Frequency Permutation Subsets for Joint Radar and Communication

TL;DR

This work addresses joint radar and communication waveform design using a random stepped frequency permutation. It introduces subset-permutation selection to trade off data reliability against radar accuracy, coupled with an IP-based optimal receiver and a computationally efficient Hungarian-based sub-optimal receiver that operate under any subset of permutations. Two subset design strategies are proposed: (i) a block-based $d_{min}=2k$ construction yielding $(M/k)!$ waveforms with $O((M/k)^3)$ receiver complexity, and (ii) a $d_{min}=3$ positive-sign subset of size $M!/2$ with efficient encoding using the floor function, plus a radar-oriented Costas-inspired subset that reduces maximum sidelobes in the ambiguity function. BLER is analyzed under AWGN and correlated Rician fading using union bounds and nearest-neighbor approximations, while the radar performance is examined via the ambiguity function, showing local accuracy independence from permutation order but improved global accuracy with radar-oriented subsets. A remapping of frequency tones to the symbol set is discussed as a means to jointly enhance communication and radar performance. These results provide a flexible framework for balancing data rate, reliability, and sensing accuracy in joint radar-communication systems.

Abstract

This paper focuses on waveform design for joint radar and communication systems and presents a new subset selection process to improve the communication error rate performance and global accuracy of radar sensing of the random stepped frequency permutation waveform. An optimal communication receiver based on integer programming is proposed to handle any subset of permutations followed by a more efficient sub-optimal receiver based on the Hungarian algorithm. Considering optimum maximum likelihood detection, the block error rate is analyzed under both additive white Gaussian noise and correlated Rician fading. We propose two methods to select a permutation subset with an improved block error rate and an efficient encoding scheme to map the information symbols to selected permutations under these subsets. From the radar perspective, the ambiguity function is analyzed with regards to the local and the global accuracy of target detection. Furthermore, a subset selection method to reduce the maximum sidelobe height is proposed by extending the properties of Costas arrays. Finally, the process of remapping the frequency tones to the symbol set used to generate permutations is introduced as a method to improve both the communication and radar performances of the selected permutation subset.

Figures (8)

• Figure 1: Two different frequency sequences under block based subset selection.
• Figure 2: The BLER versus the average received SNR under Hamming distance based permutation subsets with $M=8, N=4, K=2$ and $\rho=0.5$.
• Figure 3: The BLER versus the average received SNR under different Hamming distance based permutation subsets with $M = 6$ and $N = 2$.
• Figure 4: The BLER versus the average received SNR under $d_{min}=3$ and radar based subsets with $M=6, N=4, K=4$ and $\rho=0.5$.
• Figure 5: Normalized peak sidelobe height distribution under $d_{min}=3$ and radar based subsets with $360$ waveforms and $M=6$.

Theorems & Definitions (2)

• Lemma 1
• proof