THESIS
2018
xix, 129 pages : illustrations ; 30 cm
Abstract
Radar has been evolving itself significantly since MIMO and cognition were introduced.
One important research topic is the design of radar waveform. By exploiting the waveform
diversity, the performance of the radar systems can be improved significantly. The waveform
design needs to satisfy three requirements. First, the designed waveform should perform
well in the evaluation of some metrics. Second, the designed waveform should satisfy some
nice properties so that it will be compatible with the hardware configuration and application
scenarios. Last but not least, the design algorithm should be computationally efficient for the
real-time radar applications. The focus of this dissertation is on the development of efficient
optimization methods based on some optimization framework...[
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Radar has been evolving itself significantly since MIMO and cognition were introduced.
One important research topic is the design of radar waveform. By exploiting the waveform
diversity, the performance of the radar systems can be improved significantly. The waveform
design needs to satisfy three requirements. First, the designed waveform should perform
well in the evaluation of some metrics. Second, the designed waveform should satisfy some
nice properties so that it will be compatible with the hardware configuration and application
scenarios. Last but not least, the design algorithm should be computationally efficient for the
real-time radar applications. The focus of this dissertation is on the development of efficient
optimization methods based on some optimization frameworks for radar waveform design.
The first question is what metric is used to measure the design performance. Among many
metrics, the most important one is signal-to-interference plus noise ratio (SINR), which determines
the probability of detection. Thus, the common formulation of the design problem
is a maximization of the derived SINR subject to some waveform constraints. The existing
methods to solve this kind of problems are mostly based the semidefinite programming
(SDP). However, this kind of methods are very time-consuming, and in some cases, without
guarantee of monotonicity or further convergence. To deal with these issues, we propose
optimization methods based on the majorization-minimization framework for the SINR maximization
problem in the context of cognitive radar. Then, we extend our methodology into
the joint design problem, in which we jointly design the transmit waveforms and receive filters
in the context of MIMO radar. The derived algorithm is very flexible in that it can deal
with many waveform constraints by only a slight modification. The numerical results show
that our methods can achieve the same or even better SINR than the benchmarks but with less
computational cost.
The second question is what properties the design waveform should possess. An important
one is the desired spectral shape. Specifically, the transmit sequence should avoid certain
frequency bands or try to minimize the spectral power on those bands. The motivation behind
is spectral sharing, which becomes a solution to tackle the ever growing demand of
spectrum resources from multiple RF services. Recently proposed spectral level ratio (SLR)
is interesting and simple compared with other existing approaches. We extend th SLR to a
regularized SLR (RSLR) which is more suitable for optimization. However, the formulated
RSLR minimization problem is very hard to solve because it is fractional, nonsmooth and
nonconvex. Thus, our goal is to develop optimization methods for the RSLR problem. We
develop two algorithms by combining both the majorization-minimization and the Dinkelbach’s
algorithm. Numerical simulations show that one algorithm is suitable for generating
good initialization, and the other algorithm performs better than the benchmark in terms of
both SLR and running time.
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