Source-linked AI summary
Hybrid Block Diagonalization for Massive Multiuser MIMO Systems
Weiheng Ni, Xiaodai Dong
TL;DR
Massive MU-MIMO can reduce RF-chain counts below antenna counts, but doing so while retaining high-capacity multiuser processing is challenging. The paper proposes Hy-BD, which uses phase-only RF precoding and combining to harvest array gain before digital block diagonalization on an equivalent baseband channel. Across Rayleigh and mmWave settings, simulations report capacity close to or sometimes higher than traditional BD with lower implementation and computational cost.
Problem
Conventional massive MU-MIMO implementations can require RF chains matching the antenna count, creating high implementation cost, while multiple-antenna-user hybrid RF design was not available in prior work.
Method
Hy-BD uses phase-only RF precoding and combining to harvest array gain, then performs low-dimensional digital block diagonalization on the equivalent baseband channel.
Results
Hy-BD achieves capacity close to, and sometimes higher than, full-complexity traditional BD with lower implementation and computational cost.
Takeaways & Limitations
Hy-BD is presented as a promising practical option for massive MU-MIMO systems with limited RF chains.
Abstract
from arXiv · showhide
For a massive multiple-input multiple-output (MIMO) system, restricting the number of RF chains to far less than the number of antenna elements can significantly reduce the implementation cost compared to the full complexity RF chain configuration. In this paper, we consider the downlink communication of a massive multiuser MIMO (MU-MIMO) system and propose a low-complexity hybrid block diagonalization (Hy-BD) scheme to approach the capacity performance of the traditional BD processing method. We aim to harvest the large array gain through the phase-only RF precoding and combining and then digital BD processing is performed on the equivalent baseband channel. The proposed Hy-BD scheme is examined in both the large Rayleigh fading channels and millimeter wave (mmWave) channels. A performance analysis is further conducted for single-path channels and large number of transmit and receive antennas. Finally, simulation results demonstrate that our Hy-BD scheme, with a lower implementation and computational complexity, achieves a capacity performance that is close to (sometimes even higher than) that of the traditional high-dimensional BD processing.
I. INTRODUCTION
Massive MU-MIMO can approach high capacity with simple processing but conventional implementations require many costly RF chains. The paper proposes Hy-BD, using limited-chain hybrid processing for multi-antenna users and targeting comparable capacity at lower cost.
- Massive MIMO uses large antenna arrays to provide array gain, but conventional processing may require hundreds of RF chains matching the antenna count.
- Hybrid processing combines high-dimensional phase-only RF control with low-dimensional digital baseband processing under limited RF-chain constraints.
- Existing hybrid MU-MIMO studies primarily address single-antenna users or leave analog RF processing undesigned for multiple-antenna users.
- Hy-BD designs RF combiners from DFT bases and a BS RF precoder from the phases of an aggregate intermediate channel for multiple-antenna users and multiple streams.
- Hy-BD offers low implementation and computational complexity, applies to Rayleigh and mmWave channels, requires CSI rather than individual path information, and reduces RF-domain feedback overhead.
- Simulation results show capacity close to, and sometimes higher than, full-complexity BD while using lower implementation and computational cost.
A. System Model
The system is a downlink massive MU-MIMO architecture with multi-antenna users, limited RF chains, and hybrid precoding and combining. Digital processing operates on the resulting low-dimensional equivalent channels under constant-amplitude RF constraints.
- A base station with NBS antennas and MBS RF chains serves K mobile stations, each with NMS antennas and MMS RF chains and NS data streams.
- RF and baseband dimensions are constrained by KNS ≤ MBS ≤ NBS at the base station and NS ≤ MMS ≤ NMS at each mobile station.
- The RF precoder F provides phase-only control, while the baseband precoder B modifies both amplitudes and phases.
- The transmitted signal follows yk = HkFBs + nk under a narrowband flat-fading channel model with additive complex Gaussian noise.
- The equivalent baseband channel is formed after RF combining and precoding, and digital processing assigns baseband precoding and combining across users.
- Joint RF/baseband optimization is generally intractable under constant-amplitude analog constraints, motivating lower-dimensional design procedures.
B. Channel Model
The paper evaluates massive MU-MIMO under large i.i.d. Rayleigh fading and clustered limited-scattering mmWave channels. It uses normalized channel models with path gains and array responses, primarily studying ULA configurations while also examining UPA arrays.
- Two channel models are considered: large i.i.d. Rayleigh fading and limited-scattering clustered mmWave channels.
- In the Rayleigh model, each normalized channel-matrix entry follows an i.i.d. CN(0, 1) distribution.
- The mmWave model uses clusters and paths with complex path gains, angular parameters, and receive and transmit array response vectors.
- The mmWave channel is modeled as limited scattering by keeping the numbers of clusters and paths relatively small.
- The study primarily employs uniform linear arrays, while the proposed Hy-BD scheme can apply to arbitrary antenna arrays and simulations also examine uniform planar arrays.
III. HYBRID BLOCK DIAGONALIZATION
Hy-BD reduces the RF-chain burden by harvesting massive-array gain in the analog domain and applying block diagonalization digitally on the equivalent baseband channel.
- Traditional generalized zero-forcing or block diagonalization is impractical when RF-chain counts approach the large antenna counts.
- Hy-BD uses BS RF precoding and mobile-station RF combining to harvest array gain with far fewer RF chains than antenna elements.
- After RF processing determines the multiuser equivalent baseband channel, low-dimensional block diagonalization designs the digital precoder and combiners.
A. Array Gain Harvesting
The Hy-BD design uses phase-only RF processing to harvest large array gain while selecting orthogonal RF combiners, then leaves inter-user interference cancellation to low-dimensional baseband processing.
- Design requirements: The equivalent channel must be rank-sufficient for multi-stream transmission and provide large array gain through strong diagonal entries.The design seeks rank at least KNS and maximizes the sum of squared diagonal entries of Heq.
- RF precoding: Phase-only RF precoding uses equal gain transmission based on the phases of the intermediate channel.The EGT precoder requires MBS = KMMS RF chains and makes Heq square.
- RF precoding: The RF design enhances diagonal equivalent-channel gains, while inter-chain and inter-user interference is left for baseband processing.Off-diagonal entries represent interference rather than the gain targeted by RF processing.
- Design limitation: The RF-combiner optimization is heuristic: it does not suppress inter-user interference or guarantee optimal sum-rate maximization, but improves tractability.The direct non-convex problem is replaced by selection from a DFT-basis set.
- RF combining: DFT bases provide orthogonal RF combiner candidates that satisfy rank sufficiency and large-array-gain requirements.The candidates are formed by discretizing spatial frequency into NMS levels.
- RF combining: Each MS selects the first MMS DFT bases after sorting projection magnitudes, making exhaustive search acceptable when NMS is relatively small.Only NS phase-shift elements per MS need to be fed back for reconstructing Wk.
B. Baseband Block Diagonalization
After RF processing forms an equivalent baseband channel, Hy-BD applies low-dimensional block diagonalization to cancel inter-user interference and then uses SVD-based processing on each effective sub-channel.
- Inter-user interference cancellation: Baseband BD chooses Bk so that the effective channel for user k nulls the interference from every other user.The imposed condition is ˜HkBi = 0 for i ≠ k.
- Effective channels: The resulting HBD has nonzero user-specific blocks, enabling inter-user-interference-free multi-stream transmission.Further SVD processing optimizes each user’s effective sub-channel.
- Effective channels: Each ˜Hk is an MMS-by-MMS full-rank sub-channel that can support at least NS data streams when MMS ≥ NS.The final precoder and combiner use the corresponding leading singular vectors.
- Spectral efficiency: The Hy-BD spectral efficiency uses water-filling over the singular-value blocks of the effective channels.Λ is a KNS × KNS diagonal power-allocation matrix.
- Channel information: The RF and baseband processing require only channel-matrix knowledge, so the scheme does not depend on explicit propagation-path information.The stated scope includes arbitrary massive MU-MIMO channel types represented by the channel matrices.
C. Proportional Water-Filling Power Allocation for Weighted Sum-Rate Maximization
For fairness-aware transmission, Hy-BD extends ordinary water-filling to weighted sum-rate maximization through proportional water-filling, which assigns variable water levels across users.
- Weighted objective: Weighted sum-rate maximization introduces positive user weights to favor proportional fairness for high-priority or distant MSs.Pure sum-rate maximization does not guarantee performance for such users.
- Optimization: The weighted allocation problem is rewritten as a convex optimization problem using per-stream weights inherited from each user’s weight.For user k, each of its NS streams receives weight wk.
- Allocation rule: Proportional water-filling modifies traditional water-filling by incorporating the weights of all MSs.The resulting allocation can be interpreted as assigning variable water levels.
- Allocation rule: A user with a greater weight receives a higher water level and can be allocated more power.This is the interpretation given for the revised water-filling solution.
D. Performance Analysis in ULA Single-Path Channels
In ULA single-path channels with large transmit and receive arrays, the selected analog combiners align with array responses and the equivalent channel becomes approximately diagonal.
- Analysis setting: The analysis is restricted to ULA single-path channels and the asymptotic regime NBS, NMS →∞.The authors identify this setting as a tractable special case for analyzing hybrid-BD spectral performance.
- Analog combining: With one analog-combiner column per MS, increasingly fine DFT resolution selects a combiner approximately equal to the receive array response.The approximation is wk ≈ ak^MS(θk).
- Equivalent channel: EGT determines the entries of Heq after analog precoding and combining.The operator g(·) imposes unit amplitude on the input vector’s elements.
- Asymptotic behavior: Distinct path spatial frequencies make off-diagonal equivalent-channel entries infinitesimal relative to diagonal entries as antenna counts grow.This yields an approximately diagonal baseband equivalent channel.
- Asymptotic behavior: Under these assumptions, only water-filling power allocation is needed at baseband to achieve the optimal approximate sum spectral efficiency.The stated analytical result is evaluated in the simulations.
IV. SIMULATION RESULTS
This section evaluates the spectral efficiency and robustness of the proposed Hy-BD scheme in massive MU-MIMO channels.
- The simulations assess Hy-BD spectral efficiency and performance robustness in massive MU-MIMO channels.
A. Spectral Efficiency Evaluation
The evaluation compares Hy-BD with traditional BD and other hybrid-processing baselines across Rayleigh fading and mmWave MU-MIMO settings. Hy-BD generally approaches or exceeds traditional BD while using fewer implementation and computational resources.
- A. Spectral Efficiency Evaluation: The simulations compare Hy-BD with traditional high-dimensional BD in Rayleigh and mmWave channels, and with spatially sparse and limited-feedback hybrid schemes in mmWave channels.
- A. Spectral Efficiency Evaluation: Hy-BD consistently approaches traditional BD spectral efficiency in both 256 × 16 and 64 × 4 antenna settings, with lower implementation and computational complexity.
- A. Spectral Efficiency Evaluation: In the evaluated mmWave scenario, Hy-BD achieves slightly higher spectral efficiency than traditional BD, while both Hy-BD and spatially sparse coding improve with UPA instead of ULA.
- A. Spectral Efficiency Evaluation: The limited-feedback hybrid scheme underperforms Hy-BD when each mobile station has one RF-chain pair and the channel contains 80 paths, because it tracks only one propagation path.Hy-BD aggregates channel gains through equal-gain transmission enabled by its RF precoder.
B. Robustness Evaluation
The evaluation varies multiplexing settings across Rayleigh fading and mmWave MU-MIMO channels, comparing Hy-BD with traditional BD under different SNRs. Hy-BD closely tracks BD while using fewer RF chains, with performance depending on supported data streams.
- Robustness Evaluation: The study varies the number of data streams per user, number of users, SNR, and channel type to assess Hy-BD robustness.Experiments cover i.i.d. Rayleigh fading and mmWave channels, including changes in NS and K.
- Rayleigh fading channels: In Rayleigh fading, Hy-BD's sum spectral efficiency remains close to traditional BD across NS = 1, 2, 4 and SNR values from −40 dB to 0 dB.The comparison uses an 8-user system with MBS = 8MMS for Hy-BD.
- Rayleigh fading channels: Hy-BD requires RF chains matching supported data streams, up to MBS = 32 and MMS = 4, versus MBS = 256 and MMS = 16 for traditional BD.This comparison is reported for the 8-user Rayleigh fading system.
- Rayleigh fading channels: At SNR = 0 dB, traditional BD supports K ∗NS = 128 streams, whereas Hy-BD supports about K ∗NS = 64 with 64 BS and 8 MS RF chains.The reduced-stream configuration reflects inter-stream interference introduced during RF-domain array-gain harvesting.
- mmWave channels: Increasing NS or K in mmWave channels provides robustness tests for the two schemes across SNR = −10, −5, and 0 dB.Fig. 9 varies NS from 1 to 16 with K = 8, while Fig. 10 varies K from 1 to 16 with NS = 4.
V. CONCLUSION
The paper proposes Hy-BD for massive MU-MIMO with limited RF chains, combining phase-only RF processing with baseband BD. It reports lower complexity while approaching traditional high-dimensional BD capacity, supporting practical implementation.
- Conclusion: Hy-BD applies phase-only RF precoding and combining to harvest array gain before BD processing on the equivalent baseband channel.The scheme targets downlink massive MU-MIMO with a limited number of RF chains.
- Conclusion: Hy-BD achieves capacity performance approaching traditional high-dimensional baseband BD with lower implementation and computational complexity.The conclusion presents this as the demonstrated performance-complexity trade-off.
- Conclusion: The low-complexity, low-cost Hy-BD scheme is identified as a promising option for practical massive MU-MIMO implementation.This practical implication follows the reported complexity and capacity results.