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In this paper we focus on deriving an approximate Cramer–Rao lower bound (CRLB) for the parameters of a multicomponent linear frequency modulated continuous wave (LFMCW) signal corrupted by complex additive white Gaussian noise. The approximation is necessary due to the discontinuities inherent in the mathematical model of the instantaneous phase of each LFMCW signal model. By comparing our approximate bound to a simulation of the maximum likelihood estimator (MLE) of the LFMCW parameters, we confirm our analysis. In general, the CRLB is a useful tool for feasibility studies or in evaluating the degree of suboptimality that non-MLE methods exhibit. For passive detection and estimation of LFMCW signals, the Generalized Likelihood Ratio Test and the associated MLE are difficult to implement in practice, primarily due to their large computational requirements. So, lower bounds on performance, such as those provided by the CRLB, are necessary to evaluate suboptimal methods that are more suited for practical implementations.

Many modern radar systems are overcoming the need for high-power transmitters by utilizing low peak-power, high duty-cycle waveforms, making noncooperative detection methods by traditional electronic surveillance a difficult task. This technological difficulty is driving a need for computationally tractable detection and characterization algorithms. Here, a practical method for detecting and fully characterizing an arbitrary number of low-power linear frequency modulated continuous wave (LFMCW) radar signals is achieved by dividing the time-domain signal into contiguous segments and treating each signal segment as a sum of harmonic components corrupted by noise with an unknown, time-varying power spectral density. This method is developed analytically and evaluated experimentally, revealing that the practicality of the method comes at the ex-pense of a loss in estimation accuracy when compared to the Cramer–Rao lower bound. Experimental results indicate that the parameters of two simultaneous LFMCW signals can be estimated to within $10\%$ of their true values with probability greater than $90\%$ when input signal-to-noise ratios are $-$ 10 dB and above with a 25 MHz bandwidth receiver.

This work considers the design of optimal, energy-constrained transmit signals for active sensing for the case when the designer has incomplete or uncertain knowledge of the target and/or environment. The mathematical formulation is that of a multi-objective optimization problem, wherein one can incorporate a plurality of potential targets, interference, or clutter models and in doing so take advantage of the wide range of results in the literature related to modeling each. It is shown, via simulation, that when the objective function of the optimization problem is chosen to maximize the minimum (i.e., maxmin) probability of detection among all possible model combinations, the optimal waveforms obtained are advantageous. The advantage results because the maxmin waveforms judiciously allocate energy to spectral regions where each of the target models respond strongly and each of the environmental models affect minimal detection performance degradation. In particular, improved detection performance is shown compared to linear frequency modulated transmit signals and compared to signals designed with the wrong target spectrum assumed. Additionally, it is shown that the maxmin design yields performance comparable to an optimal design matched to the correct target/environmental model. Finally, it is proven that the maxmin problem formulation is convex.