Joint Design of Mismatched Filter and Phase Coded Waveform via Mainlobe Broadening

The joint design of mismatched filter and waveform is an important technique in suppressing sidelobes of phase coded waveform. Conventionally, an implied constraint that the mainlobe response is of the same width as a chip or bit is included. In fact, a slightly broadened mainlobe is acceptable in most cases. More importantly, relaxation of the mainlobe width will provide more design freedom in sidelobe suppression. In this work, the mainlobe response is broadened into a fixed window shape. Under the constraints of the shape of mainlobe and waveform constant modular, the optimization problem is to minimize the integrated sidelobe level (ISL). The optimization problem is solved by Lagrange multiplier method and Alternating Direction Multiplier Method (ADMM). This method will obtain low sidelobes with a slight loss of signal-to-noise ratio. Additionally, the explanation that mainlobe broadening can further reduce the sidelobe is given in the frequency domain.