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Joint Activity and Data Detection for Massive Grant-Free Access Using Deterministic Non-Orthogonal Signatures

Nam Yul Yu, Wei Yu

TL;DR

The paper tackles scalable joint activity and data detection for massive grant-free access in mMTC by deriving a coherence-based sufficient condition for covariance-based ML recovery and proposing a deterministic framework that uses unimodular masking to create low-coherence non-orthogonal signatures. It proves that the signature matrix coherence satisfies $\mu({\bf S})=\mathcal{O}(1/\sqrt{L})$, enabling reliable recovery of up to $K=\mathcal{O}(L)$ active devices with many antennas, while generating $\mathcal{O}(L^3)$ sequences of length $L$. Four concrete constructions (cubic, power-residue, Sidelnikov, and trace) provide practical, on-the-fly generated signatures with bounded coherence, closely approaching the Welch bound. Simulations with covariance-based ML (CD-ML) and MMV-AMP show that the proposed deterministic signatures outperform random baselines in joint activity and data detection, especially for $K>L$ with many base-station antennas and for short sequence lengths, underscoring the practical impact for low-signaling-overhead massive grant-free access.

Abstract

Grant-free access is a key enabler for connecting wireless devices with low latency and low signaling overhead in massive machine-type communications (mMTC). For massive grant-free access, user-specific signatures are uniquely assigned to mMTC devices. In this paper, we first derive a sufficient condition for the successful identification of active devices through maximum likelihood (ML) estimation in massive grant-free access. The condition is represented by the coherence of a signature sequence matrix containing the signatures of all devices. Then, we present a design framework of non-orthogonal signature sequences in a deterministic fashion. The design principle relies on unimodular masking sequences with low correlation, which are applied as masking sequences to the columns of the discrete Fourier transform (DFT) matrix. For example constructions, we use four polyphase masking sequences represented by characters over finite fields. Leveraging algebraic techniques, we show that the signature sequence matrix of proposed non-orthogonal sequences has theoretically bounded low coherence. Simulation results demonstrate that the deterministic non-orthogonal signatures achieve the excellent performance of joint activity and data detection by ML- and approximate message passing (AMP)-based algorithms for massive grant-free access in mMTC.

Joint Activity and Data Detection for Massive Grant-Free Access Using Deterministic Non-Orthogonal Signatures

TL;DR

The paper tackles scalable joint activity and data detection for massive grant-free access in mMTC by deriving a coherence-based sufficient condition for covariance-based ML recovery and proposing a deterministic framework that uses unimodular masking to create low-coherence non-orthogonal signatures. It proves that the signature matrix coherence satisfies , enabling reliable recovery of up to active devices with many antennas, while generating sequences of length . Four concrete constructions (cubic, power-residue, Sidelnikov, and trace) provide practical, on-the-fly generated signatures with bounded coherence, closely approaching the Welch bound. Simulations with covariance-based ML (CD-ML) and MMV-AMP show that the proposed deterministic signatures outperform random baselines in joint activity and data detection, especially for with many base-station antennas and for short sequence lengths, underscoring the practical impact for low-signaling-overhead massive grant-free access.

Abstract

Grant-free access is a key enabler for connecting wireless devices with low latency and low signaling overhead in massive machine-type communications (mMTC). For massive grant-free access, user-specific signatures are uniquely assigned to mMTC devices. In this paper, we first derive a sufficient condition for the successful identification of active devices through maximum likelihood (ML) estimation in massive grant-free access. The condition is represented by the coherence of a signature sequence matrix containing the signatures of all devices. Then, we present a design framework of non-orthogonal signature sequences in a deterministic fashion. The design principle relies on unimodular masking sequences with low correlation, which are applied as masking sequences to the columns of the discrete Fourier transform (DFT) matrix. For example constructions, we use four polyphase masking sequences represented by characters over finite fields. Leveraging algebraic techniques, we show that the signature sequence matrix of proposed non-orthogonal sequences has theoretically bounded low coherence. Simulation results demonstrate that the deterministic non-orthogonal signatures achieve the excellent performance of joint activity and data detection by ML- and approximate message passing (AMP)-based algorithms for massive grant-free access in mMTC.
Paper Structure (27 sections, 9 theorems, 50 equations, 4 figures, 1 table)

This paper contains 27 sections, 9 theorems, 50 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Grant-Free Random Access
  4. Covariance-Based Maximum-Likelihood (ML) Estimation
  5. Sufficient Condition for Maximum Likelihood Estimation
  6. Asymptotic Performance Analysis for ML Estimation
  7. Coherence-Based Analysis for ML Estimation
  8. Design of Deterministic Non-Orthogonal Signatures
  9. General Framework
  10. Example Constructions
  11. Signatures from Cubic Masking Sequences
  12. Signatures from Power-Residue Masking Sequences
  13. Signatures from Sidelnikov Masking Sequences
  14. Signatures from Trace Masking Sequences
  15. Simulation Results
  16. ...and 12 more sections

Key Result

Theorem 1

( Yu:phase) Let ${\boldsymbol \gamma}^0 = (\gamma_1 ^0, \cdots, \gamma_{N} ^0)^T$ be a true solution of ${\boldsymbol \gamma}$ in eq:Y_mat, corresponding to true indicator vectors ${\bf a}_1, \cdots, {\bf a}_{N_d}$, where $\mathcal{Z} = \{ i \mid \gamma_i ^0 = 0\}$ denotes the index set of zero el where ${\bf x} = (x_1, \cdots, x_{N} ) \in \mathbb R^{N}$. As the number of BS antennas increases i

Figures (4)

  • Figure 1: Probability of errors of tested signatures over the number of BS antennas by CD-ML, where $N_d = 200, J=2$, and $Q=4$. The number of active devices is (a) $K=20 <L$ and (b) $K=40 > L$, respectively, where $L = 23$ for random, C-SIDCO, U-SIDCO, cubic, and PR based sequences, and $L=24$ for Sidelnikov and trace based ones.
  • Figure 2: Probability of errors of tested signatures over the number of BS antennas by CD-ML, where $N_d = 500, J=1$, and $Q=2$. The number of active devices is (a) $K=20 < L$ and (b) $K=40 > L$, respectively, where $L = 23$ for random, C-SIDCO, U-SIDCO, cubic, and PR based sequences, and $L=24$ for Sidelnikov and trace based ones.
  • Figure 3: Probability of errors of tested signatures over the number of BS antennas by MMV-AMP, where (a) $N_d = 200, J=2, Q=4$ and (b) $N_d = 500, J=1, Q=2$, respectively. The number of active devices is $K=20 < L$, where $L = 23$ for random, C-SIDCO, U-SIDCO, cubic, and PR based sequences, and $L=24$ for Sidelnikov and trace based ones.
  • Figure 4: Probability of errors of tested signatures over the number of active devices by (a) CD-ML and (b) MMV-AMP, where $N_d = 200, J=2$, and $Q=4$. The number of BS antennas is $M=192$ for (a) CD-ML, and $M=10$ for (b) MMV-AMP, respectively. The sequence lengths are $L = 23$ for random, C-SIDCO, U-SIDCO, cubic, and PR based sequences, while $L=24$ for Sidelnikov and trace based ones.

Theorems & Definitions (14)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Remark 1
  • Theorem 4
  • Definition 1
  • Theorem 5
  • Definition 2
  • Theorem 6
  • Definition 3
  • ...and 4 more