摘要：

为了有效估计在水声信道多径效应影响下的跳频信号, 针对现有对跳频信号进行稀疏表示时存在的基不匹配问题, 提出一种基于原子范数的水声跳频信号参数估计算法。首先考虑到信号经过水声信道所受的影响, 对水声跳频信号进行数学建模时时间变量上会多一个时延, 之后按照采样频率对信号进行离散化表示, 然后定义原子集合并将水声跳频信号频率估计问题转化为原子范数最小化问题。通过凸公式的强对偶性证明目标位置可以通过求解原问题的对偶问题得到, 接着进一步将问题转化为一个对偶问题, 通过交替方向乘子法(ADMM)计算出对偶多项式在单位圆上模的值为1的点, 进而完成对信号支撑集的估计。最后对每段信号频率分量的个数进行分析, 估计出含有跳变点的分段信号, 再通过对分段信号进行处理, 精确估计出跳变时刻。仿真结果表明, 该算法采用无网格压缩感知理论, 能够有效地避免基不匹配问题, 与现有算法相比, 使用该算法估计水声跳频信号的参数具有更高的估计精度。

关键词: 水声跳频信号, 参数估计, 原子范数, 无网格压缩感知, 多径效应

Abstract:

To effectively estimate the Frequency Hopping(FH) signal under the influence of multipath effect in underwater acoustic channels, an Atomic-norm-based Parameter Estimation Algorithm(APEA) is proposed for underwater acoustic FH signals, to address the existing base mismatch problem in the sparse representation of FH signals. This algorithm first considers the impact of signals passing through underwater acoustic channels, which introduce an additional delay on the time variable when mathematically modelling the underwater acoustic FH signal. Subsequently, the signal is discretely represented by sampling at the specified frequency, to define a set of atoms and transform the frequency estimation problem of the underwater acoustic FH signal into a problem of atomic norm number minimization. The strong duality of the convex formula proves that the target position can be obtained by solving the dual of the original problem. Therefore, the problem is further reformulated into a dual problem. The points of the dual polynomials on the unit circle with modulus one are computed using the Alternating Direction Method of Multipliers(ADMM), which completes the estimation of the signal support. Finally, the number of frequency components of the signal in each segment is analyzed to estimate the segmented signals containing jump points, whereby jump moments are accurately estimated by processing the segmented signals. The algorithm uses the gridless compressed perception theory, which can effectively prevent the base mismatch problem. The simulation results demonstrate that compared with the current algorithms, the parameters of the underwater acoustic FH signals estimated using this algorithm have higher estimation accuracy.

Key words: underwater acoustic frequency-hopping signals, parameter estimation, atomic norm, gridless compressed sensing, multipath effect