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Electromagnetic Lens-focusing Antenna Enabled Massive MIMO: Performance Improvement and Cost Reduction
Yong Zeng, Rui Zhang, Zhi Ning Chen
TL;DR
Massive MIMO’s large antenna arrays improve wireless communication but increase hardware and signal-processing costs. This paper integrates an EM lens with the array to focus energy and reject spatial interference, analytically demonstrating strictly improved average uplink SNR while enabling substantial cost reductions with slight performance degradation.
Problem
Massive MIMO requires very large antenna arrays whose hardware, energy, and processing costs can undermine practical deployment.
Method
The paper proposes EM-lens enabled MIMO together with small-MIMO processing and channel-covariance-based antenna selection.
Results
The EM-lens enabled system strictly improves average received SNR through energy focusing and spatial interference rejection, while enabling substantial cost reductions with slight performance degradation.
Takeaways & Limitations
The design combines EM-lens performance gains with reduced signal-processing complexity, RF-chain requirements, hardware costs, and energy consumption.
Abstract
from arXiv · showhide
Massive multiple-input multiple-output (MIMO) techniques have been recently advanced to tremendously improve the performance of wireless communication networks. However, the use of very large antenna arrays at the base stations (BSs) brings new issues, such as the significantly increased hardware and signal processing costs. In order to reap the enormous gain of massive MIMO and yet reduce its cost to an affordable level, this paper proposes a novel system design by integrating an electromagnetic (EM) lens with the large antenna array, termed the EM-lens enabled MIMO. The EM lens has the capability of focusing the power of an incident wave to a small area of the antenna array, while the location of the focal area varies with the angle of arrival (AoA) of the wave. Therefore, in practical scenarios where the arriving signals from geographically separated users have different AoAs, the EM-lens enabled system provides two new benefits, namely energy focusing and spatial interference rejection. By taking into account the effects of imperfect channel estimation via pilot-assisted training, in this paper we analytically show that the average received signal-to-noise ratio (SNR) in both the single-user and multiuser uplink transmissions can be strictly improved by the EM-lens enabled system. Furthermore, we demonstrate that the proposed design makes it possible to considerably reduce the hardware and signal processing costs with only slight degradations in performance. To this end, two complexity/cost reduction schemes are proposed, which are small-MIMO processing with parallel receiver filtering applied over subgroups of antennas to reduce the computational complexity, and channel covariance based antenna selection to reduce the required number of radio frequency (RF) chains. Numerical results are provided to corroborate our analysis.
I. INTRODUCTION
The paper proposes EM-lens enabled MIMO to address the hardware, energy, and processing costs of massive MIMO while preserving its communication gains. The design focuses incident energy according to users’ AoAs, improving uplink SNR and supporting lower-cost processing and RF-chain configurations.
- Motivation: Massive MIMO improves wireless performance but large antenna arrays create high hardware, energy, and signal-processing costs.RF elements are required at each transmit/receive antenna, while advanced processing can have cubic complexity in the antenna count.
- Proposed design: The paper integrates an electromagnetic lens with a large antenna array, forming the EM-lens enabled MIMO system.The lens can be fabricated from dielectric material with curved surfaces and is integrated with the antenna array as a single part.
- Proposed design: The EM lens focuses incident signal energy onto a smaller antenna region, with the focused spatial distribution determined by the signal’s angle of arrival.As the incident angle changes from 0° to 30°, the strongest E-field location sweeps accordingly.
- Performance benefits: Under imperfect channel estimation in single-cell multiuser uplink transmission, majorization analysis shows performance gains over systems without the lens.The single-user gain comes from energy focusing, while multiuser gains additionally arise when sufficiently separated AoAs enable spatial interference rejection.
- Complexity and cost reduction: The EM-lens enabled system supports lower-cost operation through small-MIMO processing and channel-covariance-based antenna selection.Parallel MMSE filtering over antenna subgroups reduces computational complexity, while covariance-based selection reduces RF chains and avoids excessive instantaneous-channel training.
II. SYSTEM MODEL
The system model describes multiuser uplink transmission to a ULA and extends it with an AoA-dependent EM lens that focuses received power onto a small antenna subset. The channel model accommodates spatially correlated and i.i.d. fading while preserving total received energy.
- K single-antenna users simultaneously transmit independent messages to a BS equipped with an M-element uniform linear array.
- Each user’s signal arrives through L_k plane-wave paths with AoAs decomposed into a nominal user-dependent angle and path offsets.The offsets follow a power azimuth spectrum with angular spread σ_φ.
- With zero angular spread, antenna signals are completely correlated, whereas sufficiently separated elements yield i.i.d. channels when angular spread is nonzero.Thus, the model covers both spatially correlated and i.i.d. channel scenarios.
- The EM lens modifies each user’s channel through an AoA-dependent power distribution that concentrates energy on at most 2∆+1 antennas.The power peak shifts along the array as AoA increases, and the distribution is normalized to preserve total power.
- The EM-lens channel covariance is altered by the power distribution and user AoA, while the total signal energy remains unchanged for the same array aperture.The no-lens model is recovered by setting a(θ_k)=1, equivalently A(θ_k)=I_M.
III. UPLINK CHANNEL ESTIMATION AND ACHIEVABLE RATE
The BS estimates instantaneous uplink channels through pilot-assisted training while treating channel covariance matrices as known slowly varying statistics. MMSE estimation separates the channel estimate from its error through their orthogonality.
- A. Channel Estimation: The BS assumes the channel covariance matrices are perfectly known because second-order statistics vary slowly and are relatively easy to estimate.
- A. Channel Estimation: Instantaneous channel vectors are estimated from uplink training over τ symbol durations within each coherent block.
- A. Channel Estimation: To estimate each user’s channel, the BS projects the received training matrix onto that user’s pilot sequence and rescales the resulting sufficient statistic.
- A. Channel Estimation: The training observation contains received pilot signals and additive noise, with training quality controlled by the training SNR ρ_tr.
- A. Channel Estimation: MMSE estimation decomposes each channel into an estimate and an uncorrelated estimation error.Because the channel is CSCG distributed, both components have corresponding Gaussian distributions.
B. Achievable Rate
The achievable-rate analysis models uplink detection with imperfect channel estimates and evaluates performance using average received SNR. It compares systems with and without the EM lens for finite-dimensional single-user and multiuser settings.
- B. Achievable Rate: After training, users transmit uplink data, and the BS applies a linear filter to detect each user’s signal amid estimation errors, interference, and noise.
- B. Achievable Rate: The achievable rate uses a worst-case uncorrelated-noise bound in which only the desired estimated-channel term is treated as signal.
- B. Achievable Rate: The MMSE filter maximizes the instantaneous received SNR, whose corresponding maximum is used in the achievable-rate analysis.
- B. Achievable Rate: Because finite-dimensional rates are difficult to characterize directly, the analysis adopts average received SNR and compares MIMO systems with versus without the EM lens.
- B. Achievable Rate: The average-SNR lower bound depends on the users’ channel covariance matrices and is analyzed for both single-user and multiuser uplink configurations.
A. Single-User System
The single-user analysis shows that EM-lens energy focusing can strictly improve average received SNR under finite-power conditions, while the benefit depends on channel structure and power regime.
- Performance analysis: For finite training and data powers, the EM-lens system achieves strictly higher average received SNR when its covariance eigenvalues strictly majorize those of the conventional system.The result follows from strict Schur-convexity and applies when the eigenvalue vectors are not permutations.
- Limitations and boundary cases: The single-user gain vanishes when training or data power tends to infinity, and also under the stated LOS channel condition.In LOS, complete antenna correlation makes focusing onto one subset ineffective for average received SNR.
- Performance analysis: With ideal focusing in a non-LOS channel, transmit power can scale as 1/M without average-SNR loss despite imperfect CSI.This scaling contrasts with the conventional system discussed in the paper.
- Performance analysis: For spatially uncorrelated channels, any nonuniform EM-lens power distribution improves average received SNR.The paper attributes this benefit to uneven power distribution during channel estimation and data transmission.
- Performance analysis: Under low SNR with non-LOS channels, practical EM-lens focusing yields higher average received SNR even with spatially correlated channels.The condition is ρd + ρtr ≪ 1/(βM).
B. Multiuser System
In the multiuser uplink, EM-lens focusing improves performance through both desired-signal concentration and spatial separation of interference, especially when users’ AoAs are sufficiently separated.
- Performance analysis: For spatially uncorrelated multiuser channels, Theorem 2 establishes a strict performance gain for each user under the stated power-distribution conditions.The theorem compares the EM-lens and conventional systems through their covariance structures.
- Spatial interference rejection: Sufficiently separated AoAs can produce non-overlapping antenna support sets, enabling ideal spatial interference rejection.The stated separation condition is |m⋆(θk) − m⋆(θu)| ≥ 2∆ + 1 for all users.
- Performance gains: Multiuser gains arise from two factors: energy focusing of desired signals and spatial separation of interfering signals.The single-user gain is attributed only to desired-signal energy focusing.
- Performance gains: Unlike the single-user gain, the multiuser performance gain persists even as training or data transmit power tends to infinity.The paper attributes this persistence to spatial interference rejection.
- Complexity and cost reduction: The proposed system supports two reduction strategies: subgroup-based small-MIMO processing for signal-processing complexity and covariance-based antenna selection for RF-chain costs.Antenna selection also reduces hardware and energy consumption costs.
A. Small-MIMO Processing
Small-MIMO processing divides the antenna array into groups, performs filtering in parallel, and combines group outputs to reduce receiver complexity while preserving performance under ideal grouping.
- Scheme and complexity: The proposed scheme’s dominant matrix-inversion cost is reduced to an order determined by the subgroup dimensions rather than the full array.The paper identifies the group-wise matrix inversion as the main computational cost.
- Ideal grouping: Under ideal grouping, the EM-lens covariance matrices become block diagonal because each user’s focused antennas lie within one group.This structure enables separate group processing.
- Performance: With ideal antenna grouping, small-MIMO processing achieves the same performance as the full-scale MMSE receiver.The equivalence holds under Assumption 1 and the specified grouping condition.
- Practical grouping: When ideal grouping is unavailable because interference couples antennas across groups, simulations report marginal performance loss for sufficiently separated user AoAs.This is an empirical result for the general grouping scenario.
B. Channel Covariance Based Antenna Selection
Channel covariance based antenna selection reduces RF-chain requirements by selecting a smaller antenna subset using second-order channel statistics rather than instantaneous CSI for every antenna.
- Trade-offs: Using fewer RF chains can reduce hardware and energy costs, but conventional sequential estimation with N < M chains increases training time by a factor M/N.The paper notes that reduced training time for data transmission can compromise spectral efficiency.
- Motivation: Antenna selection reduces the number of required RF chains from M to N when N is much smaller than M.Only the selected subset processes the received signals.
- Covariance-based selection: The proposed selection scheme uses channel covariance matrices, so instantaneous channel estimation is required only for selected antennas.The method is designed for EM-lens channels whose covariances vary with AoA-dependent focusing.
- Selection algorithm: A greedy antenna-selection algorithm is proposed because exhaustive search becomes costly for large M and moderate N.The algorithm incrementally builds the selected set until it contains N antennas.
A. Single-User System
The EM-lens enabled system improves uplink performance through energy focusing and spatial interference rejection, while enabling lower-complexity processing and fewer active RF chains.
- Single-user performance: The EM-lens enabled system strictly outperforms the conventional system in average received SNR at all training-SNR values, although the single-user gap narrows at high ρtr.The gain is more pronounced when training power is low because focused training energy improves channel estimation for dominant antenna elements.
- Multiuser performance: In multiuser reception, covariance-based lower bounds closely match actual SNR for the EM-lens system because ignoring other users’ instantaneous channels causes little performance loss.Without the lens, severe interference across antennas makes instantaneous channel knowledge of all users important for suppression.
- Multiuser performance: The EM-lens enabled system achieves higher sum rate for every number of UTs, with larger gains as K increases because spatial interference rejection becomes more effective.For both systems, sum rate increases more slowly at larger K as inter-user interference limits further improvement.
- Complexity reduction: Small-MIMO processing causes marginal performance loss with the EM lens and can outperform conventional full-scale MMSE processing.The conventional system incurs significant rate loss from the same grouped processing.
- RF-chain reduction: With covariance-based antenna selection, the EM-lens system achieves 81% or 57% rate gains at N = 15 or N = 20, respectively.More than 99% of maximum rate requires 30 active antennas with the lens versus almost all 50 without it; 20 lens-enabled antennas match the 50-antenna conventional sum rate.
VII. CONCLUSION AND FUTURE WORK
The paper integrates an EM lens with a large antenna array to improve uplink performance and reduce processing and hardware costs. It analytically establishes SNR gains and proposes reduced-complexity receiver and antenna-selection techniques.
- Core design: The EM-lens enabled MIMO design integrates an EM lens with a large antenna array to provide energy focusing and spatial interference rejection.The lens focuses desired-signal energy and rejects interference according to users’ AoAs.
- Analytical results: Under imperfect channel estimation from uplink training, the EM-lens enabled system strictly improves average received SNR.The paper attributes single-user gains to energy focusing and adds spatial-interference-rejection gains in multiuser transmission.
- Cost reduction: Small-MIMO processing is proposed as a multiuser receiver to reduce signal-processing complexity.The receiver is designed as a reduced-complexity technique for the EM-lens enabled system.
- Cost reduction: Channel covariance-based antenna selection is proposed to reduce the number of required RF chains, hardware, and energy costs.Simulation results are presented to validate the analysis and demonstrate the potential advantages of the design.
APPENDIX A
Appendix A introduces majorization and Schur-convexity tools used to establish analytical comparisons of antenna power distributions and received SNR.
- Majorization theory: Majorization defines a preorder between vectors, and Schur-convex functions preserve that ordering.These concepts provide the mathematical basis for comparing power distributions.
- Schur-convexity lemmas: The appendix states lemmas giving sufficient conditions for scalar and matrix-derived functions to be Schur-convex.The conditions involve convexity, ordered gradients, and inequalities among matrix entries.
- Single-user covariance: For a LOS single-user channel without the EM lens, the covariance matrix is rank one and has only one non-zero eigenvalue.This characterization supports subsequent bounds involving the maximum eigenvalue and low-SNR simplifications.
- Analytical comparison: Lemma 6 establishes a strict received-SNR inequality in the low-SNR non-LOS regime when the power distribution is nonuniform.The proof uses Schur-convexity and majorization after relating the relevant covariance matrices and power vectors.
- Scope of the lemma: The appendix notes that Lemma 6 requires the peak power location at the ULA center, which may fail when θ ≠ 0.A subsequent construction relates the off-center case to the centered formulation.
APPENDIX D
Appendix D formulates average SNR through desired-signal and interference power distributions, then uses Schur-convexity and majorization to compare EM-lens and conventional systems.
- Power distributions: For a user in the EM-lens system, the effective received-power vector includes the AoA-dependent focusing factor a_m(θ_k).The corresponding conventional-system vectors omit this lens-dependent factor.
- SNR formulation: The average SNR expressions are represented by a function ψ of desired-signal and interference-related vectors for both systems.The comparison reduces to proving two inequalities under the stated condition.
- Proof strategy: Schur-convexity of ψ with respect to the desired-signal vector yields the first comparison inequality.The argument invokes the identical-entry structure of κ and a Schur-convexity lemma.
- Proof strategy: The second comparison follows by ordering the vectors, defining a Schur-convex function on the ordered domain, and applying majorization.The proof uses the implication ξ_m < ξ_n ⇒ κ_m ≥ κ_n and permutation-invariant majorization.