ITTC Project

Optimal Space-Time Waveform Design of Adaptive, Multi-Mode Radar

Project Award Date: 08-01-2003


Researchers will develop and evaluate the mathematical theory and algorithms associated with optimal space-time transmit waveforms for multi-static; bistatic, and mono static radar systems. Of particular interest is the development of adaptive (i.e., data-driven) space-time, transmit waveforms.

This effort shall result in the mathematical and algorithmic knowledge required to construct adaptive space-time transmit waveforms that are optimal with respect to specific performance criteria. The efficacy of these methods shall be demonstrated and evaluated using numerical simulations and other mathematical measures.

Additionally, this effort shall link to the state-estimation signal processing approach to enable optimal integration of adaptive waveforms into the overall sensor signal-processing algorithms, including SAR and MTI radar modes.

A key characteristic of any radar sensor is the form of its transmit signal. The ambiguity function of its transmit waveform specifies the ability of the sensor to resolve targets as a function of delay and Doppler. The ideal transmit signal would produce an ambiguity function with zero value for all non-zero delay and Doppler (i.e., a "thumbtack"), indicating that the responses from dissimilar targets are perfectly uncorrelated. However, a fundamental property of the delay-Doppler ambiguity function is that the energy of the function is an invariant. Through proper signal design, the energy in an ambiguity function can be moved to specific regions in the delay-Doppler plane, but it cannot be eliminated. Thus, the ideal ambiguity function cannot be formedthere is no ideal radar signal. Accordingly, a long-standing radar engineering problem is transmit waveform designan effort to design a signal with a desired, but realizable, ambiguity function. Examples of these efforts include Costas, Barker, and Frank Codes.

The delay-Doppler ambiguity function is most relevant for traditional single-aperture, monostatic radar designs. However, advances in microwave monolithic technology, coupled with the constant improvement in data processing capabilities, have enabled the development of multi-static radar systems. These sensors are formed with spatial arrays of antenna elements, each implemented with its own coherent receiver and/or transmitter. These antennas in this array may be arranged contiguously, or dispersed widely over a large volume to form a sparse radar array. These systems thus sample scattered fields as a function of both space and time, and thus can resolve targets in terms of delay, Doppler, and two dimensions of spatial frequency.

In addition to receiving scattered information across space and time, these transmit signals for these systems are also a function of space and time. Although the space-time transmit signal can be described as a separable function of space and time (with the spatial function describing the array weighting function), we can likewise transmit a more general (non-separable) space-time signal. In other words, each transmit element can send independent, dissimilar signals in time. A two-dimensional ambiguity function can likewise be defined for these space-time sensors, again defining the resolving capabilities of the radar. However, an important characteristic of this space-time ambiguity function is that its energy is not an invariant. Thus, for a given system design, there are optimum space-time transmit codes, in the sense that energy in the ambiguity function can be minimized.

The design of space-time codes and waveforms has become an important research topic in wireless communication systems, and is beginning to generate interest in the radar community as well. To see how these waveforms can be useful, and how optimal codes can be designed, we present a linear model of the radar problem, where the measured space-time values are described in terms of the illuminated targets and the transmitted space-time waveform.


Faculty Investigator(s): James Stiles (PI)

Student Investigator(s): Atulya Deekonda, Vishal Sinha, Ambika Nanda, James Jenshak

Project Sponsors

Primary Sponsor(s): Science Applications International Corporation (SAIC)

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