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Hybrid Procoder and Combiner Design for Secure Transmission in mmWave MIMO Systems
Xiaowen Tian, Ming Li, Zihuan Wang, Qian Liu
TL;DR
Secure hybrid beamformer design for mmWave MIMO has received limited investigation, despite the use of hybrid architectures to address propagation loss and full-digital hardware demands. The paper proposes designs for known and unknown eavesdropper CSI; simulations report improved secrecy performance over other hybrid beamforming algorithms.
Problem
Secure hybrid beamformer design for mmWave MIMO has not been well investigated, and existing secure designs are not directly applicable to its hybrid architecture.
Source: §I · pp. 1–2Method
The paper jointly designs analog precoders and combiners with known eavesdropper CSI, and uses artificial noise with unknown CSI while maintaining intended-receiver QoS.
Source: §I · p. 2Results
The proposed algorithms significantly improve secrecy performance compared with other hybrid beamforming algorithms.
Source: §IV · p. 5, §V · p. 6Takeaways & Limitations
Abstract
from arXiv · showhide
Millimeter wave (mmWave) communications have been considered as a key technology for future 5G wireless networks. In order to overcome the severe propagation loss of mmWave channel, mmWave multiple-input multiple-output (MIMO) systems with analog/digital hybrid precoding and combining transceiver architecture have been widely considered. However, physical layer security (PLS) in mmWave MIMO systems and the secure hybrid beamformer design have not been well investigated. In this paper, we consider the problem of hybrid precoder and combiner design for secure transmission in mmWave MIMO systems in order to protect the legitimate transmission from eavesdropping. When eavesdropper's channel state information (CSI) is known, we first propose a joint analog precoder and combiner design algorithm which can prevent the information leakage to the eavesdropper. Then, the digital precoder and combiner are computed based on the obtained effective baseband channel to further maximize the secrecy rate. Next, if prior knowledge of the eavesdropper's CSI is unavailable, we develop an artificial noise (AN)-based hybrid beamforming approach, which can jam eavesdropper's reception while maintaining the quality-of-service (QoS) of intended receiver at the pre-specified level. Simulation results demonstrate that our proposed algorithms offer significant secrecy performance improvement compared with other hybrid beamforming algorithms.
I. INTRODUCTION
Hybrid precoding and combining offer a practical mmWave MIMO architecture, but secure hybrid beamformer design remains underinvestigated. This paper proposes secure designs for cases with known and unknown eavesdropper CSI.
I. INTRODUCTION
- MmWave’s wide bandwidth and compact large antenna arrays motivate hybrid transceivers, which avoid the many costly RF chains and energy-intensive ADCs of full-digital designs.The paper positions hybrid architecture as an economic and energy-efficient solution.Source: §I · p. 1
- Hybrid precoding uses many analog phase shifters and a few RF chains to combine high-dimensional analog and flexible low-dimensional digital beamforming.Existing designs are codebook-based or codebook-free; codebook-based designs are described as more popular for their lower complexity and satisfactory performance.Source: §I · p. 1
- Secure hybrid beamformer design for mmWave MIMO had not been studied, while prior secure beamformer designs used full-digital architectures considered impractical for mmWave systems.Earlier work focused on secrecy analysis rather than hybrid beamformer design.Source: §I · p. 2
- The paper proposes joint analog precoder and combiner design when Eve’s CSI is known, and AN-based hybrid beamforming when it is unavailable.For known CSI, digital precoders and combiners are then computed from the effective baseband channel to further maximize secrecy rate; the unknown-CSI approach maintains intended-receiver QoS.Source: §I · p. 2
A. System Model
The system is a mmWave MIMO wiretap link in which Alice sends data streams to Bob while Eve attempts to overhear. Hybrid precoding and combining process the transmitted and received signals using limited RF chains.
A. System Model
- Alice transmits Ns data streams to Bob, while Eve attempts to overhear; the system assumes NRF = NRF,b and Ns ≤ NRF.Alice, Bob, and Eve have Na, Nb, and Ne antennas, respectively, and use N_RF,a, N_RF,b, and N_RF,e RF chains.Source: A. System Model · p. 2
- The transmitter applies a digital baseband precoder before RF conversion and analog precoding, whose phase-shifter entries have constant magnitude.The analog precoder is selected from a codebook of constant-magnitude vectors, and the transmitted signal obeys a normalized power constraint.Source: A. System Model · p. 2
- Alice-to-Bob and Alice-to-Eve channels are denoted Hb and He, with receiver noise vectors nb and ne.The noise vectors are modeled with independent, identically distributed complex Gaussian entries.Source: A. System Model · p. 2
- Bob’s received signal passes through analog combining followed by digital combining, and Eve uses the same signal-processing procedure.The combined receive and transmit beamformers are denoted Wb and F, respectively.Source: A. System Model · p. 2
B. MmWave MIMO Channel Model
The channel model represents mmWave propagation through a limited number of paths and assumes uniform linear arrays. It also considers shared scatterers that can give Eve a strong signal when its angles align with Bob’s.
B. MmWave MIMO Channel Model
- The limited-scattering model assumes L scatterers, each contributing one propagation path to the Alice-to-Bob channel.The Alice-to-Eve channel is modeled similarly, with different AoAs and AoDs.Source: B. MmWave MIMO Channel Model · pp. 2–3
- Each path has a complex gain assumed Rayleigh distributed, while its AoD and AoA specify the departure and arrival directions.The model uses uniform linear arrays; their response vectors depend on wavelength and antenna-element spacing.Source: B. MmWave MIMO Channel Model · pp. 2–3
- Shared scatterers can give Eve a strong signal when Bob and Eve have similar AoDs, making eavesdropping possible in this model.The paper motivates this setting by noting that diffuse scattering can arise from rough surfaces and tiny building cracks.Source: B. MmWave MIMO Channel Model · p. 3
C. Problem Formulation
The formulation targets secrecy-rate maximization with codebook-constrained hybrid beamformers and treats known and unknown eavesdropper CSI separately. The supplied comparisons show a substantial secrecy-rate gap between hybrid and full-digital beamforming.
C. Problem Formulation
- The secrecy-rate objective is a positive-part log-det difference between legitimate- and eavesdropper-channel terms.The formulation uses the secrecy rate as its performance metric.Source: C. Problem Formulation · p. 3
- Ordinary full-digital beamforming leaks information at high SNR, while GED outperforms GSVD in sparse mmWave channels.The paper uses full-digital GED as the secrecy-performance benchmark in later simulations.Source: C. Problem Formulation · p. 3, Figure 2 · p. 3
- Hybrid precoding and combining show a dramatic secrecy-rate decrease and a large gap from the full-digital benchmark.The comparison uses codebook-based SSP and codebook-free PE-AltMin.Source: C. Problem Formulation · p. 3, Figure 3 · p. 3
- The analog precoder and combiner are constrained to select columns from their respective codebooks, and the design is split by eavesdropper-CSI availability.The known-CSI case uses a joint analog design followed by digital refinement; the unknown-CSI case adopts artificial noise.Source: C. Problem Formulation · p. 4
A. Known Eavesdropper’s Channel
With Eve’s channel known, the algorithm suppresses its directional components while selecting analog beam pairs for Bob’s channel. It then uses the resulting effective channel for digital refinement.
A. Known Eavesdropper’s Channel
- The algorithm first decomposes Eve’s channel by SVD and retains its leading nonzero singular components to identify directions to avoid.The channel model attributes this structure to mmWave channel sparsity.Source: A. Known Eavesdropper’s Channel · p. 4
- It removes Eve’s angle-of-departure components from Bob’s channel, leaving a channel with Bob’s components but almost none of Eve’s.This is the initial processing step for the secure transmission design.Source: A. Known Eavesdropper’s Channel · p. 4
- The algorithm successively selects analog precoder–combiner pairs to maximize channel gain while suppressing co-channel interference.Previously selected stream components are removed through Gram–Schmidt orthogonalization to avoid similar beams across streams.Source: A. Known Eavesdropper’s Channel · p. 4
- After analog beam selection, an SVD-based digital precoder operates on the effective baseband channel to further suppress interference and maximize sum-rate.The algorithm summary is presented in Table I.Source: A. Known Eavesdropper’s Channel · p. 4
B. Unknown Eavesdropper’s Channel
When Eve’s CSI is unavailable, the design first meets Bob’s QoS threshold with a minimum-power transmission, then uses residual power for artificial noise. The approach assumes more RF chains than data streams and aims to preserve Bob’s reception.
B. Unknown Eavesdropper’s Channel
- The design finds the minimum transmit power that satisfies Bob’s QoS threshold, then assigns residual power to artificial noise.The threshold is expressed as Rb ≥ Rγ, and residual power as (P − Ps)+.Source: B. Unknown Eavesdropper’s Channel · p. 4
- The AN-based approach assumes NRF > Ns and designs the artificial-noise precoder so the noise should not degrade Bob’s reception.The design uses the obtained optimal combiner when enforcing this principle.Source: B. Unknown Eavesdropper’s Channel · pp. 4–5
- For Ns < NRF, the passage specifies a digital AN precoder form alongside the data precoder obtained from the effective-channel SVD.The excerpt identifies the construction but does not provide its expression.Source: B. Unknown Eavesdropper’s Channel · p. 5
IV. SIMULATION STUDIES
The simulations evaluate secure hybrid beamforming with known and unknown eavesdropper CSI. The proposed design outperforms SSP in the known-CSI case, while artificial noise reduces Eve’s reception under unknown CSI without violating Bob’s required QoS.
IV. SIMULATION STUDIES
- The simulations use 192-element ULAs at Alice, Bob, and Eve, with randomly selected propagation paths from 20 scatterers and 128-angle-resolution codebooks.Bob and Eve select 3–8 scatterers and may share some scatterers; codebook angles are uniformly quantized over [0, 2π].Source: §IV · p. 5
- The proposed design significantly outperforms SSP in secrecy rate with known Eve CSI, though it remains below the full-digital benchmark.The comparison is reported for 2 RF chains and 2 data streams, with a similar conclusion at 4 RF chains and 4 streams.Source: §IV · p. 5
- With unknown Eve CSI, the AN-based design reduces Eve’s spectrum efficiency while maintaining Bob’s required QoS; using 16 RF chains improves secrecy performance.The simulations use 8 RF chains and 4 data streams before increasing the RF-chain count to 16.Source: §IV · p. 5
V. CONCLUSION
The paper concludes that hybrid precoder and combiner design can secure mmWave MIMO transmission. Its simulations report improved secrecy performance over other hybrid beamforming algorithms.
V. CONCLUSION
- The proposed hybrid precoder and combiner design targets secure transmission in a mmWave MIMO wiretap system.Source: §V · p. 5
- Figures 4 and 5 plot secrecy rate versus SNR for 2 and 4 RF chains, respectively, with matching numbers of data streams.Source: Figure 4 · p. 6, Figure 5 · p. 6
- The conclusion reports significant secrecy-performance improvement over other hybrid beamforming algorithms.Source: §V · p. 6