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Spectrum and Energy Efficient Beamspace MIMO-NOMA for Millimeter-Wave Communications Using Lens Antenna Array
Bichai Wang, Linglong Dai, Zhaocheng Wang, Ning Ge, Shidong Zhou
TL;DR
Existing beamspace MIMO reduces RF-chain needs but limits supported users to the RF-chain count. This paper integrates NOMA with beamspace MIMO, adds equivalent-channel ZF precoding and joint dynamic power allocation, and reports higher spectrum and energy efficiency than existing beamspace MIMO.
Problem
Existing beamspace MIMO can reduce RF-chain requirements but supports no more users than RF chains at the same time-frequency resources.
Method
The paper combines beamspace MIMO with NOMA, uses equivalent-channel ZF precoding, and jointly optimizes intra-beam and inter-beam power allocation.
Results
The proposed scheme achieves higher spectrum efficiency and about 25% higher energy efficiency than existing beamspace MIMO.
Takeaways & Limitations
Beamspace MIMO-NOMA supports more users than RF chains while improving spectrum and energy efficiency relative to existing beamspace MIMO.
Abstract
from arXiv · showhide
The recent concept of beamspace multiple input multiple output (MIMO) can significantly reduce the number of required radio-frequency (RF) chains in millimeter-wave (mmWave) massive MIMO systems without obvious performance loss. However, the fundamental limit of existing beamspace MIMO is that, the number of supported users cannot be larger than the number of RF chains at the same time-frequency resources. To break this fundamental limit, in this paper we propose a new spectrum and energy efficient mmWave transmission scheme that integrates the concept of non-orthogonal multiple access (NOMA) with beamspace MIMO, i.e., beamspace MIMO-NOMA. By using NOMA in beamspace MIMO systems, the number of supported users can be larger than the number of RF chains at the same time-frequency resources. Particularly, the achievable sum rate of the proposed beamspace MIMO-NOMA in a typical mmWave channel model is analyzed, which shows an obvious performance gain compared with the existing beamspace MIMO. Then, a precoding scheme based on the principle of zero-forcing (ZF) is designed to reduce the inter-beam interferences in the beamspace MIMO-NOMA system. Furthermore, to maximize the achievable sum rate, a dynamic power allocation is proposed by solving the joint power optimization problem, which not only includes the intra-beam power optimization, but also considers the inter-beam power optimization. Finally, an iterative optimization algorithm with low complexity is developed to realize the dynamic power allocation. Simulation results show that the proposed beamspace MIMO-NOMA can achieve higher spectrum and energy efficiency compared with existing beamspace MIMO.
I. INTRODUCTION
Beamspace MIMO reduces RF-chain requirements for mmWave massive MIMO, but existing systems cannot serve more users than RF chains. The paper proposes beamspace MIMO-NOMA to overcome this limit using power-domain multiplexing.
- RF components may consume up to 70% of total transceiver energy, making large RF-chain deployments costly and impractical.
- Beamspace MIMO uses a lens antenna array to reduce required RF chains without obvious performance loss.
- The proposed beamspace MIMO-NOMA combines beamspace MIMO with NOMA to support multiple users per beam and potentially exceed the RF-chain count.
- The paper develops achievable-sum-rate analysis, ZF-based precoding, and joint dynamic power allocation for intra-beam and inter-beam interference management.
- Existing beamspace MIMO supports at most one user per beam, so K ≤ NRF at the same time-frequency resources.
B. Proposed Beamspace MIMO-NOMA
Beamspace MIMO-NOMA assigns multiple users to each selected beam through NOMA, while accounting for intra-beam and inter-beam interference. SIC handles superposition interference, and beam precoding is designed to control cross-beam interference.
- More than one user can be simultaneously served within each selected beam in the proposed beamspace MIMO-NOMA scheme.
- The selected beams contain user sets Sn, allowing the simultaneously served user count K to be larger than the number of RF chains NRF.
- The received signal contains desired signal, intra-beam interference, inter-beam interference, and noise, motivating careful precoder design.
- Successive interference cancellation orders users by increasing equivalent channel gains so stronger users remove designated weaker-user signals.
- NOMA superposition creates intra-beam interference, while users also experience interference from other beams.
III. ACHIEVABLE SUM RATE
The paper derives user SINR and achievable rates after SIC, then sums these rates to obtain the beamspace MIMO-NOMA achievable sum rate under the assumed mmWave channel model.
- SIC removes detectable higher-index user signals from each user’s received signal according to equivalent channel-gain ordering.
- The post-SIC received signal yields the SINR for the mth user in the nth beam.
- The achievable rate of each user is obtained from its post-SIC SINR.
- The analysis assumes that the base station knows the beamspace channel, which can be estimated using compressive sensing with low pilot overhead.
- The achievable sum rate is formed by aggregating user rates and can be improved through careful precoder design.
IV. PRECODING IN DOWNLINK SYSTEMS
Because the number of users can exceed the number of beams, conventional beamspace-channel ZF is unavailable. The paper instead constructs an equivalent channel for each beam to generate ZF precoders.
- Conventional ZF cannot be directly applied when K ≥ NRF because the NRF × K beamspace-channel pseudo-inverse does not exist.
- The proposed solution determines an equivalent channel for each beam before generating its precoding vector.
- Two equivalent-channel constructions are considered: strongest-user-based and SVD-based methods.
A. The strongest user-based equivalent channel
The strongest user-based equivalent channel supports ZF precoding for suppressing inter-beam interference. After SIC, the first user in each beam can completely remove inter-beam interference.
- A. The strongest user-based equivalent channel: The LoS-dominated sparse beamspace channel motivates constructing an equivalent channel from the strongest user in each beam.The beamspace channel sparsity represents users’ directions, while LoS components primarily characterize mmWave multipath channels.
- A. The strongest user-based equivalent channel: The precoding matrix is generated and normalized to produce one precoding vector for each beam.The resulting nth-beam vector is normalized before transmission.
- A. The strongest user-based equivalent channel: The first user in each beam can completely remove inter-beam interference under the proposed precoding scheme.After SIC, its SINR is rewritten using the interference-suppressed received signal model.
B. SVD-based equivalent channel
When users within a beam are not sufficiently correlated, the paper forms an SVD-based equivalent channel using all users’ beamspace channel vectors, then applies ZF precoding and joint dynamic power optimization. The resulting iterative updates converge to a stationary solution under the transmitted-power constraint.
- B. SVD-based equivalent channel: The SVD-based scheme uses all users’ beamspace channel vectors in a beam when intra-beam channel correlation is insufficient.This setting is considered when the LoS component is absent or NLoS effects are significant.
- B. SVD-based equivalent channel: SVD decomposes each beam’s channel matrix into singular components, and the left singular vector associated with the maximum singular value generates the equivalent channel vector.The singular values are ordered non-increasingly before selecting the corresponding singular vector.
- B. SVD-based equivalent channel: ZF precoding is generated from the SVD-based equivalent channel matrix after forming and normalizing the precoding vectors.MMSE and Wiener-filter precoding are also feasible with the equivalent channel matrix.
- V. DYNAMIC POWER ALLOCATION: The proposed power allocation jointly optimizes intra-beam and inter-beam powers while allowing multiple users per beam.The objective is to maximize achievable sum rate while reducing both intra-beam and inter-beam interference.
- V. DYNAMIC POWER ALLOCATION: The optimization enforces nonnegative user powers, a maximum total transmitted power, and per-user minimum data rates.The nonlinear data-rate constraint is transformed into a linear constraint before reformulation.
- V. DYNAMIC POWER ALLOCATION: Because the objective is non-convex, the paper iteratively updates equalization coefficients, auxiliary variables, and user powers.Each subproblem is optimized in sequence using the reformulated objective and convex subproblems.
- V. DYNAMIC POWER ALLOCATION: The iterative algorithm produces a monotonically non-decreasing bounded objective sequence and converges to a stationary solution.Its stated complexity is O(TmaxK^2log2(δ)).
VI. SIMULATION RESULTS
The simulations evaluate the proposed beamspace MIMO-NOMA against fully digital MIMO, beamspace MIMO, and MIMO-OMA using typical mmWave massive MIMO settings. Results are reported for spectrum and energy efficiency.
- Simulation setup: The evaluation considers a downlink mmWave massive MIMO system with N = 256 antennas, K users, total transmitted power P = 32 mW, one LoS component, and L = 2 NLoS components.The compared schemes are fully digital MIMO, beamspace MIMO, MIMO-OMA, and the proposed beamspace MIMO-NOMA.
- Compared schemes: The study compares the proposed scheme with baselines that differ in RF-chain configuration and multiple-access strategy.Fully digital MIMO uses NRF = N, beamspace MIMO uses NRF = K with one user per beam, and MIMO-OMA allocates orthogonal frequency resources to conflicting users.
A. Spectrum Efficiency
The proposed beamspace MIMO-NOMA improves spectrum efficiency over beamspace MIMO and MIMO-OMA, with gains that become larger as the number of users increases. A low-complexity strongest-user equivalent channel provides similar performance to the SVD-based alternative.
- Equivalent-channel precoding: The strongest-user equivalent channel and SVD-based equivalent channel achieve similar spectrum-efficiency results, supporting low-complexity precoding without SVD in subsequent simulations.The similarity is attributed to strong correlation among beamspace channels in the same beam.
- Metric definition: Spectrum efficiency is defined as the achievable sum rate when normalized bandwidth is considered.The definition refers to achievable sum rate Rsum.
- Spectrum efficiency versus SNR: About 3 dB SNR gain is achieved by beamspace MIMO-NOMA compared with beamspace MIMO for K = 32.The gain is attributed to NOMA serving multiple users in each beam.
- Spectrum efficiency versus SNR: Beamspace MIMO-NOMA achieves higher spectrum efficiency than beamspace MIMO and MIMO-OMA.Fully digital MIMO achieves the best spectrum efficiency in the comparison because it uses NRF = N RF chains and does not perform beam selection.
- Spectrum efficiency versus users: As K increases at SNR = 10 dB, the performance gap between beamspace MIMO-NOMA and beamspace MIMO becomes larger.The larger gap is associated with the increasing probability that different users select the same beam.
B. Energy Efficiency
Energy efficiency is defined as achievable sum rate divided by total power consumption.
- Metric definition: Energy efficiency ε is the ratio between the achievable sum rate Rsum and total power consumption.This definition measures efficiency using both the communication rate and the system's power consumption.
P + NRFPRF + NRFPSW + PBB
The energy-efficiency results favor beamspace MIMO-NOMA across SNR and user-count settings, while iterative power allocation stabilizes after approximately 10 iterations.
- Energy efficiency versus SNR: About 25% energy efficiency improvement is achieved by beamspace MIMO-NOMA compared with existing beamspace MIMO for K = 32.The comparison is reported for energy efficiency against SNR.
- Energy-efficiency comparison: Beamspace MIMO-NOMA achieves higher energy efficiency than fully digital MIMO because it uses far fewer RF chains than the number of antennas.The comparison adopts PRF = 300 mW per RF chain, making RF-chain consumption a major difference between the schemes.
- Energy efficiency versus users: Beamspace MIMO-NOMA remains more energy efficient than all three other schemes even when 50 users are simultaneously served.This result is reported for energy efficiency against the number of users at SNR = 10 dB.
C. Convergence of power allocation
The proposed iterative power allocation algorithm converges, with spectrum efficiency becoming stable after 10 iterations under K = 32 users and SNR = 10 dB.
- C. Convergence of power allocation: 10 iterations are sufficient for spectrum efficiency to become stable in the convergence evaluation.The setting uses K = 32 users and SNR = 10 dB.
- C. Convergence of power allocation: The convergence experiment evaluates the iterative power allocation algorithm proposed in Section V.
- C. Convergence of power allocation: The observed stabilization verifies the algorithm’s convergence as discussed in Section V.
D. The user fairness
The proposed beamspace MIMO-NOMA scheme supports user rates above the minimum constraint while allowing more users than RF chains and improving spectrum and energy efficiency over beamspace MIMO.
- D. The user fairness: Each user achieves a data rate larger than Rmin = 1 bit/s/Hz under K = 32 users and SNR = 20 dB.This follows from the per-user data-rate constraint C3 in (23).
- VII. CONCLUSIONS: The scheme can support more users than RF chains, unlike existing beamspace MIMO systems.
- VII. CONCLUSIONS: 25% energy efficiency gain can be achieved compared with existing beamspace MIMO.The conclusion also reports better spectrum efficiency.