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Reliable Beamspace Channel Estimation for Millimeter-Wave Massive MIMO Systems with Lens Antenna Array

Xinyu Gao, Linglong Dai, Shuangfeng Han, Chih-Lin I, Xiaodong Wang

arXiv:1707.07624v2cs.IT

TL;DR

The paper addresses accurate beamspace channel estimation under large beamspace dimensions and limited RF chains. It formulates estimation as sparse recovery, proposes support detection using beamspace structure, and reports reliable low-overhead accuracy, including in low-SNR settings.

  • Problem

    Accurate beamspace channel information is difficult to acquire because the beamspace channel is large while the number of RF chains is limited.

  • Method

    The paper designs an adaptive selecting network, formulates beamspace estimation as sparse signal recovery, and estimates channel supports using structural characteristics with support detection.

  • Results

    The proposed scheme achieves low pilot overhead, low complexity, and higher or comparable support-detection and NMSE accuracy than conventional schemes, including in low-SNR regions.

  • Takeaways & Limitations

    Exploiting beamspace channel structure makes support detection attractive for reliable beamspace channel estimation in lens-array mmWave massive MIMO systems.

Abstract

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Millimeter-wave massive MIMO with lens antenna array can considerably reduce the number of required radio-frequency (RF) chains by beam selection. However, beam selection requires the base station to acquire the accurate information of beamspace channel. This is a challenging task, as the size of beamspace channel is large while the number of RF chains is limited. In this paper, we investigate the beamspace channel estimation problem in mmWave massive MIMO systems with lens antenna array. Specifically, we first design an adaptive selecting network for mmWave massive MIMO systems with lens antenna array, and based on this network, we further formulate the beamspace channel estimation problem as a sparse signal recovery problem. Then, by fully utilizing the structural characteristics of mmWave beamspace channel, we propose a support detection (SD)-based channel estimation scheme with reliable performance and low pilot overhead. Finally, the performance and complexity analyses are provided to prove that the proposed SD-based channel estimation scheme can estimate the support of sparse beamspace channel with comparable or higher accuracy than conventional schemes. Simulation results verify that the proposed SD-based channel estimation scheme outperforms conventional schemes and enjoys satisfying accuracy, even in the low SNR region as the structural characteristics of beamspace channel can be exploited.

I. INTRODUCTION

mmWave massive MIMO offers higher data rates but faces prohibitive RF-chain cost and energy consumption as antenna counts grow. Lens antenna arrays and an SD-based estimator are introduced to reduce RF requirements and estimate beamspace channels with low pilot overhead.

  • mmWave massive MIMO can increase data rates through wider bandwidth and higher spectral efficiency, but practical implementation is challenging.
  • 256 antennas can require 64 Watts for RF chains, motivating lens antenna arrays to reduce the required number of RF chains.The cited example compares about 250 mW per mmWave RF chain with 30 mW at cellular frequencies.
  • Beam selection requires accurate large beamspace-channel information despite limited RF chains, making low-overhead estimation difficult.
  • The paper designs an adaptive selecting network that measures the beamspace channel and formulates estimation as sparse signal recovery.The network uses a small number of 1-bit phase shifters and can select beams for transmission or combine measurements for estimation.
  • The SD-based scheme detects each sparse channel component’s support, estimates its nonzero elements, removes its influence, and repeats across components.
  • The proposed scheme is reported to provide more accurate support detection than classical CS algorithms, with low complexity and satisfying accuracy at low SNR.

B. MmWave massive MIMO with lens antenna array

A lens antenna array transforms the spatial-domain channel into a sparse beamspace channel using orthogonal beams. Selecting only a small set of beams reduces RF-chain requirements while retaining performance without obvious loss.

  • The lens antenna array acts as an N × N spatial DFT matrix whose orthogonal beams cover the entire spatial direction range.
  • The resulting beamspace channel is sparse because mmWave propagation has a limited number of dominant scatterers.
  • Beam selection chooses a small set of appropriate beams from the sparse beamspace channel to reduce the MIMO-system dimension.
  • The lens-array architecture can significantly reduce required RF chains without obvious performance loss; the paper considers N_RF = K for K users.
  • Estimating the large beamspace channel with low pilot overhead remains challenging because the number of RF chains is limited.

III. BEAMSPACE CHANNEL ESTIMATION

The channel-estimation section combines pilot transmission, an adaptive selecting network, and SD-based recovery to estimate the beamspace channel with reliable performance and low pilot overhead.

  • The proposed workflow introduces pilots, designs an adaptive selecting network for efficient beamspace-channel measurements, and applies SD-based estimation.

A. Pilot transmission

The uplink pilot strategy uses orthogonal user pilots over channel-coherence intervals, producing noisy beamspace measurements for channel estimation. The channel is assumed unchanged across the Q pilot instants.

  • All users transmit known pilot sequences over Q instants while the beamspace channel remains unchanged during the channel coherence time.
  • The Q instants are divided into M blocks of K instants, so each block uses a K × K pilot matrix of mutually orthogonal pilot sequences.
  • For each block, the received uplink signal follows the beamspace-channel model with the pilot matrix and an additive noise matrix.
  • The noise entries are independent identically distributed complex Gaussian variables with variance σ^2_UL, and 1/σ^2_UL represents uplink SNR under normalized pilot power.

B. Adaptive selecting network

The paper replaces switch-based beam selection with an adaptive network of 1-bit phase shifters that supports both beam selection and channel-estimation combining. This enables beamspace channel estimation to be formulated as sparse signal recovery with fewer pilot symbols.

  • B. Adaptive selecting network: The channel-estimation measurements are formed by combining received uplink signals across pilot-transmission blocks.The combiner Wm has dimensions K × N, and the resulting baseband observations are sampled by K RF chains.
  • B. Adaptive selecting network: The proposed adaptive selecting network uses 1-bit phase shifters and can operate as either a beam selector or analog combiner.It replaces the selecting network with switches and supports adaptive combining during uplink channel estimation.
  • B. Adaptive selecting network: Using the adaptive network, the beamspace channel is cast as a sparse signal recovery problem with pilot count Q potentially much smaller than N.This reduces pilot symbols at the cost of some SNR loss.
  • B. Adaptive selecting network: A Bernoulli random matrix is selected for the analog combiner because its equal-amplitude ±1 entries suit 1-bit phase shifters.The design targets low mutual coherence while reducing phase-shifter cost and energy consumption.

C. SD-based channel estimation

The SD-based estimator exploits structural properties of beamspace channel components to detect supports reliably, estimate their nonzero values, and limit error propagation. It is designed for low-SNR operation while retaining low pilot overhead and complexity.

  • C. SD-based channel estimation: Classical CS support detection can become inaccurate at low SNR, so the proposed SD scheme uses beamspace channel structure to improve support detection.The paper specifically contrasts the proposed method with OMP and CoSaMP under noise-dominated conditions.
  • C. SD-based channel estimation: As N grows, distinct beamspace channel components become approximately orthogonal, allowing the total estimation problem to decompose into independent component-wise subproblems.The cited result applies to large lens antenna arrays, such as N = 256.
  • C. SD-based channel estimation: The proposed 1-bit phase-shifter network may be somewhat complicated to realize in practice, although switches can replace it if some performance loss is acceptable.The estimation scheme can then be used without modification.
  • C. SD-based channel estimation: Each component is treated as sparse because most of its power is concentrated in a small number of dominant beamspace elements.The structural model places the strongest elements around the strongest element, with support size V.
  • C. SD-based channel estimation: The iterative algorithm detects only the strongest element, infers the component support, estimates its nonzero entries by least squares, and removes its influence before proceeding.After all components are processed, the total support and original measurements are used for a final channel estimate, reducing error propagation.
  • C. SD-based channel estimation: Estimating additional nonzero elements can help identify selected beams and suppress multi-user interference without requiring more pilot symbols.The trade-off is slightly increased computational complexity.

D. Performance analysis of SD-based channel estimation

The analysis shows that SD-based estimation detects beamspace-channel support through the strongest element and structural sparsity, with accuracy improving as effective SNR and pilot symbols increase. Compared with classical CS methods, it is expected to provide more accurate support detection.

  • Support-detection accuracy: SD-based estimation determines support-detection accuracy primarily through correctly locating the strongest beamspace-channel element.The analysis evaluates the probability that the strongest element’s position is correctly estimated.
  • Scope of analysis: The analytical conclusions also extend to NLoS components, with only the expressions of η and κ changing.The text states that this extension is verified in Appendix A.
  • Pilot and SNR effects: For large pilot-symbol counts, the effective SNR parameter increases, leading to a higher probability of correctly estimating the strongest element.The analysis attributes this trend to a smaller mutual-coherence-related term when Q is large.
  • Support-detection accuracy: Once the strongest element is located, SD-based estimation directly obtains the remaining nonzero positions from the channel structure.This makes the probability of recovering the complete support depend on the strongest-element detection event.
  • Comparison with classical CS: Classical CS methods become less reliable for weaker elements because their probability of correctly estimating an element’s position decreases as its amplitude decreases.The analysis links weaker amplitudes to a decrease in the relevant detection probability.
  • Comparison with classical CS: The proposed algorithm is expected to detect support more accurately than classical CS algorithms, as illustrated by its segmented performance curve.The segments arise because each channel component is treated independently.

E. Complexity analysis of SD-based channel estimation

The proposed SD-based estimator has low complexity because its main operations involve inner products, least-squares estimation, and interference removal, while the relevant structural dimensions are usually small. Its complexity is therefore comparable to LS and can require fewer pilots than beam-scanning SMD.

  • Complexity components: The main complexity contributions arise from steps 1, 3, 5, and 8 of the proposed SD-based estimation algorithm.These steps perform inner-product computation, least-squares estimation, channel-component removal, and another least-squares estimation.
  • Complexity components: Step 1 computes N inner products between Q × 1 vectors with complexity O(QN).
  • Complexity bound: The overall SD-based estimation complexity is concluded to be quite low and comparable to that of the LS algorithm.The conclusion follows from the small values typically associated with L_k and V.
  • Complexity bound: The detected support satisfies Card(S_T) ≤ V L_k, and L_k and V are usually small.This bounds the support dimension used in the final estimation stage.
  • Comparison with SMD: SMD has lower complexity because it directly obtains a dimension-reduced beamspace channel by scanning all beams, whereas SD further reduces pilot symbols using compressive-sensing tools.SMD still requires a number of pilot symbols proportional to N, which can be large, such as N = 256.

IV. SIMULATION RESULTS

Simulations compare SD-based channel estimation with SMD- and OMP-based schemes for NMSE, pilot overhead, and IA beam-selection sum rate. SD achieves accuracy close to SMD with fewer instants, performs especially well against OMP at low uplink SNR, and improves low-SNR beam-selection performance.

  • Simulation setup: The simulations use a 256-antenna lens array, 16 RF chains, and 16 users, with two NLoS components per user.The uplink and downlink SNRs are defined through the corresponding noise variances.
  • NMSE performance: SD-based and OMP-based estimation use Q = 96 instants, whereas SMD-based estimation uses Q = N = 256 instants.For SD, V = 8 strongest elements are retained per channel component; OMP uses sparsity level 24.
  • NMSE performance: SD with Q = 96 achieves NMSE close to SMD with Q = N = 256 and higher accuracy than OMP when uplink SNR is below 15 dB.At high uplink SNR, the performance gap between SD and OMP becomes smaller.
  • Pilot overhead: At uplink SNR 10 dB, achieving NMSE 5 × 10^-2 requires Q = 190 for OMP but only Q = 120 for SD.The results also indicate that SD requires fewer instants than SMD, whose requirement is Q ≥ N = 256.
  • IA beam selection: IA beam selection with SD-based estimation achieves better sum rate than with OMP-based estimation, especially at low uplink SNR.At moderate uplink SNR such as 10 dB, SD approaches the sum-rate performance obtained with perfect CSI.
  • IA beam selection: When downlink SNR reaches about 40 dB, IA beam-selection sum rates saturate because channel-estimation error dominates noise.This saturation occurs across the considered channel-estimation schemes.
  • IA beam selection: At high uplink SNR, SMD-based estimation can outperform SD, while SD slightly outperforms SMD at uplink SNR 0 dB.SMD scans all beams and can estimate weak beams accurately, but its unsuppressed noise makes strong-beam selection suboptimal at low uplink SNR.

V. CONCLUSIONS

The paper develops adaptive beamspace channel estimation for lens-array mmWave massive MIMO by combining an adaptive selecting network with support detection. Analyses and simulations report accurate, low-complexity estimation with reduced pilot overhead, especially at low SNR.

  • V. CONCLUSIONS: The adaptive selecting network converts beamspace channel estimation into a sparse signal recovery problem.The network uses a small number of 1-bit phase shifters and functions as a beam selector for data transmission and a combiner for channel estimation.
  • V. CONCLUSIONS: The proposed SD-based scheme exploits beamspace-channel structure to reduce pilot overhead while detecting sparse-channel support accurately.The paper reports higher support-detection accuracy than classical compressive-sensing algorithms.
  • V. CONCLUSIONS: Complexity analysis shows that SD-based estimation has low complexity comparable to least-squares estimation.Simulation results report much better NMSE than conventional schemes, including in the low-SNR region.
  • V. CONCLUSIONS: Future work will extend SD-based channel estimation to scenarios where users employ multiple antennas.

APPENDIX A PROOF OF LEMMA 3

The appendix proves Lemma 3 by bounding noise-related terms under a complex Gaussian uplink-noise assumption and combining those bounds with structural properties of the beamspace channel. The result lower-bounds correct detection of the strongest channel element and extends to NLoS components.

  • APPENDIX A PROOF OF LEMMA 3: Lemma 4 assumes a complex Gaussian uplink noise vector and establishes a bound involving σ²_UL, α, and ln N.
  • APPENDIX A PROOF OF LEMMA 3: The proof uses columns of the combiner matrix and the condition Q < N to derive the Lemma 4 bound.
  • APPENDIX A PROOF OF LEMMA 3: The lower and upper bounds rely on the triangle inequality, an assumption on the combiner, and the structural characteristic established in Lemma 2.
  • APPENDIX A PROOF OF LEMMA 3: Combining the bounds yields a lower bound on the probability that the strongest beamspace-channel element is correctly located.
  • APPENDIX A PROOF OF LEMMA 3: The Lemma 3 conclusions extend to NLoS components because the channel components are approximately orthogonal.
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