The performance of distributed arrays and distributed isotropic receivers in EM source localizations are numerically studied in this paper. The Possible Localization Regions (PLR) of the source in the free space obtained using these two kinds of receivers are analytically studied first. The source PLR obtained using distributed arrays in free space is demonstrated to be smaller than that obtained using distributed isotropic receivers. At the end of this paper, a numerical source localization result in complex urban environment obtained by ray tracing technique confirms this argument. Introduction With the development of wireless communication, the electromagnetic (EM) source localization becomes a hot topic in seeking the EM pollution sources, enhancing the communication performances, and so on. Many localization techniques have been proposed in the literature, e.g., blind signal separation (BSS) using independence component analysis technique (ICA) [1], and ray tracing method [2]-[4], and so forth. In this paper, we only concern on the ray tracing method. In the ray tracing method, the fields on the receivers generated by the source are measured first. Subsequently, the interesting region in which the source is located is divided into some discrete grid points. Each of these grid points maybe the approximation of the true source, which depends on whether it satisfies the judgment of a criterion, viz., cost function. The definitions of the cost functions can be diverse. It can be defined as the average square root of the relative differences between the fields on the receivers generated by the true source and that by the guessed source. I also can be defined as the 2-norm between the normalized field vectors generated by the guessed source and that by the true source. (The elements in the field vectors are the fields on the receivers.) In this paper, if the power of the source is known, we use the former one. Otherwise, we use the later definition. No matter what definitions of the cost function we use, there always exists a problem, viz., the numerical methods exist the modeling errors, which will cause the uncertainty of localization. This suggests that we can’t localize the true source points but just delimit a region that contains this source points. Assume that the upper bound of the modeling error is e0. Thus we can only get a region whose points ~r ′satisfy the inequality‖u(~r, ~r′)− u∗(~r, ~r′ 0)‖ ≤ e0, where u(r, r′) and u ∗ (~r, ~ r′) denote the simulated field and the measured field, respectively, while ~r0 is the true source point. (Note, u(r, r ′)and u ∗ (~r, ~ r′)can have different definitions as discussed in the next sections.) We call this region the Possible Localization Region (PLR). In the next section, we will analytically study the free space PLRs obtained by using distributed isotropic receivers and arrays, respectively. By the way, we would like to mention that because the measured data generated by the true source can’t be easily obtained, thus we just use the simulated data, and then, the points in the PLR should satisfy ‖u(~r, ~r′)− u(~r, ~r′ 0)‖ ≤2e0. (For saving space, its derivation will not be presented here.) Analytically Studying the PLR for Socalization in Free Space Because it is difficult to analytically study the source localization in complex urban environment, we only analytically study the PLR for free space localization problem. At first, let us study the PLR obtained using the distributed isotropic receivers. The field at point ~rgenerated by the source at point ~r′ in the free space can be expressed as u(~r, ~ r′) = E0/ ∣∣~r − ~ r′ ∣∣ c (1) Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26 741 where the superscript c denotes the range index and c=0.5 (for 2D case) or 1 (for 3D case). Assume the true source and the n receivers are located at the original point ~ O = (0, 0) and the points ~ri, respectively, where i = 1, · · · , n. At receiver ~ri, the relative difference between the field generated by the source at any point ~ r′and the original point is written as ∆u(~ri, ~r ′) = (u(~ri, ~r ′)− u(~ri, ~ O))/u(~ri, ~ O) (2) We define the cost function as Cost Function = ‖∆ū(~r′)‖ , (3) where ∆ū(~r′) = [∆u(~r1, ~ r′), · · · ,∆u(~rn, ~ r′)]T . From the discussion in the introduction, we know that the PLR in the interested region is defined as a region whose space points ~ r′ satisfy the inequality Cost Function = ‖∆ū(~r′)‖ ≤ 2e0 (4) Substituting (1) and (2) into (4) we obtain ||∆u|| = √√√√ n ∑ i=1 [[1 + (|~ r′|/|~ri|)2 − 2|~ r|/|~ri | cos(θ′ − θi)]− c 2 − 1] ≤ 2e0 (5) where θ′ and θi are the polar angles of points ~ r′ and ~ri. To directly solve (5) is difficult. Fortunately, when n ≥ 2, the PLR becomes some small areas in the interesting region. It means that the inequality |~r′|/|~ri| << 1 must holds in one small area of the PLR that contains the true source point. Hence, applying the Taylor approximation in (5) and neglecting the higher order terms of |~r′|/|~ri|, we simplify (5) as, |~r′|2 ≤ 4e 2 0 c2 n ∑ i=1 cos2(θ′−θi) |~ri|2 (6) Hence the area of PLR is analytically expressed as