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Hybrid MIMO Architectures for Millimeter Wave Communications: Phase Shifters or Switches?

Roi Méndez-Rial, Cristian Rusu, Nuria González-Prelcic, Ahmed Alkhateeb, Robert W. Heath

arXiv:1512.03032v1cs.IT

TL;DR

The paper addresses the complexity and power consumption of phase-shifter-based hybrid mmWave MIMO architectures. It proposes switch-based architectures, a hardware-independent open-loop compressive channel estimator, and switch-specific combining algorithms. Switch-based designs achieve comparable channel-estimation performance with lower power consumption, while equal-power architectures provide close spectral efficiencies.

  • Problem

    Phase-shifter-based hybrid mmWave MIMO architectures require evaluation against switching alternatives across hardware complexity, power consumption, channel estimation, and spectral efficiency.

  • Method

    The paper develops switch-based hybrid architectures, channel-estimation algorithms compatible with all architectures, and hybrid combining algorithms for switches.

  • Results

    Switch-based architectures achieve comparable channel-estimation performance to phase-shifter architectures with lower power consumption, while equal-power architectures provide close spectral efficiencies.

  • Takeaways & Limitations

    Switching networks offer a lower-power alternative to phase-shifter networks while retaining close spectral efficiency at equal power consumption.

Abstract

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Hybrid analog/digital MIMO architectures were recently proposed as an alternative for fully-digitalprecoding in millimeter wave (mmWave) wireless communication systems. This is motivated by the possible reduction in the number of RF chains and analog-to-digital converters. In these architectures, the analog processing network is usually based on variable phase shifters. In this paper, we propose hybrid architectures based on switching networks to reduce the complexity and the power consumption of the structures based on phase shifters. We define a power consumption model and use it to evaluate the energy efficiency of both structures. To estimate the complete MIMO channel, we propose an open loop compressive channel estimation technique which is independent of the hardware used in the analog processing stage. We analyze the performance of the new estimation algorithm for hybrid architectures based on phase shifters and switches. Using the estimated, we develop two algorithms for the design of the hybrid combiner based on switches and analyze the achieved spectral efficiency. Finally, we study the trade-offs between power consumption, hardware complexity, and spectral efficiency for hybrid architectures based on phase shifting networks and switching networks. Numerical results show that architectures based on switches obtain equal or better channel estimation performance to that obtained using phase shifters, while reducing hardware complexity and power consumption. For equal power consumption, all the hybrid architectures provide similar spectral efficiencies.

I. INTRODUCTION

mmWave systems use large antenna arrays and hybrid analog/digital processing to obtain beamforming gains while limiting the number of RF chains. This paper proposes switch-based hybrid architectures, hardware-independent channel estimation, and switch-specific combining designs to reduce power and complexity while studying spectral-efficiency trade-offs.

  • Motivation: Large mmWave antenna arrays provide array gain, but high-frequency analog and mixed-signal hardware makes assigning one RF chain per antenna difficult.The resulting architectures use fewer RF chains than antennas and motivate new transceiver structures for precoding, combining, and channel estimation.
  • Hybrid architectures: Hybrid architectures split MIMO processing between analog and digital domains, providing more design freedom than analog-only beamforming for multi-stream and multi-user transmission.Analog beamforming reduces RF chains but is limited to single-stream transmission and practical phase-shifter constraints.
  • Phase-shifter limitations: Phase-shifter networks can suffer from finite phase precision, higher complexity and power with more bits, insertion loss, and increased LNA requirements.These practical limitations motivate alternatives to phase shifters in mmWave hybrid architectures.
  • Proposed architectures: The paper proposes switch-based hybrid architectures that replace phase shifters to reduce cost, complexity, and power while incurring a small system-performance loss.The two designs select one antenna per RF chain or select and combine an antenna subset; the latter uses array gain better, while the former has lower complexity.
  • Evaluation: A power-consumption model evaluates architectures as functions of antenna and RF-chain counts, showing reasonable switch-based power reductions, especially for large arrays.The study compares switching and phase-shifter architectures through power consumption, hardware complexity, channel estimation, and spectral efficiency.
  • Channel estimation and combining: The proposed open-loop compressive channel estimator is independent of the analog hardware and supports both phase-shifter and switching networks.It incorporates hybrid constraints during training, exploits angular sparsity, and is paired with switch-specific combiner-design algorithms.
  • Results: Switch-based architectures achieve comparable channel-estimation performance to phase-shifter architectures while requiring lower power consumption.For equal power consumption, the architectures provide similar spectral efficiencies; at equal RF-chain counts, switch-based designs use less power with a small array-gain loss.

II. SYSTEM MODEL

The system uses hybrid MIMO processing, splitting operations between analog and digital domains while focusing on receiver-side combining and architecture trade-offs. Six architectures span phase-shifter, switch-based, full-array, subset, and antenna-selection designs.

  • The receiver applies a hybrid combiner W = W_RF W_BB, with analog RF and digital baseband components subject to hardware-specific constraints.
  • A1: Phase shifting network: Phase-shifter architecture A1 connects every transceiver to every antenna and provides full array gain through coherent combining.
  • A2: Phase shifting network in subsets: Subset phase-shifter architecture A2 uses Nr RF paths instead of Nr × Lr, reducing complexity while reducing each transceiver’s maximum gain by 1/Lr.
  • A3–A4: Switching networks: Switch-based architectures replace phase shifters with binary routing, but analog combining can be noncoherent and degrade SNR, complicating combiner design.
  • A5–A6: Antenna selection: A5 and A6 select antennas rather than combine them, lowering complexity and insertion losses but limiting effective gain or array size suitability.

III. POWER CONSUMPTION MODEL

The paper develops an approximate receiver power model for hybrid architectures using reference consumption values for LNAs, ADCs, phase shifters, switches, RF chains, and baseband processing. It compares architectures across array size, RF-chain count, and front-end reduction.

  • The power model includes LNAs, ADCs, RF chains, analog components, and baseband processing, using common component assumptions across architectures.
  • The assumed reference consumptions are P_LNA = 20 mW, P_ADC = 200 mW, P_PS = 30 mW, P_SW = 5 mW, and P_RFC = 40 mW.
  • A1 and A2 power expressions account for phase-shifter and LNA counts, RF chains, ADCs, and baseband processing.
  • A4–A6 use switch-based expressions that account for selected antennas, switches, RF chains, ADCs, and baseband processing.
  • A2 power consumption depends on the number of RF chains rather than the array size.

IV. DOWNLINK COMPRESSED SENSING BASED CHANNEL ESTIMATION

The paper presents compressed-sensing channel estimation for sparse mmWave channels that works across the considered analog architectures. It focuses on receiver design and notes simultaneous multi-user estimation as a potential advantage.

  • The proposed compressed-sensing approach estimates channels while working with all considered hybrid architectures.
  • The method focuses on receiver-side channel estimation for single-user mmWave systems but can also operate in multi-user MIMO systems.
  • All mobile stations can simultaneously estimate their downlink channels in the multi-user setting.
  • This simultaneous estimation reduces training overhead compared with user-specific approaches whose complexity scales with the number of mobile stations.

A. Sparse multipath channel model

The channel is modeled as a sparse multipath mmWave channel represented in angular dictionaries. This converts channel estimation into recovery of a small number of nonzero virtual-channel coefficients.

  • Sparse multipath channel model: The physical channel is modeled as contributions from scattering clusters and propagation rays with complex path gains and array responses.
  • Sparse multipath channel model: Limited scattering motivates assuming a small number of propagation paths, K = N_cl N_ray.
  • Virtual channel representation: Angular dictionaries are constructed from receiver and transmitter array-response vectors sampled on fine angle-of-arrival and angle-of-departure grids.
  • Virtual channel representation: The channel is represented through a K-sparse virtual matrix whose nonzero entries contain quantized path gains.
  • Virtual channel representation: With half-wavelength uniform linear arrays and grid sizes G_r = N_r and G_t = N_t, the array-response matrices become unitary DFT matrices.

B. Compressed channel sensing

The paper formulates mmWave channel estimation as open-loop compressed sensing using training precoders and combiners, then reconstructs the sparse virtual channel with OMP. Recovery quality depends on sensing-matrix coherence, sparsity, SNR, and measurement count.

  • Measurement model: The BS and MS collect successive compressed channel measurements using training precoders and combiners, then stack them into a sensing model.The approach supports one or multiple RF chains at the receiver.
  • Multiple-combiner operation: The receiver produces more measurements per snapshot when it simultaneously uses more RF chains.The compressed-measurement count depends on receiver RF chains, not transmitter RF chains.
  • Sparse channel representation: The compressed-sensing dictionary represents channel-path directions, while nonzero coefficients represent path gains.The effective sensing matrix is A = ΦΨ.
  • Recovery algorithm: Orthogonal Matching Pursuit provides a polynomial-complexity approximate solution for the sparse channel-reconstruction problem.The manuscript selects OMP for its simplicity and fast implementation.
  • Recovery conditions: Lower mutual coherence supports sparse recovery, with OMP guaranteeing noiseless recovery when µ(A) < 1/(2K−1).The mutual coherence is the largest absolute normalized inner product between distinct columns.
  • Measurement requirements: At low SNR or high sparsity, the required measurement count can approach or exceed the signal dimension.When sparsity is low, good recovery can require only M ≪ N measurements.

D. Training sequences and mutual coherence

The paper designs hardware-constrained training sequences by minimizing the mutual coherence of the effective sensing matrix. It compares phase-shifter and switching architectures using pseudorandom and deterministic constructions against Welch-bound references.

  • Sensing design: The effective sensing matrix A = ΦΨ governs compressed-sensing recovery guarantees, so the training design targets low coherence.Φ depends on the deployed hybrid architecture and its hardware constraints.
  • Hardware constraints: Phase shifters constrain precoding and combining vectors to unit-magnitude entries, whereas switches constrain them to one nonzero entry and zeros elsewhere.These constraints define different feasible sensing-matrix structures.
  • Single-combiner design: Using a fixed combiner sequence enables independent BS and MS design because the Kronecker-product factors can be treated separately.This independence benefits multi-user settings with heterogeneous MS architectures and antenna counts.
  • Measurement allocation: For a fixed measurement budget M = MtMr, the coherence-minimizing allocation balances the Welch bounds of the two Kronecker-product factors.The optimum exists only when the resulting Mt and Mr are integer values.
  • Welch-bound comparison: The single-combiner Welch bound is significantly worse than the general Welch bound for matrices of the same dimensions.Figure 4 compares the bounds as the total measurement count varies.
  • Deterministic designs: Deterministic switching designs use selected Fourier rows, while phase-shifter designs use unit-magnitude matrices and numerical incoherent-frame construction.Difference-set designs can attain the Welch bound only for some dimensions, whereas almost-difference sets cover a broader range near-optimally.

2) Multiple combiners (MC):

The multiple-combiner architecture adds receiver-side degrees of freedom to construct lower-coherence measurement matrices. In the reported comparison, switching networks achieve lower coherence than phase-shifter networks while reducing power consumption.

  • 2) Multiple combiners (MC):: The multiple-combiner measurement matrix is designed by selecting rows of BS and MS factors so the overall Kronecker-product coherence is minimized.A greedy procedure iteratively selects rows that maximally reduce current coherence until a full sweep makes no improvement.
  • 2) Multiple combiners (MC):: Multiple combiners add degrees of freedom to the measurement matrix and can lower coherence relative to the single-combiner case.The final matrix has size MtMr × NtNr.
  • 2) Multiple combiners (MC):: The proposed pseudorandom MC design with switches at both BS and MS achieves coherence below the single-combiner Welch bound.The comparison uses Nt = Gt = 64, Nr = Gr = 16, and one MS RF chain.
  • 2) Multiple combiners (MC):: Switches A5-A5 provide better coherence than phase shifters A1-A1 with a noticeable power-consumption reduction.This comparison is reported for the pseudorandom MC case.
  • 2) Multiple combiners (MC):: The MC construction supports multiple RF chains at the receiver, with binary switch-based vectors and matrices containing one active entry per row or column as specified.The analyzed architecture is A5-A5 with multiple RF chains.
  • 2) Multiple combiners (MC):: For deterministic designs, the switching architecture achieves the lowest coherence, and results are below the SC-WB in most cases.These deterministic designs outperform the random sequences in the Figure 5(b) comparison.
  • 2) Multiple combiners (MC):: The proposed methods include multiple-combiner matrices and deterministic low-coherence sequences for A1 and A5 based on Legendre and maximum-length sequences.The multiple-combiner structure is presented as an alternative to the single-combiner case.

E. Least squares estimation

The least-squares section derives sensing-matrix conditions and architecture-specific training designs under power and hardware constraints. Multiple RF chains complicate optimality because combining generally correlates the post-combining noise.

  • E. Least squares estimation: The hybrid channel-estimation model incorporates RF precoding and combining matrices into the sensing matrix Φ.The sensing matrix must be full column rank for channel estimation.
  • E. Least squares estimation: The least-squares design minimizes channel-estimation error subject to transmit-power and hardware constraints.The derivation uses Lagrange multipliers and yields architecture-specific implementable sensing matrices.
  • E. Least squares estimation: Any sensing matrix satisfying the stated orthogonality condition achieves the minimum mean-squared error under the idealized least-squares model.The corresponding minimum MSE is reported in the section.
  • E. Least squares estimation: The estimation error increases with the square of the number of transmit antennas.This is stated for the derived minimum-MSE result.
  • E. Least squares estimation: For one RF chain, A1 uses Fourier or Hadamard rows, while A3 and A5 repeat identity matrices to satisfy the optimality conditions.A2, A4, and A6 use block-diagonal constructions tailored to their RF-chain structures.
  • E. Least squares estimation: With multiple receiver RF chains, least-squares optimality is not straightforward because post-combining noise is generally correlated.For A5 and A6, the specified condition preserves uncorrelated noise.

V. HYBRID COMBINING WITH SWITCHES

The section develops hybrid combiner designs for switching architectures, addressing combinatorial or intractable optimization under hardware constraints. It proposes low-complexity approaches based on antenna selection and sparse reconstruction, while characterizing flexibility, complexity, power, and performance trade-offs across architectures.

  • Problem: Switch-based hybrid combiner design is constrained by architecture-specific hardware, making direct spectral-efficiency maximization intractable for some structures.For subset antenna-selection architectures, exact optimization is combinatorial and exhaustive search is time consuming.
  • Antenna selection: For antenna-selection architectures A5 and A6, greedy incremental selection activates antennas that provide the largest capacity increase while respecting subset constraints.The hybrid antenna-selection procedure evaluates candidate supports using the associated channel and baseband combiner.
  • Proposed designs: Two low-computational-complexity hybrid combiner designs are proposed for architectures A2, A3, and A4.The designs use constrained approximations based on feasible RF combiners and sparse reconstruction.
  • Dictionary-based designs: The A2 design uses a block-diagonal dictionary of steering vectors, treating the architecture as Lr lower-dimensional phased arrays.Each RF chain is connected to a subset of antennas, and the feasible combiner dictionary is constructed block by block.
  • Architecture trade-offs: A3 and A4 offer more flexibility and can increase effective antenna area and array gain relative to A5 and A6, but require greater complexity and power.Non-co-phased signal combining can nevertheless cause significant degradation.
  • Complexity limits: For A3, the feasible-combiner dictionary grows exponentially as 2^Nr, becoming intractable for higher Nr.Although Nd = 256 is reasonable for Nr = 8, the paper identifies reduced-dictionary selection as an open problem.

VI. SIMULATIONS

The simulations evaluate channel-estimation error and spectral-efficiency trade-offs for compressed-sensing and least-squares methods under different channel models and training strategies. Results favor sparse recovery in quantized sparse settings, while unquantized clustered channels expose support-recovery and sparsity limitations.

  • Evaluation setup: The evaluation measures channel-estimation MSE, achievable spectral efficiency, and spectral-efficiency–power-consumption trade-offs across hybrid architectures.The experiments summarize which estimation and combining algorithms apply to each architecture.
  • Training overhead: 256 measurements are required by exhaustive search for K = 4 paths, Lr = 4 RF chains, and Gr = Gt = 64.The comparison uses the same grid resolution and training-step budget for the proposed CS and LS schemes.
  • Quantized channel model: OMP achieves similar NMSE to exhaustive search and about 5 dB improvement over adaptive CS in the quantized-grid channel model.LS performs worst, with a large gap relative to the other methods.
  • Unquantized channel model: In the unquantized clustered channel model, OMP, adaptive CS, and exhaustive-search performance degrades, while LS maintains the same NMSE.The degradation is attributed to off-grid path angles and channel rank exceeding the number of discovered paths.
  • Estimator behavior: OMP maintains reasonable NMSE across the SNR range because its residual-based stopping criterion can retain sparsity while searching for more nonzero virtual-channel elements.Adaptive CS and exhaustive search do not scale well with SNR in the unquantized model.

B. Spectral efficiency with unconstrained precoding/combining and estimated channels

This section relates channel-estimation quality to achievable spectral efficiency using unconstrained precoding and combining based on estimated channels. Sparse recovery reaches near-optimal spectral efficiency with fewer training steps in the quantized model, whereas unquantized clustered channels require more measurements and reduce the OMP advantage.

  • Evaluation objective: NMSE alone does not directly capture the effect of channel-estimation error on achievable spectral efficiency, motivating a joint evaluation.The analysis therefore examines spectral efficiency as the final performance objective.
  • Simulation assumptions: The theoretical spectral-efficiency bound uses equal power allocation, Ns = Lr = 4 data streams, and unconstrained singular-vector precoding and combining.Hybrid-architecture constraints are excluded from this bound.
  • Unquantized channel model: For unquantized clustered channels, reconstruction is worse, the OMP–LS gap decreases, and more measurements are required for good reconstruction.The support cannot be perfectly recovered because of noise and insufficient sparsity.
  • Measurement designs: Random and deterministic designs perform similarly in MSE when sparsity is insufficient because both produce tight measurement matrices in noise.The deterministic design has lower mutual coherence, but this does not yield a large MSE difference in this regime.

C. Spectral efficiency with hybrid combining and estimated channels

The section compares six hybrid receiver architectures using estimated channels, evaluating spectral efficiency alongside hardware complexity and power consumption. Phase-shifter architectures offer high spectral efficiency, while switch-based designs provide favorable complexity and energy trade-offs.

  • Spectral efficiency: Around Lr = 6 RF chains are sufficient for the phase-shifter architecture A1 to achieve the channel capacity.A1 achieves the highest spectral efficiency and has a significant gap over the other architectures in the reported comparison.
  • Spectral efficiency: Antenna-selection architectures A5 and A6 achieve similar spectral efficiencies to A2, despite A6 having lower hardware complexity than A5.Their performance almost overlaps in the reported spectral-efficiency comparison.
  • Spectral efficiency: A3 and A4 do not provide significant spectral-efficiency improvement over simple hybrid antenna selection, while A4 gives the worst results in these simulations.The reported A4 result depends on the specific combining algorithm used, and near-optimal algorithms for A2, A3, and A4 remain an open problem.
  • Power-performance trade-offs: For equal power consumption, antenna-selection architectures A5 and A6 provide the highest bit rates, with only a small gap over A2 and A4.A1 and A3 become the most energy-inefficient architectures as the number of RF chains increases because their power consumption rises rapidly.
  • Evaluation setup: The evaluation compares six hybrid combining architectures using achievable spectral efficiency with estimated channels.The study applies hybrid combiner designs for phase-shifter and antenna-selection architectures under a common downlink channel setting.
  • Overall trade-offs: Switch-based receivers reduce power consumption per RF chain, allowing more RF chains at equal power consumption while maintaining close spectral efficiencies across architectures.The conclusion reports similar channel reconstruction across architectures and a reduction in required training steps when using more RF chains, at the expense of circuit power.
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