Simultaneous Estimation of Azimuth DOA and Angular Spread of Incident Radio Waves by DOA-Matrix Method Using Planar Array Makoto Jomoto † , Nobuyoshi Kikuma ‡ , and Kunio Sakakibara ‡ † Dept. of Computer Science and Engineering ‡ Dept. of Electrical and Mechanical Engineering Nagoya Institute of Technology, Nagoya 466-8555, Japan Email: [email protected] Abstract – In estimating DOA of incident waves with high accuracy, we often have to take into consideration the angular spread (AS) of each wave due to reflection, diffraction, and scat- tering. As a method of estimating DOA and AS simultaneously, DOA-Matrix method was proposed. In this paper, we extend the array configuration from the linear array to the planar array for simultaneous estimation of DOA and AS over whole azimuth angles. Index Terms — DOA, angular spread, DOA-Matrix method, planar array. 1. Introduction In order to clarify the radio environments, it is effective to estimate the DOA of individual incident waves at the receiving point. For estimating the DOA, the algorithms such as MUSIC and ESPRIT[1] with array antennas are attractive because of high estimation accuracy and high computational efficiency. However, we often have to take into consideration the angular spread of each wave due to reflection, diffraction, and scattering[2]. As a method of estimating DOA and AS simultaneously, the use of DOA-Matrix method[3] was proposed. In this paper, we extend the array configuration from the linear array to the planar array for simultaneous estimation of DOA and AS over whole azimuth angles. Then, we propose DOA-Matrix method in which the integrated mode vector [3] is applied to the planar array. 2. Array Antenna and Signal Model Fig. 1 shows the K = K x × K y element planar array antenna with element spacing of ∆x and ∆y, which receives L clustered waves with angular spread in azimuth. We assume that the M l element waves of the l-th clustered wave are in phase and continuously distributed in the angular spread ∆θ l with the center angle θ l (DOA). Then, the array input vector x(t) can be expressed as follows. x(t) = L ∑ l=1 s l (t) a(θ l , ∆θ l ) + n(t) (1) a(θ l , ∆θ l ) = [ a 1,1 (θ l , ∆θ l ), a 2,1 (θ l , ∆θ l ), ··· , a K x ,K y (θ l , ∆θ l ) ] T (2) a k x ,k y (θ, ∆θ) = a ok x (θ)a ok y (θ)ψ k x ,k y (θ, ∆θ) (3) a ok x (θ) = e - j 2π λ (k x -1)∆x cos θ (k x = 1, ··· , K x ) (4) a ok y (θ) = e - j 2π λ (k y -1)∆y sin θ (k y = 1, ··· , K y ) (5) ψ k x ,k y (θ, ∆θ) = sinc [ π λ ∆θ{(k y - 1)∆y cos θ - (k x - 1)∆x sin θ} ] (6) where s l (t) is the complex amplitude of the l-th clustered wave. 3. AS Estimation by DOA-Matrix Method If we make the following approximation ψ k x ,k y (θ, ∆θ) ≃ ψ k x ,k y +1 (θ, ∆θ) (7) then the array input vectors of two subarrays in Fig. 1, x 1 (t) and x 2 (t), are expressed as follows. x 1 (t) = A 1 s(t) + n 1 (t) (8) x 2 (t) = A 2 s(t) + n 2 (t) (9) A 1 = [ a 1 (θ 1 , ∆θ 1 ), ··· , a 1 (θ L , ∆θ L )] (10) a 1 (θ l , ∆θ l ) = [ a 1,1 (θ l , ∆θ l ), ··· , a K x ,K y -1 (θ l , ∆θ l ) ] T (11) A 2 = [ a 2 (θ 1 , ∆θ 1 ), ··· , a 2 (θ L , ∆θ L )] (12) a 2 (θ l , ∆θ l ) = [ a 1,2 (θ l , ∆θ l ), ··· , a K x ,K y (θ l , ∆θ l ) ] T (13) A 2 ≃ A 1 Φ (14) s(t) = [ s 1 (t), s 2 (t), ··· , s L (t)] T (15) Φ = diag ( ϕ 1 , ··· ,ϕ L ) (ϕ l = e - j 2π λ ∆y sin θ l ) (16) where n 1 (t) and n 2 (t) are noise vectors of subarray 1 and subarray 2, respectively. From the auto-correlation matrix R 11 = E[ x 1 (t) x H 1 (t)] and the cross-correlation matrix R 21 = E[ x 2 (t) x H 1 (t)], we make R = R 21 R 11 -1 . Since R has the relation RA 1 = A 1 Φ, we can obtain the A 1 and Φ from the eigendecomposition of R . We derive the DOA and AS estimates over the whole azimuth angles from A 1 and Φ by rearranging the mode vector a 1 according to the DOA estimates. Specifically, in the case of 45 ◦ ≤| θ | < 135 ◦ , we obtain the AS estimates from comparison between ψ k x ,k y (θ, ∆θ) and ψ k x +1,k y (θ, ∆θ). On the other hand, in the case of 0 ◦ ≤| θ | < 45 ◦ and 135 ◦ ≤| θ | < 180 ◦ , we obtain the AS estimates from comparison between ψ k x ,k y (θ, ∆θ) and ψ k x ,k y +1 (θ, ∆θ). 4. Computer Simulation Computer simulation is carried out under the conditions described in Table I. Fig. 2 shows the validity of approxima- tion of (7) or (14) by spatial correlation between a 1 and a 2 . Figs. 3 and 4 show the estimation accuracy as a function of DOA. In both figures, two methods i.e. the proposed method and DOA-Matrix method without the rearrangement of mode vector are compared. It is found from Fig. 2 that the value of correlation coefficient between a 1 and a 2 is greater than 0.9992 within AS of 10 ◦ . Therefore, it is demonstrated that the approximation of (7) or (14) is valid enough, and also that DOA-Matrix Proceedings of ISAP2016, Okinawa, Japan Copyright ©2016 by IEICE 4C2-2 1020