## 1. Introduction

[2] Superresolution direction-finding (DF) algorithms for linear arrays fall into two broad categories: search-based algorithms, as exemplified by MUSIC [*Schmidt*, 1981; *Roy and Kailath*, 1989] and root-based algorithms such as Root-MUSIC [*Barabell*, 1983; *Rao and Hari*, 1989], Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) [*Roy and Kailath*, 1989]. Search algorithms make no assumptions about the algebraic structure of the array steering vectors but require that they be known to great accuracy, especially if a high degree of angular resolution is called for. In that case they can also be computationally quite demanding. In practice the determination of the array steering vector amounts to an accurate measurement of the magnitude and phase of the array element patterns, sometimes referred to as array manifold calibration. Normal accuracies attained in such measurements are a few tenths of a dB in amplitude and about 1 degree in phase, which generally is insufficient for the design of high-resolution DF systems. Admittedly an alternative technique would be to rely on numerical computer simulations (either computing the element patterns directly or inferring them from the array geometry and the computed impedance or scattering matrix). However, our experience with comparisons of numerical simulations using the latest commercially available software with experimental data indicates that presently this is not yet a fruitful approach [*Abdallah et al.*, 2004].

[3] Root-based algorithms on the other hand require no array calibration and afford substantial computational efficiency over search algorithms. They require that the elements be uniformly spaced and physically identical, which a search algorithm such as MUSIC does not. The more significant restriction however is that the array steering vector must have the form of an array factor of a linear array of uniformly spaced elements. Unfortunately, because of interelement mutual coupling this idealized form of the steering vector is practically unattainable. Indeed when root-based DF algorithms are applied to a real array without some form of compensation significant angle estimation errors can result (W. Wasylkiwskyj et al., Direction finding using root algorithms with mutual coupling compensation, submitted to *IEEE Transactions on Antennas and Propagation*, 2004, hereinafter referred to as Wasylkiwskyj et al., submitted manuscript, 2004). Compensation for the effects of mutual coupling can be realized either through the use of a decoupling transform (Wasylkiwskyj et al., submitted manuscript, 2004) or by employing extra “dummy” elements to equalize the active element radiation patterns [*Wasylkiwskyj and Kopriva*, 2004; *Lundgren*, 1996]. Under the assumption that element radiation patterns are sufficiently equalized the nonnegative pseudospectrum function becomes a polynomial and the DF problem is reduced to polynomial rooting problem [*Barabell*, 1983; *Rao and Hari*, 1989], ESPRIT [*Roy and Kailath*, 1989]. In the case of the Root Multiple Signal Classification (Root MUSIC (RM)) algorithm the degree of the polynomial equals 2*N* − 2, where *N* represents number of array elements and 2*N* − 2 roots have to be calculated. The directions of arrivals (DOA) are calculated from the *L* roots closest to the unit circle where *L* represents number of emitters. This selection process can introduce serious errors especially in low SNR and coupled array environments. Here we formulate a root algorithm with the property that the polynomial that follows from the nonnegative pseudospectrum function has degree 2*L*. Unlike of the case of RM algorithm there are no extraneous roots produced by our modified root polynomial (MRP) algorithm. Its chief advantage over the classical RM algorithm is that it yields only roots corresponding to the actual DOA. The algorithm is derived in section 3. Results of comparative performance evaluation of the MRP and RM algorithms are presented in section 4. The hardware emulation of the decoupled array environment shows excellent agreement with theory. The conclusion is given in section 5.