optimization in a small number of steps when prior information about the channel distribution is available.The approach is also described as appealing for frequency-selective channels when channel-response correlation is incorporated.
  • Broadband estimation: Closed-form maximum-likelihood estimation is tractable for one-tap SISO channels but intractable for frequency-selective channels.Prior work therefore estimates taps separately or exploits channel-response correlation and sparsity.
  • Multiuser estimation: Random beamforming and measurement matrices allow users to estimate downlink channel parameters, which are fed back to construct transmission beams.The estimated parameters include quantized angles of arrival, angles of departure, and path gains.
  • At least an order of magnitude fewer compressed-sensing measurements are needed than exhaustive-search solutions in some multiuser mmWave cases.
  • Open problems: Further work is needed for multiuser channel estimation with hybrid precoding, low-resolution ADCs, and broadband channels.
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