Design and Optimization of Physical Waveform-Diverse and Spatially-Diverse Radar Emissions

With the advancement of arbitrary waveform generation techniques, new radar transmission modes can be designed via precise control of the waveform's time-domain signal structure. The finer degree of emission control for a waveform (or multiple waveforms via a digital array) presents an opportunity to reduce ambiguities in the estimation of parameters within the radar backscatter. While this freedom opens the door to new emission capabilities, one must still consider the practical attributes for radar waveform design. Constraints such as constant amplitude (to maintain sufficient power efficiency) and continuous phase (for spectral containment) are still considered prerequisites for high-powered radar waveforms. These criteria are also applicable to the design of multiple waveforms emitted from an antenna array in a multiple-input multiple-output (MIMO) mode. In this work, three spatially-diverse radar emission design methods are introduced that provide constant amplitude, spectrally-contained waveforms implemented via a digital array radar (DAR). The first design method, denoted as spatial modulation, designs the radar waveforms via a polyphase-coded frequency-modulated (PCFM) framework to steer the coherent mainbeam of the emission within a pulse. The second design method is an iterative scheme to generate waveforms that achieve a desired wideband and/or widebeam radar emission. However, a wideband and widebeam emission can place a portion of the emitted energy into what is known as the `invisible' space of the array, which is related to the storage of reactive power that can damage a radar transmitter. The proposed design method purposefully avoids this space and a quantity denoted as the Fractional Reactive Power (FRP) is defined to assess the quality of the result. The third design method produces simultaneous radar and communications beams in separate spatial directions while maintaining constant modulus by leveraging the orthogonal complement of the emitted directions. This orthogonal energy defines a trade-space between power efficiency gained from constraining waveforms to be constant amplitude and power efficiency lost by emitting energy in undesired directions. The design of FM waveforms via traditional gradient-based optimization methods is also considered. A waveform model is proposed that is a generalization of the PCFM implementation, denoted as coded-FM (CFM), which defines the phase of the waveform via a summation of weighted, predefined basis functions. Therefore, gradient-based methods can be used to minimize a given cost function with respect to a finite set of optimizable parameters. A generalized integrated sidelobe level (GISL) metric is used as the optimization cost function to minimize the correlation range sidelobes of the radar waveform. System specific waveform optimization is explored by incorporating the linear models of three different loopback configurations into the GISL metric to match the optimized waveforms to the particular systems

Multi-Objective Optimization of FM Noise Waveforms via Generalized Frequency Template Error Metrics

FM noise waveforms have been experimentally demonstrated to achieve high time bandwidth products and low autocorrelation sidelobes while achieving acceptable spectral containment in physical implementation. Still, it may be necessary to further reduce sidelobe levels for detection or improve spectral containment in the face of growing spectral use. The Frequency Template Error (FTE) and the Logarithmic Frequency Template Error (Log-FTE) metrics were conceived as means to achieve FM noise waveforms with good spectral containment and good autocorrelation sidelobes. In practice, FTE based waveform optimizations have been found to produce better autocorrelation responses at the expense of spectral containment while Log-FTE optimizations achieve excellent spectral containment and interference rejection at the expense of autocorrelation sidelobe levels. In this work, the notion of the FTE and Log-FTE metrics are considered as subsets of a broader class of frequency domain metrics collectively termed as the Generalized Frequency Template Error (GFTE). In doing so, many different P-norm based variations of the FTE and Log-FTE cost functions are extensively examined and applied via gradient descent methods to optimize polyphase-coded FM (PCFM) waveforms. The performance of the different P-norm variations of the FTE and Log-FTE cost functions are compared amongst themselves, against each other, and relative to a previous FM noise waveform design approach called Pseudo-Random Optimized FM (PRO-FM). They are evaluated in terms of their autocorrelation sidelobes, spectral containment, and their ability to realize spectral notches within the 3 dB bandwidth for the purpose of interference rejection. These comparisons are performed in both simulation and experimentally in loopback where it was found that P-norm values of 2 tend to provide the best optimization performance for both the FTE and Log-FTE optimizations except in the case of the Log-FTE optimization of a notched spectral template where a P-norm value of 3 provides the best results. In general, the FTE and Log-FTE cost functions as subsets of the GFTE provide diverse means to optimize physically robust FM noise waveforms while emphasizing different performance criteria in terms of autocorrelation sidelobes, spectral containment, and interference rejection

Addressing Spectrum Congestion by Spectrally-Cooperative Radar design

This dissertation attempts to address a significant challenge that is encountered by the users of the Radio Frequency (RF) Spectrum in recent years. The challenge arises due to the need for greater RF spectrum by wireless communication industries such as mobile telephony, cable/satellite and wireless internet as a result of growing con-sumer base and demands. As such, it has led to the issue of spectrum congestion as radar systems have traditionally maintain the largest share of the RF spectrum. To resolve the spectrum congestion problem, it has become even necessary for users from both radar and communication systems to coexist within a finite spectrum allocation. However, this then leads to other problems such as the increased likelihood of mutual interference experienced by all systems that are coexisting within the finite spectrum.. In order to address this challenge, the dissertation will seek to resolve it via a two-step approach that are described as follows. For the first step of this approach, it will present a structured and meticulous approach to design a sparse spectrum allocation optimization scheme that will lead to the release of valuable spectrum previously allocated to radar applications for reallocation to other players such as the wireless video-on-demand and telecommunication industries while maintaining the range resolution performance of these radar applications. This sparse bandwidth allocation scheme is implemented using an optimization process utilizing the Marginal Fisher information (MFI) measure as the main metric for optimization. Although the MFI approach belongs to the class of greedy optimization methods that cannot guarantee global convergence, the results obtained indicated that this approach is able to produce a locally optimal solution. For the second step of this approach, it will present on the design of a spectral efficient waveform that can be used to ensure that the allocated spectrum limits will not be violated due to poor spectral emission containment. The design concept of this waveform is based on the joint implementation of the first and higher orders of the Poly-phase coded Frequency Modulated (PCFM) waveform that expands previous research on first order PCFM waveform. As any waveform generated using the PCFM framework possesses good spectral containment and is amenable to high power transmit operations such as radar due to its constant modulus property, thus the combined-orders of PCFM waveform is a very suitable candidate that can be used in conjunction with the sparse bandwidth allocation scheme in the first step for any radar application such that the waveform will further mitigate the issue of interference experienced by other users coexisting within the same band

Applications of FM Noise Radar Waveforms: Spatial Modulation and Polarization Diversity

Two possible radar application spaces are explored through the exploitation of highdimensional nonrecurrent FM-noise waveforms. The first involving a simultaneous dual-polarized emission scheme that provides good separability with respect to co- and cross-polarized terms and the second mimicking the passive actuation of the human eye with a MIMO emission. A waveform optimization scheme denoted as pseudorandom optimized (PRO) FM has been shown to generate FM-noise radar waveforms that are amenable to high power transmitters. Each pulse is generated and optimized independently and possesses a non-repeating FM-noise modulation structure. Because of this the range sidelobes of each pulse are unique and thus are effectively suppressed given enough coherent integration. The PRO-FM waveform generation scheme is used to create two independent sets of FM-noise waveforms to be incorporated into a simultaneous dual-polarized emission; whereby two independent PRO-FM waveforms will be transmitted simultaneously from orthogonal polarization channels. This effectively creates a polarization diverse emission. The random nature of these waveforms also reduce cross-correlation effects that occur during simultaneous transmission on both channels. This formulation is evaluated using experimental open-air measurements to demonstrate the effectiveness of this high-dimensional emission. This research aims to build upon previous work that has demonstrated the ability to mimic fixational eye movements (FEM) employed by the human eye. To implement FEM on a radar system a MIMO capable digital array must be utilized in conjunction with spatial modulation beamforming. Successful imitation of FEM will require randomized fast-time beamsteering from a two-dimensional array. The inherent randomness associated with FEM will be paired with the PRO-FM waveforms to create an emission possessing randomness in the space and frequency domains, called the FEM radar (FEMR). Unlike traditional MIMO, FEMR emits a coherent and time varying beam. Simulations will show the inherent enhancement to spatial resolution in two-dimensional space (azimuth and elevation) relative to standard beamforming using only the matched filter to process returns

Optimal Transmit Beamforming for Integrated Sensing and Communication

This paper studies the transmit beamforming in a downlink integrated sensing and communication (ISAC) system, where a base station (BS) equipped with a uniform linear array (ULA) sends combined information-bearing and dedicated radar signals to simultaneously perform downlink multiuser communication and radar target sensing. Under this setup, we maximize the radar sensing performance (in terms of minimizing the beampattern matching errors or maximizing the minimum weighted beampattern gains), subject to the communication users' minimum signal-to-interference-plus-noise ratio (SINR) requirements and the BS's transmit power constraints. In particular, we consider two types of communication receivers, namely Type-I and Type-II receivers, which do not have and do have the capability of cancelling the interference from the {\emph{a-priori}} known dedicated radar signals, respectively. Under both Type-I and Type-II receivers, the beampattern matching and minimum weighted beampattern gain maximization problems are globally optimally solved via applying the semidefinite relaxation (SDR) technique together with the rigorous proof of the tightness of SDR for both Type-I and Type-II receivers under the two design criteria. It is shown that at the optimality, radar signals are not required with Type-I receivers under some specific conditions, while radar signals are always needed to enhance the performance with Type-II receivers. Numerical results show that the minimum weighted beampattern gain maximization leads to significantly higher beampattern gains at the worst-case sensing angles with a much lower computational complexity than the beampattern matching design. We show that by exploiting the capability of canceling the interference caused by the radar signals, the case with Type-II receivers results in better sensing performance than that with Type-I receivers and other conventional designs.Comment: submitted for possible journal publicatio

Design and Evaluation of Stochastic Processes as Physical Radar Waveforms

Recent advances in waveform generation and in computational power have enabledthe design and implementation of new complex radar waveforms. Still despite these advances, in a waveform agile mode where the radar transmits unique waveforms for every pulse or a nonrepeating signal continuously, effective operation can be difficult due the waveform design requirements. In general, for radar waveforms to be both useful and physically robust they must achieve good autocorrelation sidelobes, be spectrally contained, and possess a constant amplitude envelope for high power operation. Meeting these design goals represents a tremendous computational overhead that can easily impede real-time operation and the overall effectiveness of the radar. This work addresses this concern in the context of random FM waveforms (RFM) that have been demonstrated in recent years in both simulation and in experiments to achieve low autocorrelation sidelobes through the high dimensionality of coherent integration when operating in a waveform agile mode. However, while they are effective, the approaches to design these waveforms require optimization of each individual waveform, making them subject to costly computational requirements. This dissertation takes a different approach. Since RFM waveforms are meant to be noise like in the first place, the waveforms here are instantiated as the sample functions of an underlying stochastic process called a waveform generating function (WGF). This approach enables the convenient generation of spectrally contained RFM waveforms for little more computational cost than pulling numbers from a random number generator (RNG). To do so, this work translates the traditional mathematical treatment of random variables and random processes to a more radar centric perspective such that the WGFs can be analytically evaluated as a function of the usefulness ofthe radar waveforms that they produce via metrics such as the expected matched filter response and the expected power spectral density (PSD). Further, two WGF models denoted as pulsed stochastic waveform generation (Pulsed StoWGe) and continuouswave stochastic waveform generation (CW-StoWGe) are devised as means to optimize WGFs to produce RFM waveform with good spectral containment and design flexibility between the degree of spectral containment and autocorrelation sidelobe levels for both pulsed and CW modes. This goal is achieved by leveraging gradient descent optimization methods to reduce the expected frequency template error (EFTE) cost function. The EFTE optimization is shown analytically using the metrics above, as well as others defined in this work and through simulation, to produce WGFs whose sample functions achieve these goals and thus produce useful random FM waveforms. To complete the theory-modeling-experimentation design life cycle, the resultant StoWGe waveforms are implemented in a loop-back configuration and are shown to be amenable to physical implementation