## 1. Introduction

[2] Recently, *Kudeki et al.* [2003] and *Feng et al.* [2003] described a new incoherent scatter radar technique for measuring *F* region plasma densities with the Jicamarca radar. The new technique makes use of a pair of orthogonal polarized antenna beams pointed perpendicular to the geomagnetic field . *F* region density estimates *N*_{e}(*z*) are obtained by least squares fitting the differential phase and average power of southward and eastward polarized antenna outputs *V*_{θ} and *V*_{ϕ} to density dependent data models ∠〈*V*_{θ}*V**_{ϕ}〉 and 〈∣*V*_{θ}∣^{2}〉 + 〈∣*V*_{ϕ}∣^{2}〉. Detailed descriptions of 〈*V*_{θ}*V**_{ϕ}〉 and 〈∣*V*_{θ}∣^{2}〉 + 〈∣*V*_{ϕ}∣^{2}〉 models are given in *Feng et al.* [2003]. As described in *Kudeki et al.* [2003] and *Feng et al.* [2003], the new technique was developed to obtain density measurements during Jicamarca drifts experiments which rely on antenna beams pointed perpendicular to .

[3] In this paper we will describe a recently introduced feature of the new technique that makes use of the real and imaginary parts of the complex cross-correlation 〈*V*_{θ}*V**_{ϕ}〉 of *V*_{θ} and *V*_{ϕ} data instead of their phase difference ∠〈*V*_{θ}*V**_{ϕ}〉. The advantage of using 〈*V*_{θ}*V**_{ϕ}〉 instead of ∠〈*V*_{θ}*V**_{ϕ}〉 is as follows: When signal-to-noise ratio (SNR) is low the standard deviation of phase errors approaches and the error distribution takes a flat non-Gaussian character. Phase estimates with flat error distributions are not usable in data inversions. Differential-phase based inversion procedures described in *Kudeki et al.* [2003] and *Feng et al.* [2003] have therefore avoided using cross-correlation data from upper *F* region heights with low SNR values. However, as it is well known, real and imaginary components of cross-correlation 〈*V*_{θ}*V**_{ϕ}〉 remain Gaussian random variables even under low SNR conditions. Therefore, by reformulating the inversion procedure in terms of real and imaginary parts of 〈*V*_{θ}*V**_{ϕ}〉 the use of cross-correlation data from upper *F* region heights becomes possible and the overall quality of inversion results can be improved.

[4] The present paper describes the details of the revisions outlined above. It is organized as follows: In section 2 we review the data models 〈*V*_{θ}*V**_{ϕ}〉 and 〈∣*V*_{θ}∣^{2}〉 + 〈∣*V*_{ϕ}∣^{2}〉 from *Feng et al.* [2003] and describe their joint covariance matrix needed in a revised formulation of a χ^{2} expression representing the data/model misfit. Density estimation is carried out by minimizing χ^{2} over the model parameters as described earlier in *Feng et al.* [2003]. Section 3 describes the modified χ^{2} in detail and experimental results are shown and discussed in section 4.