Richard C. Chen

A spectrally clean transmitting system for solid-state phased-array radars

Navy radar operations are being curtailed in a littoral environment. This is due to two factors: the encroachment of cell phone systems into the naval radar bands; in-band interference from other radars. The spectral width of most pulsed radars is significantly wider than necessary with present modulation schemes. Most radars utilize some form of constant envelope pulse with phase or frequency modulation. This causes the spectrum to broaden to several times the information bandwidth. If both the amplitude and phase of the transmitted signal are allowed to change, a significantly narrower bandwidth can be achieved. The paper presents a method to create waveforms with instantaneous bandwidths of 20 MHz confined within -100 dB. The theoretical spectral results of three popular phase modulation schemes (phase shift keying, minimum phase shift keying and derivative phase shift keying) are compared with the spectrally clean results. In addition, the Chireix out-phasing method is presented as an alternative to generating amplitude and phase modulated waveforms. The Chireix method provides a way of improving the efficiency compared to the conventional class A power amplifier. Preliminary results are shown for a spectrally clean waveform.

Dynamic programming equations for discounted constrained stochastic control

In this paper, the application of the dynamic programming approach to constrained stochastic control problems with expected value constraints is demonstrated. Specifically, two such problems are analyzed using this approach. The problems analyzed are the problem of minimizing a discounted cost infinite horizon expectation objective subject to an identically structured constraint, and the problem of minimizing a discounted cost infinite horizon minimax objective subject to a discounted expectation constraint. Using the dynamic programming approach, optimality equations, which are the chief contribution of this paper, are obtained for these problems. In particular, the dynamic programming operators for problems with expectation constraints differ significantly from those of standard dynamic programming and problems with worst-case constraints. For the discounted cost infinite horizon cases, existence and uniqueness of solutions to the dynamic programming equations are explicitly shown by using the Banach fixed point theorem to show that the corresponding dynamic programming operators are contractions. The theory developed is illustrated by numerically solving the constrained stochastic control dynamic programming equations derived for simple example problems. The example problems are based on a two-state Markov model that represents an error prone system that is to be maintained.

Highly bandlimited radar signals

This paper describes a method for generating highly bandlimited or spectrally clean signals and investigates an amplification scheme for physically realizing such signals. The method for generating spectrally clean signals involves interpolating discrete-time signals with Gaussian-windowed sinc functions to obtain highly-bandlimited continuous-time signals. Using this technique, spectrally clean continuous-time signals were obtained which are reasonably efficient and have desirable autocorrelation functions as well as being bandlimited. The modulation technique is illustrated with several examples using the thirteen bit Barker code. The amplifier configuration known as LINC (linear amplification using nonlinear components) is proposed as a means of generating spectrally clean signals.

Non-randomized policies for constrained Markov decision processes

This paper addresses constrained Markov decision processes, with expected discounted total cost criteria, which are controlled by non-randomized policies. A dynamic programming approach is used to construct optimal policies. The convergence of the series of finite horizon value functions to the infinite horizon value function is also shown. A simple example illustrating an application is presented.

Dynamic programming equations for constrained stochastic control

It is demonstrated that the dynamic programming approach provides a simple and versatile means for analyzing constrained stochastic control problems. Specifically, three such problems are analyzed using this approach. The problems analyzed are the problem of minimizing a discounted cost infinite horizon expectation objective subject to an identically structured constraint, the problem of minimizing a discounted cost infinite horizon minimax objective subject to a discounted expectation constraint, and the problem of minimizing a discounted expected cost objective subject to a minimax constraint. Using a dynamic programming approach, optimality equations are obtained for these problems. The optimality equations derived for the first two problems are apparently novel. Existence and uniqueness of solutions to the dynamic programming equations for the discounted cost infinite horizon problems are explicitly shown using the Banach fixed point theorem. Thus, the paper demonstrates that the dynamic programming theory for unconstrained stochastic control problems can be extended in a direct way to constrained stochastic control problems. The theory developed is illustrated by numerically solving the constrained stochastic control dynamic programming equations derived for simple example problems.

Constrained stochastic control with probabilistic criteria and search optimization

The dynamic programming approach is applied to both fully and partially observed constrained Markov process control problems with both probabilistic and total cost criteria that are motivated by the optimal search problem. For the fully observed case, point-wise convergence of the optimal cost function for the finite horizon problem to that of the infinite horizon problem is shown. For the partially observed case, a constrained finite horizon problem with both probabilistic and expected total cost criteria is formulated that is demonstrated to be applicable to the radar search problem. This formulation allows the explicit inclusion of certain probability of detection and probability of false alarm criteria, and consequently it allows integration of control and detection objectives. This is illustrated by formulating an optimal truncated sequential detection problem involving minimization of resources required to achieve specified levels of probability of detection and probability of false alarm. A simple example of optimal truncated sequential detection that represents the optimization of a radar detection process is given.

Golay waveforms and adaptive estimation

An iterative range profile estimation process is derived for Golay waveforms. The Re-Iterative Super Resolution (RISR) algorithm is used in conjunction with Golay waveforms and processing for radar range-Doppler estimation. Various additional range-Doppler estimation methods that use RISR and Golay waveforms and processing are simulated for the sake of comparison. Range and Doppler sidelobes are seen in simulation to be mitigated to a significant extent by using RISR in conjunction with Golay waveforms and processing.

Compactness of the space of non-randomized policies in countable-state sequential decision processes

For sequential decision processes with countable state spaces, we prove compactness of the set of strategic measures corresponding to nonrandomized policies. For the Borel state case, this set may not be compact (Piunovskiy, Optimal control of random sequences in problems with constraints. Kluwer, Boston, p. 170, 1997) in spite of compactness of the set of strategic measures corresponding to all policies (Schäl, On dynamic programming: compactness of the space of policies. Stoch Processes Appl 3(4):345–364, 1975b; Balder, On compactness of the space of policies in stochastic dynamic programming. Stoch Processes Appl 32(1):141–150, 1989). We use the compactness result from this paper to show the existence of optimal policies for countable-state constrained optimization of expected discounted and nonpositive rewards, when the optimality is considered within the class of nonrandomized policies. This paper also studies the convergence of a value-iteration algorithm for such constrained problems.

Constrained Partially Observed Markov Decision Processes With Probabilistic Criteria for Adaptive Sequential Detection

Dynamic programming equations are derived which characterize the optimal value functions for a partially observed constrained Markov decision process problem with both total cost and probabilistic criteria. More specifically, the goal is to minimize an expected total cost subject to a constraint on the probability that another total cost exceeds a prescribed threshold. The Markov decision process is partially observed, but it is assumed that the constraint costs are available to the controller, i.e., they are fully observed. The problem is motivated by an adaptive sequential detection application. The application of the dynamic programming results to optimal adaptive truncated sequential detection is demonstrated using an example involving the optimization of a radar detection process.

Doppler tolerant time separated Golay waveforms

A radar transmission and processing scheme is developed which yields range profile estimates with target mainlobes which are as narrow as possible and sidelobe levels which are low. Specifically, Golay waveforms are implemented via time separated waveform transmission and the Re-Iterative Super Resolution (RISR) algorithm [9]. Doppler tolerance is achieved by using Golay quads in addition to Doppler bin specific fast-time Doppler compensation. The four waveforms of the Golay quad are transmitted in four sequential bursts at a fixed pulse repetition interval. The RISR algorithm is used to separate the received signal into discrete Doppler bins. The separated signal components are then compensated appropriately so that the Golay complementarity property can be exploited. The time separated Golay transmission and processing scheme is illustrated with simple simulation examples.