Design of Optimal Multiple Phase-Coded Signals for Broadband Acoustical Doppler Current Profiler

Traditional broadband acoustical Doppler current profilers utilize binary phase-coded signals (BPCSs), like Barker code or
$M$
-sequence, as their transmitted signals. However, these BPCSs may not be optimal in terms of measurement deviation of current velocity. By analyzing the properties of broadband transmitted signals that influence the measurement deviation, this paper gives a mathematical explanation that the measurement deviation is essentially determined by the integral of the square of the single baseband pulse's autocorrelation function (SBPAF), namely the energy of SBPAF, when the duration and energy of the single transmitted pulse are fixed. To minimize the measurement deviation, a multiple phase-coded signal (MPCS) is adopted and the design method to obtain the optimized MPCS is proposed, which takes the energy of SBPAF as the objective function and coded phases as optimization variables. Simulations show that compared with the reference BPCS, the average measurement deviation is approximately reduced by 15% and 10% in the case of the optimized MPCS (the code length being 63), when the number of single baseband pulses is two and four, respectively. The longer the length is, the better the MPCS performs over the BPCS. When the transmitted power is beyond a certain value, the nonlinear effect will be significant and the second harmonic signal of the optimized MPCS can be used to estimate current velocity in conjunction with the fundamental signal because the second harmonic signal of the optimized MPCS is still broadband. In this situation, the measurement deviation of using the optimized MPCS will be 44% smaller than that of using the reference BPCS. Since the second harmonic signals of the BPCSs which are modulated with 0
$^{\circ}$
and 180
$^{\circ}$
are equivalent to no phase coding and become narrowband, they have no contribution to the estimation of current velocity.