Joint Design of Doppler-Resilient Unimodular Discrete-Phase Waveforms and Receiving Filters for MIMO Radars

Designing Doppler-resilient unimodular discrete phase-coded waveforms (DPWs) with low delay-Doppler sidelobes is critical for multiple-input multiple-output (MIMO) radar. Existing block coordinate descent (BCD) methods suffer from high computational cost for designing long sequences or large waveform sets. Meanwhile, learning-based alternatives such as the soft-quantization network (SQN) only address correlation optimization in the delay domain, without considering ambiguity function (AF) optimization in the joint delay-Doppler domain. To address these issues, this paper proposes a novel Doppler-resilient DPW design framework, termed SQNGD, for joint transmit-receive optimization that simultaneously optimizes the auto-AF, cross-AF (CAF), and signal-to-noise ratio loss (SNRL) under unimodular constraints. To solve the multi-objective optimization problem (MOOP), a joint transmit-receive design and an alternating optimization strategy are developed. The transmit waveforms are optimized via soft-quantization-based differentiable parameterization, while the receive filters are updated by gradient descent (GD) with an energy constraint and SNRL penalty. An FFT-accelerated evaluation of the AF and CAF is further incorporated, reducing the optimization time by 1.9x - 11x compared with the state-of-the-art (SOTA) majorization-minimization-coordinate descent (MMCD) method. Numerical results show that SQNGD achieves a peak sidelobe level (PSL) of approximately -43 dB over the Doppler range [-0.5,0.5] and -31 dB over [-600,600], respectively, outperforming MMCD by 5.85 dB and 3.45 dB, while maintaining the same SNRL of 0.5 dB.

The Optimal Tradeoff Between PAPR and Ambiguity Functions for Generalized OFDM Waveform Set in ISAC Systems

Integrated sensing and communications (ISAC) has been identified as one of the six usage scenarios for IMT-2030. Compared with communication performance, sensing performance is much more vulnerable to interference, and the received backscattered sensing signal with target information is usually too weak to be detected. It is interesting to understand the optimal tradeoff between interference rejection and signal strength improvement for the best sensing performance, but unfortunately it still remains unknown. In this paper, the trinity of auto-ambiguity function (AF), cross-AF and peak-to-average-power ratio (PAPR) is proposed to describe the interference and coverage related aspects for ISAC systems where multi-carrier waveform is usually assumed. We extend the existing orthogonal frequency division multiplexing (OFDM) waveforms in 5G to a generalized OFDM waveform set with some new members and a unified parametric representation. Then the optimal Pareto tradeoff between PAPR, auto-AF and cross-AF (i.e., the union bound) is developed for the generalized OFDM waveform set. To achieve the optimal Pareto union bound with reasonable computational complexity, we further propose a framework to optimize waveform parameters and sequences jointly. Finally, some practical design examples are provided and numerical results reveal that significant improvements can be achieved compared to the state-of-the-art 5G waveforms and sequences.