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Jamming Detection and Channel Estimation for Spatially Correlated Beamspace Massive MIMO

Pengguang Du, Cheng Zhang, Yindi Jing, Chao Fang, Zhilei Zhang, Yongming Huang

TL;DR

This paper investigates the problem of jamming detection and channel estimation during multi-user uplink beam training under random pilot jamming attacks in beamspace massive multi-input-multi-output (MIMO) systems and proposes a jamming detection scheme based on the locally most powerful test (LMPT).

Abstract

In this paper, we investigate the problem of jamming detection and channel estimation during multi-user uplink beam training under random pilot jamming attacks in beamspace massive multi-input-multi-output (MIMO) systems. For jamming detection, we distinguish the signals from the jammer and the user by projecting the observation signals onto the pilot space. By using the multiple projected observation vectors corresponding to the unused pilots, we propose a jamming detection scheme based on the locally most powerful test (LMPT) for systems with general channel conditions. Analytical expressions for the probability of detection and false alarms are derived using the second-order statistics and likelihood functions of the projected observation vectors. For the detected jammer along with users, we propose a two-step minimum mean square error (MMSE) channel estimation using the projected observation vectors. As a part of the channel estimation, we develop schemes to estimate the norm and the phase of the inner-product of the legitimate pilot vector and the random jamming pilot vector, which can be obtained using linear MMSE estimation and a bilinear form of the multiple projected observation vectors. From simulations under different system parameters, we observe that the proposed technique improves the detection probability by 32.22% compared to the baseline at medium channel correlation level, and the channel estimation achieves a mean square error of -15.93dB.

Jamming Detection and Channel Estimation for Spatially Correlated Beamspace Massive MIMO

TL;DR

This paper investigates the problem of jamming detection and channel estimation during multi-user uplink beam training under random pilot jamming attacks in beamspace massive multi-input-multi-output (MIMO) systems and proposes a jamming detection scheme based on the locally most powerful test (LMPT).

Abstract

In this paper, we investigate the problem of jamming detection and channel estimation during multi-user uplink beam training under random pilot jamming attacks in beamspace massive multi-input-multi-output (MIMO) systems. For jamming detection, we distinguish the signals from the jammer and the user by projecting the observation signals onto the pilot space. By using the multiple projected observation vectors corresponding to the unused pilots, we propose a jamming detection scheme based on the locally most powerful test (LMPT) for systems with general channel conditions. Analytical expressions for the probability of detection and false alarms are derived using the second-order statistics and likelihood functions of the projected observation vectors. For the detected jammer along with users, we propose a two-step minimum mean square error (MMSE) channel estimation using the projected observation vectors. As a part of the channel estimation, we develop schemes to estimate the norm and the phase of the inner-product of the legitimate pilot vector and the random jamming pilot vector, which can be obtained using linear MMSE estimation and a bilinear form of the multiple projected observation vectors. From simulations under different system parameters, we observe that the proposed technique improves the detection probability by 32.22% compared to the baseline at medium channel correlation level, and the channel estimation achieves a mean square error of -15.93dB.

Paper Structure

This paper contains 20 sections, 5 theorems, 82 equations, 9 figures.

Table of Contents

  1. Introduction
  2. System Model and Beam Training Model Under Jamming Attack
  3. Pilot Transmission Model and Channel Model
  4. Beam Training Model
  5. Channel-Statistics-Assisted Jamming Detection Scheme
  6. Formulation of the Hypothesis Testing Problem
  7. LMPT-Based Detection Assisted by Channel Statistics
  8. Performance Analysis of the LMPT-Based Scheme
  9. MMSE-Based Two-Step Channel Estimation For the Jammer and Legitimate Users
  10. Multiple Projected Observation Vectors Based MMSE Jamming Channel Estimation
  11. MMSE Criterion-Based Users' Channel Estimation
  12. Estimation Scheme for the Jamming Pilot's Inner-Product
  13. Simulation and Discussion
  14. Simulation Setup
  15. Performance of the Proposed Jamming Detection Schemes
  16. ...and 5 more sections

Key Result

Theorem 1

The PDF of $T_{\rm{LMPT}}$ under ${\mathcal{H}}_0$ is where $\beta_{k}=\frac{\rho_k}{2\sum_{j=1}^{\rho_k}\left(\lambda_{k,n}\sigma^2 \right) ^{-1}}$, The PDF of $T_{\rm{LMPT}}$ under $\mathcal{H}_1$ is where $\varphi_k = {{rank}}\left( {\bf{B}}_k \right)$, and $\epsilon_{k,1},\ldots,\epsilon_{k,\varphi_k}$ are the positive eigenvalues of ${\bf{B}}_k$.

Figures (9)

  • Figure 1: Multi-user beam cycle training procedure under jamming attacks.
  • Figure 2: Theoretical and simulation performance of the proposed LMPT-based jamming detection scheme for $\tau = 2,5$.
  • Figure 3: Theoretical and simulation ROC of the LMPT-based jamming detection scheme for ${\rm{JNR}}=0$, $5$, $10\,{\rm{dB}}$.
  • Figure 4: ROC of the proposed LMPT-based jamming detection scheme for $\rho=0.2$, $0.8$ and ${\rm{JNR}}=0$, $5\,{\rm{dB}}$.
  • Figure 5: Comparison of ROC between the jamming detection schemes based on the LMPT and modified GLRT, where ${\text{JNR}} =2\,{\text{dB}}$ and $\tau = 5$.
  • ...and 4 more figures

Theorems & Definitions (10)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof