CPM-based radar waveforms for efficiently bandlimiting a transmitted spectrum

Abstract

In this paper we shall demonstrate how a polyphasecoded radar waveform can be implemented using a continuous phase modulation (CPM) framework so as to achieve spectral containment while maintaining a constant envelope to maximize energy-on-target. Current modulation techniques such as derivative phase shift keying (DPSK) and minimum shift keying (MSK), which are applicable to binary-coded waveforms, are well-known implementation schemes for spectral containment. The CPM implementation is applicable to polyphase codes and can also achieve better spectral containment, though a byproduct is increased range sidelobes that result due to the deviation from the idealized code (implicitly defined for squared-shaped chips). To ameliorate the increased range sidelobes, a version of Least-Squares mismatched filtering is employed that accommodates the continuous nature of the CPM structure. Also, continuous rise/fall-time transitions of the pulse are addressed as part of the holistic implementation of the CPM-based waveform. It is observed that for the CPM implementation the rise/fall-time becomes the limiting factor on spectral containment and a rather simple scheme based on Chireaux out-phasing is suggested as a means to "slow down" the pulse rise/fall.

Transmitter-in-the-loop optimization of physical radar emissions

“…It was recently shown [1] that the continuous phase modulation (CPM) implementation of polyphase radar codes [2] provides a means with which to optimize the resulting nonlinear FM (NLFM) waveform via determination of the code values. While the method of optimization is arbitrary, in [1] the Marginal Fisher's Information (MFI) algorithm [3] was employed as its greedy structure enables rapid convergence to a solution of sufficient quality.…”

Calculation of the radar ambiguity function from time-domain measurement data for real-time, amplifier-in-the-loop waveform optimization

“…In the area of waveform optimization, the design of spectrally confined waveforms through variable-modulus techniques is described in [5], and then through constant-modulus techniques such as continuousphase modulation in [6][7] and piecewise linear chirp optimization in [8]. Skolnik discusses the connection of the ambiguity function with the waveform, including properties of frequency-modulated bursts, or chirps [9].…”

“…In [13], Sussman applies least-squares optimization to the radar waveform problem. Blunt et al and Cook demonstrate the use of continuous-phase modulation to minimize the spectral spreading of waveforms [6][7]. Finally, [4] and [14] represent our state of the art in optimizing radar systems.…”

Hardware-in-the-loop radar waveform optimization using radiated emissions

“…One innovative approach to creating radar waveforms and physical emissions is using the continuous phase modulation (CPM) implementation of polyphase radar codes [5]. This approach provides a means to optimize the resulting nonlinear FM (NLFM) waveform via the determination of code values.…”

“…This approach provides a means to optimize the resulting nonlinear FM (NLFM) waveform via the determination of code values. The advantages of this approach to optimize physical radar emissions has been shown [6], [7]. In addition, physical radar emissions based on this CPM implementation have been optimized with some of the hardware in the loop (the entire transmit chain), but not the antenna, using the peak sidelobe level as the sole metric for designing the waveform [8].…”