Source-linked AI summary
Low-Complexity Hybrid Precoding in Massive Multiuser MIMO Systems
Le Liang, Wei Xu, Xiaodai Dong
TL;DR
Massive MIMO promises substantial capacity gains but incurs high hardware complexity. The paper introduces PZF, which combines phase-only RF control with low-dimensional baseband ZF, and reports performance approaching full-complexity ZF in Rayleigh and mmWave channels.
Problem
Massive MIMO offers capacity improvement at the cost of high hardware complexity, while full-complexity ZF is practically infeasible.
Method
PZF extracts aggregate-channel phases for the RF precoder and applies low-dimensional baseband ZF using the resulting equivalent channel.
Results
PZF approaches full-complexity ZF performance and demonstrates desirable performance in Rayleigh fading and sparsely scattered mmWave channels.
Takeaways & Limitations
Low-complexity hybrid PZF can approach the desirable performance of full-complexity ZF under the evaluated channel settings.
Abstract
from arXiv · showhide
Massive multiple-input multiple-output (MIMO) is envisioned to offer considerable capacity improvement, but at the cost of high complexity of the hardware. In this paper, we propose a low-complexity hybrid precoding scheme to approach the performance of the traditional baseband zero-forcing (ZF) precoding (referred to as full-complexity ZF), which is considered a virtually optimal linear precoding scheme in massive MIMO systems. The proposed hybrid precoding scheme, named phased-ZF (PZF), essentially applies phase-only control at the RF domain and then performs a low-dimensional baseband ZF precoding based on the effective channel seen from baseband. Heavily quantized RF phase control up to $2$ bits of precision is also considered and shown to incur very limited degradation. The proposed scheme is simulated in both ideal Rayleigh fading channels and sparsely scattered millimeter wave (mmWave) channels, both achieving highly desirable performance.
I. INTRODUCTION
Massive MIMO offers high capacity but requires costly hardware when each antenna uses a dedicated RF chain. The paper proposes PZF, a phase-only RF and low-dimensional baseband ZF design that approaches full-complexity ZF performance.
- Motivation: Massive MIMO can provide high capacity, but dedicated RF chains for its many antenna elements are too expensive to implement.Current circuitry makes variable phase shifters available for high-dimensional phase-only RF processing.
- Prior work: Prior phase-only and hybrid precoding works address diversity, beamforming, multiplexing, or practical constraints, but not multiuser capacity maximization in the large-array regime.The cited works do not consider the multiuser scenario or aim to maximize capacity performance in massive MIMO.
- Proposed approach: PZF designs the RF precoder from the phases of the conjugate-transposed aggregate downlink channel to harvest large array gain.The RF stage uses phase-only control, while the baseband stage performs low-dimensional ZF on the equivalent channel.
- Results: PZF approaches the performance of full-complexity ZF precoding in massive multiuser MIMO despite its lower complexity.Full-complexity ZF is described as virtually optimal but practically infeasible.
- Results: Simulations demonstrate desirable PZF performance in both Rayleigh fading and sparsely scattered mmWave channels.The proposed scheme is evaluated across both ideal Rayleigh fading and mmWave channel settings.
II. SYSTEM MODEL
The system model uses a base station with many antennas but only K RF chains, serving K single-antenna users with hybrid baseband and RF precoding. Baseband supports amplitude and phase control, whereas the RF precoder is phase-only.
- System configuration: The base station has N_t transmit antennas but only K RF chains, limiting transmission to K streams for K scheduled single-antenna users.Each user is assumed to support single-stream transmission.
- Hybrid architecture: Downlink precoding is divided into a K × K baseband matrix W and an N_t × K RF matrix F.The hybrid structure separates baseband and RF processing.
- Signal processing constraints: The baseband precoder can modify amplitudes and phases, while variable phase shifters restrict the RF precoder to phase changes.Each RF precoder entry is normalized to unit magnitude, |F_i,j| = 1.
- Channel and signal model: The model adopts a narrowband flat-fading channel and represents the received sampled baseband signal using the hybrid precoder and additive noise.The transmitted signal vector contains the K users' signals and has average covariance specified by the total transmit power.
K IK where P is the transmit power
Massive MIMO uses linear ZF precoding to approach high-capacity performance, but full-complexity implementations require substantial RF hardware. The paper proposes PZF hybrid precoding to reduce complexity while approaching full-complexity ZF performance.
- PZF applies phase-only RF control to couple K RF-chain outputs with Nt transmit antennas.Low-dimensional baseband multi-stream processing then manages inter-user interference.
- PZF can approach the performance of full-complexity ZF precoding while substantially reducing hardware complexity.The scheme supports simultaneous transmission of K streams with fewer RF chains.
- Full-complexity ZF precoding is virtually optimal in massive multiuser MIMO but practically infeasible because it requires a dedicated RF chain for each antenna.The hardware requirement restricts how large the antenna array can scale.
- Only K RF chains are needed in the proposed architecture, compared with Nt RF chains for full-complexity ZF.This difference directly targets the hardware burden of connecting every antenna to a dedicated RF chain.
- The proposed PZF scheme is analyzed through its achieved spectral efficiency in massive multiuser MIMO.The paper reports less than 1 dB loss relative to full-complexity ZF with substantially reduced complexity.
A. Hybrid Precoder Design
The hybrid precoder extracts channel phases for RF control and uses the resulting low-dimensional effective channel for baseband ZF. Quantized phase shifters are incorporated by rounding each RF phase to its nearest available value.
- A. Hybrid Precoder Design: The RF precoder controls phases of upconverted RF signals, while the baseband precoder W modifies both amplitudes and phases of incoming complex symbols.This separates phase-only RF control from joint baseband processing.
- A. Hybrid Precoder Design: The RF precoder uses phase-only control based on phases extracted from the conjugate transpose of the composite downlink channel.This phase alignment is intended to harvest array gain from the large number of antennas.
- A. Hybrid Precoder Design: The design assumes perfect channel knowledge at the base station, potentially obtained through uplink estimation and TDD channel reciprocity.Efficient channel estimation for hybrid structures and frequency-selective channels remains an ongoing research topic.
- A. Hybrid Precoder Design: The hybrid architecture observes an equivalent K×K channel Heq = HF at baseband.Here H is the composite downlink channel and F is the RF precoder.
- A. Hybrid Precoder Design: Low-dimensional ZF precoding is applied to the equivalent channel, with a diagonal matrix Λ used for column power normalization.This baseband operation manages multi-stream transmission after RF phase processing.
- A. Hybrid Precoder Design: Practical phase shifters quantize the KNt RF phases to B bits, assigning each phase to its nearest neighbor by Euclidean distance.The baseband precoder is then recomputed using the quantized RF precoder.
B. Spectral Efficiency Analysis in Rayleigh Fading Channels
The analysis characterizes PZF spectral efficiency in Rayleigh fading by modeling effective-channel terms and deriving closed-form expressions that reveal parameter effects on capacity.
- Closed-form expressions are derived for PZF spectral efficiency, revealing how different parameters affect system capacity.
- PZF effective-channel columns are formed by extracting the phases of the corresponding user channels for RF precoding.
- The analysis treats each channel element as an i.i.d. zero-mean, unit-variance complex Gaussian variable, whose magnitude follows a Rayleigh distribution.
- The off-diagonal-term distribution is obtained by analyzing its real and imaginary parts and proving their independence.
- For large antenna arrays, the off-diagonal effective-channel term is characterized as a circularly symmetric complex Gaussian variable with zero mean and unit variance.
4. Compared with the diagonal term
The comparison shows that large arrays make PZF’s inter-user interference negligible, while baseband ZF suppresses residual interference at moderate antenna sizes and supports a tight spectral-efficiency bound.
- When the transmit antenna number is large, PZF’s off-diagonal effective-channel terms become negligible, making its closed-form upper bound tight.
- At medium-high antenna numbers, residual interference may still deteriorate performance, so PZF applies baseband ZF to suppress it.
- PZF spectral efficiency remains below the idealized case in which off-diagonal effective-channel terms are exactly zero.
- Theorem 1 gives the spectral efficiency achieved by the proposed low-complexity PZF precoding scheme.
- Full-complexity ZF constructs each stream’s unit-norm precoding vector by projecting its channel onto the nullspace of the other users’ channels.
- The full-complexity ZF asymptotic analysis uses massive-MIMO channel orthogonality and the chi-squared distribution of channel power.
A. Large Rayleigh Fading Channels
In large Rayleigh fading channels, PZF approaches full-complexity ZF with substantially lower complexity, and two-bit phase quantization causes only a small loss.
- The simulations compare PZF and its quantized version with full-complexity ZF across the SNR range using averaged spectral efficiency.
- Full-complexity ZF is treated as virtually optimal in the large-array regime but practically infeasible because it requires N_t costly RF chains.
- Less than 1 dB loss separates proposed PZF from full-complexity ZF while substantially reducing complexity.
- With B = 2 bits of phase precision, the quantized PZF scheme suffers less than 1 dB degradation.
- The derived analytical spectral-efficiency expressions are plotted alongside the simulation results.
B. Large mmWave Multiuser Channels
PZF is also evaluated in geometric sparse-multipath mmWave channels, where it is compared with beamspace MIMO under a matched RF-chain budget.
- PZF is applied to mmWave communications using a geometric channel model with limited multipath components.
- Each user is modeled as observing the same number of propagation paths, denoted by N_p.
- Beamspace MIMO steers streams toward approximate strongest paths at RF and performs low-dimensional baseband ZF on the equivalent channel.
- The comparison assumes the base station has a total of K RF chains for fairness.
- Beamspace MIMO performs desirably in line-of-sight channels but fails to capture sparse multipath components in non-line-of-sight channels.
V. CONCLUSION
The paper studies large multiuser MIMO with practical RF hardware constraints and proposes low-complexity hybrid PZF to approach full-complexity ZF. Its performance is characterized in closed form and demonstrated in Rayleigh fading and poorly scattered mmWave channels.
- The proposed hybrid PZF scheme approaches the desirable but infeasible full-complexity ZF precoding with lower complexity.The scheme targets large multiuser MIMO systems under practical RF hardware constraints.
- RF processing harvests large power gain with reasonable complexity, while baseband precoding facilitates multi-stream processing.
- PZF performance has been characterized in closed form.
- The scheme is demonstrated in both Rayleigh fading and poorly scattered mmWave channels.