Bi-parental product algorithm for coded waveform design in radar

Abstract

The problem of obtaining 10ng sequences with finite alphabet and peaky aperiodic auto-correlation is important in the context of radar, sonar and system identification and is called the coded waveform design problem, or simply the signal design problem in this limited context. It is good to remember that there are other signal design problems in coding theory and digital communication. It is viewed as a problem of optimization. An algorithm based on two operational ideas is developed. From the earlier experience of using the eugenic algorithm for the problem of waveform design, it was realised that rather than random but multiple mutations, all the first-order mutations should be examined to pick up the best one. This is called Hamming scan, which has the advantage of being locally complete, rather than random. The conventional genetic algorithm for non-local optimization leaves out the anabolic role of chemistry of allowing quick growth of complexity. Here, the Hamming scan is made to operate on the Kronecker or Chinese product of two sequences with best-known discrimination values, so that one can go to large lengths and yet get good results in affordable time. The details of the ternary pulse compression sequences obtained are given. They suggest the superiority of the ternary sequences.

Polyphase Sequences Design-Using MSAA

“…The demerit of Hamming scan algorithm is that it gets stuck in the local minimum point because it has no way to distinguish between local minimum point and a global minimum point. Hence it is sub-optimal [11,12]. The drawback in SA is that it has a slow convergence rate because even though it may get closer to the global minimum point, it may skip it because of the methodology it employs, generating the sequences randomly and accepting them with probability based on annealing schedule.…”

“…The Simulated Annealing (SA) technique, introduced by Kirkpatrick et al [10] proved to be an efficient and powerful tool to find optimal or near optimal solutions for complex multivariable nonlinear functions. The concept of Hamming scan algorithm has been employed for obtaining the pulse compression sequences at larger lengths with good correlation properties [11,12]. This algorithm has fast convergence rate but has demerit viz., the tendency to get stuck with local minima.…”

Thirty-two phase sequences design with good autocorrelation properties

“…The demerit of Hamming scan algorithm is that it gets stuck in the local minimum point because it has no way to distinguish between local minimum point and a global minimum point. Hence, it is suboptimal (Moharir et al 1996;1997). The drawback in SA is that it has a slow convergence rate because even though it may get closer to the global minimum point, it may skip it because of the methodology it employs, selecting the sequences randomly and accepting them with probability based on annealing schedule.…”

Polyphase Coded signal Design for Netted Radar Systems

“…...... (2) where E is the energy of signal SI (t) Assuming that an orthogonal polyphase code set consists of L signals with each signal containing N subpulses represented by a complex number sequence, one can express the signal set as follows [4]: {s1(n) n n=1,2, ...,N}, 1 1,2,3. L (3) where X (n) is the phase of bit n of signal I in the signal set and lies between 0 and 2,K. If the number of the distinct phases available to be chosen for each subpluse in a code sequence is M, the phase for a subpulse can only be selected from the following admissible values: (2) where the phase sequence in row 1 (1 < 1 < L ) is the polyphase sequence of signal 1 and all the elements in the matrix can only be chosen from the phase set in (4).…”

“…The simulated annealing technique, introduced by Kirkpatrick et al [1] proved efficient and powerful tool to find optimal or near optimal solutions for complex multivariable nonlinear functions. The concept of Hamming Scan Algorithm (HSA) has been employed for obtaining the pulse compression sequences at larger lengths with good correlation properties [2], [3]. This algorithm has fast convergence rate but has demerit to get stuck with local minima.…”