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For the optimization of anti-jamming agile waveform for helicopter borne fire control radar, an agile phase coding waveform suitable for multi-pulse and short code length is designed based on singular value decomposition (SVD) and cyclic algorithm. First, we construct the constrained quadric optimization problem with low sidelobe ambiguity function in the target region. Second, the quartic is transformed into the quadric according to SVD decomposition, and an iterative convergence algorithm is designed. Third, a quadric iterative convergence algorithm is deduced based on the cyclic algorithm. Finally, the simulation results show that the two algorithms are close to each other in the design of agile waveform optimization performance, but the SVD decomposition algorithm has faster convergence speed, and the cycle calculation algorithm has higher operation speed. [ABSTRACT FROM AUTHOR]