Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Performance Bounds of Joint Detection with Kalman Filtering and Channel Decoding for Wireless Networked Control Systems

Jinnan Piao, Dong Li, Zhibo Li, Ming Yang, Xueting Yu, Jincheng Dai

TL;DR

This work analyzes joint Kalman-filtered MAP decoding for wireless networked control systems, framing the problem as MAP decoding with KF-derived priors. It derives limiting MAP bounds using pairwise error probability and introduces an infinite-state Markov chain to capture consecutive packet losses, then provides a tractable bound-approximation by linking MAP bounds to state-transition probabilities. A $(64,16)$ polar code with a 16-bit CRC is used to illustrate the approach, showing that MAP performance coincides with the limiting upper bound at high SNR and achieves about a 3 dB gain over normal finite-block-rate benchmarks, with lower RMSE than ML decoding. The results illustrate the potential of jointly designing control and communication systems to leverage prior information for improved reliability and real-time performance in WNCSs.

Abstract

The joint detection uses Kalman filtering (KF) to estimate the prior probability of control outputs to assist channel decoding. In this paper, we regard the joint detection as maximum a posteriori (MAP) decoding and derive the lower and upper bounds based on the pairwise error probability considering system interference, quantization interval, and weight distribution. We first derive the limiting bounds as the signal-to-noise ratio (SNR) goes to infinity and the system interference goes to zero. Then, we construct an infinite-state Markov chain to describe the consecutive packet losses of the control systems to derive the MAP bounds. Finally, the MAP bounds are approximated as the bounds of the transition probability from the state with no packet loss to the state with consecutive single packet loss. The simulation results show that the MAP performance of $\left(64,16\right)$ polar code and 16-bit CRC coincides with the limiting upper bound as the SNR increases and has $3.0$dB performance gain compared with the normal approximation of the finite block rate at block error rate $10^{-3}$.

Performance Bounds of Joint Detection with Kalman Filtering and Channel Decoding for Wireless Networked Control Systems

TL;DR

This work analyzes joint Kalman-filtered MAP decoding for wireless networked control systems, framing the problem as MAP decoding with KF-derived priors. It derives limiting MAP bounds using pairwise error probability and introduces an infinite-state Markov chain to capture consecutive packet losses, then provides a tractable bound-approximation by linking MAP bounds to state-transition probabilities. A polar code with a 16-bit CRC is used to illustrate the approach, showing that MAP performance coincides with the limiting upper bound at high SNR and achieves about a 3 dB gain over normal finite-block-rate benchmarks, with lower RMSE than ML decoding. The results illustrate the potential of jointly designing control and communication systems to leverage prior information for improved reliability and real-time performance in WNCSs.

Abstract

The joint detection uses Kalman filtering (KF) to estimate the prior probability of control outputs to assist channel decoding. In this paper, we regard the joint detection as maximum a posteriori (MAP) decoding and derive the lower and upper bounds based on the pairwise error probability considering system interference, quantization interval, and weight distribution. We first derive the limiting bounds as the signal-to-noise ratio (SNR) goes to infinity and the system interference goes to zero. Then, we construct an infinite-state Markov chain to describe the consecutive packet losses of the control systems to derive the MAP bounds. Finally, the MAP bounds are approximated as the bounds of the transition probability from the state with no packet loss to the state with consecutive single packet loss. The simulation results show that the MAP performance of polar code and 16-bit CRC coincides with the limiting upper bound as the SNR increases and has dB performance gain compared with the normal approximation of the finite block rate at block error rate .
Paper Structure (7 sections, 9 theorems, 39 equations, 4 figures)

This paper contains 7 sections, 9 theorems, 39 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Limiting Bounds of MAP Decoding
  4. Markov Chain of Control System and Bounds
  5. Approximation of Bounds of MAP Decoding
  6. Simulation Results
  7. Conclusion

Key Result

Lemma 1

Given the transmitted bit vector ${\mathbf b}_t$, the estimated bit vector ${\mathbf b}_e$ and the Hamming weight ${d_{{{\bf{c}}_t},{{\bf{c}}_e}}}$ between ${{{\bf{c}}_t}}$ and ${{{\bf{c}}_e}}$, the PEP $P_{{\bf b}_t, {\bm\mu}, \mathbf{\Sigma}}^{{\bf b}_t \ne {\bf b}_e}$ is

Figures (4)

  • Figure 1: Markov chain of control system with MAP decoding.
  • Figure 2: BLER performance and bounds of scalar system.
  • Figure 3: BLER performance and bounds of vector system.
  • Figure 4: RMSE performance of scalar and vector systems.

Theorems & Definitions (16)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof
  • Lemma 3
  • Lemma 4
  • proof
  • Lemma 5
  • ...and 6 more