多项式相位信号求解方法比较

=
arg max ML(bp ...,bp),
(b,
•.. •
HO-WD and HO-CPF represent the trade-off between the accuracy and the computational complexity [10], [11]. With only one PD, the HO-WD and HO-CPF reduce the search space from P- to r Pl2l-dimensional with respect to the ML and, at the same time, they are more accurate than other PD­ based techniques. Multidimensional search space limits practical application of the HO-WD and HO-CPF to the sixth-order PPSs (i.e. to 3D search space). To estimate higher-order PPSs two approaches are recently proposed. The first one is based on the search optimization in the HO-WD and HO-CPF estimation procedures [12]. This optimization is performed by using genetic algorithms (GAs). The GA is a well-known tool for search optimization in science [13], but it is rarely used in PPS parameter estimation. Our aim in this paper is to test the accuracy of the ML, HO-WD and HO-CPF with the GA and to find its' limits. The second approach is based on reducing the number of PDs. In [14], the hybrid CPF-HAF (HCPF-HAF) is proposed. In comparison to the HAF, HCPF-HAF requires two PDs less which leads to lower signal-to-noise ratio (SNR) threshold and lower estimation mean squared error (MSE). The performance of the HCPF-HAF is also tested in this paper. The paper is organized as follows. In Section TT, a summary of the ML, HAF, PHAF, HO-WD, HO-CPF and HCPF-HAF is presented. Simulation results are provided in Section TIT, while concluding remarks are presented in Section IV. TT. THE ML, HAF, PHAF, HO-WD, HO-WD AND HCPFHAF ESTIMATION PROCEDURES
Mediterranean Conference on Embedded Computing
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MECD 2012
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Bar, Montenegro
RECENT ADVANCES IN THE ESTIMATION OF THE POLYNOMIAL-PHASE SIGNALS
Igor Djurovi6 and Marko Simeunovi6
I.
INTRODUCTION
Polynomial-phase signal (PPS) model, motivated by the Weierstrass theorem [I], IS widely used for signal representation in radar, sonar, biomedicine and communications [2], [3]. The PPS order depends on the application. Commonly, signals with quadratic- and cubic­ phase are used. However, some applications require consideration of higher-order PPSs. For example, radar return from a target can be modeled by a PPS up to the fifth-order [4], while some applications in sonar and communications consider higher-order PPSs [5]. These practical requirements motivated development of sophisticated algorithms for parameter estimation of higher-order PPSs. Design of estimation procedures takes into account a trade­ off between accuracy and computational complexity. The maximum likelihood (ML) estimation is the most accurate technique, but it requires search over multidimensional space which, for higher-order PPSs, cannot be done in reasonable time. Thus, techniques based on the phase differentiation (PD) are proposed: the high-order ambiguity function (HAF), product high-order ambiguity function (PHAF), integrated generalized ambiguity function (IGAF) and cubic-phase function (CPF) [6]-[9]. The PD is done by signal auto­ correlation. The search space in these procedures is reduced to I-D (for the HAF, PHAF and CPF) or 2-D (for the IGAF). However, signal auto-correlations and dechirping procedure produce cross-terms and error propagation. Lower number of auto-correlations gives better accuracy and vice versa. The
estimation of higher-order polynomial-phase signals (PPSs). The maximum likelihood (ML) technique is the most accurate estimation procedure, but requirements for multidimensional search limits its practical application to third-order PPSs. To enable estimation of higher-order PPSs in real time, techniques, based on the phase differentiation (PD), are proposed. Each PD reduces the search dimensions, but, at the same time, degrades the estimation performance. In this paper, we consider two approaches for performance improvement of PPS estimation techniques. The first one is based on the search optimization by using genetic algorithms, while the second one consider lower number ofPDs and one dimensional search.
Consider the following signal model:
yen) = x(n) + v(n),n E [-N / 2,N / 2], i x(n) = A exp( j ¢(n )) = A exP J I o ain ,
( :
)
(I)
where x(n) is a P-th order PPS, v(n) the white complex zero­ mean Gaussian noise with variance a2, A the amplitude and ¢(n) the polynomial-phase with parameters {ai, i=O, 1, ..., P}. We will assume that N is odd. The goal of PPS estimation is to estimate the parameters ofx(n) by observingy(n). The most accurate procedure for this purpose is the ML and it can be described as