Fast DOA estimation using wavelet denoising on MIMO fading channel

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1 Fast DOA estimation using wavelet denoising on MIMO ading channel A.V. Meenakshi, V.Punitham, R.Kayalvizhi, S.Asha Assistant Proessor/ECE, Periyar Maniammai University, Thanjavur Abstract This paper presents a tool or the analysis, and simulation o direction-o-arrival (DOA) estimation in wireless mobile communication systems over the ading channel. It reviews two methods o Direction o arrival (DOA) estimation algorithm. The standard Multiple Signal Classiication (MUSIC) can be obtained rom the subspace based methods. In improved MUSIC procedure called Cyclic MUSIC, it can automatically classiy the signals as desired and undesired based on the known spectral correlation property and estimate only the desired signal s DOA. In this paper, the DOA estimation algorithm using the denoising pre-processing based on time-requency conversion analysis was proposed, and the perormances were analyzed. This is ocused on the improvement o DOA estimation at a lower SR and intererence environment. This paper provides a airly complete image o the perormance and statistical eiciency o each o above two methods with QPSK signal. Keywords: MUSIC; QPSK; DOA; MIMO. Introduction The goal o direction-o-arrival (DOA) estimation is to use the data received on the downlink at the base-station sensor array to estimate the directions o the signals rom the desired mobile users as well as the directions o intererence signals. The results o DOA estimation are then used by to adjust the weights o the adaptive beam ormer. So that the radiated power is maximized towards the desired users, and radiation nulls are placed in the directions o intererence signals. ence, a successul design o an adaptive array depends highly on the choice o the DOA Estimation algorithm which should be highly accurate and robust. Array signal processing has ound important applications in diverse ields such as Radar, Sonar, Communications and Seismic explorations. The problem o estimating the DOA o narrow band signals using antenna arrays has been analyzed intensively over ast ew years.[1]-[9]. The wavelet denoising is a useul tool or various applications o image processing and acoustic signal processing or noise reduction. There are some trials or DOA estimation by applying the wavelet transorm method into several sub bands MUSIC and CYCLIC MUSIC scenarios [6{8]. But they do not consider larger noise bandwidth with intererence signal included in processing samples. In this paper, the DOA estimation algorithm using a time-requency conversion pre-processing method with a signal OBW (Occupied Bandwidth) analysis was proposed or CYCLIC MUSIC and the eectiveness was veriied through the simulation. This is ocused on the improvement o DOA estimation perormance at lower SR and intererence environment. This is in compliance with the radio usage trends o lower power and widening signal bandwidth especially. This paper is organized as ollows. Section I presents the narrow band signal model with QPSK signal. In section II the above mentioned data model is extended to multi path ading channel. ere we describe two-channel models namely coherent and noncoherent requency selective slow ading channels. Section III. a and b briely describes the algorithms we have used. Section IV deal with MUSIC and Cyclic MUSIC algorithms with proposed model. MUSIC procedures are computationally much simpler than the MLM but they provide less accurate estimate [2]. The popular methods o Direction inding such as MUSIC suer rom various drawbacks such as 1.The total number o signals impinges on the antenna array is less than the total number o receiving antenna array. 2. Inability to resolve the closely spaced signals 3. eed or the knowledge o the existing characteristics such as noise characteristics. Cyclic MUSIC algorithm overcomes the above drawbacks. It exhibits cyclostationarity, which improves the DOA estimation. Finally Section V describes the simulation results and perormance comparison. Section VI concludes the paper. A.V. Meenakshi is with the Periyar Maniammai University-Thanjavur meenu_gow@yahoo.com

2 jφ j( 1)φ I. ARROW BAD SIGAL MODEL The algorithm starts by constructing a real-lie signal model. Consider a number o plane waves rom M narrow-band sources impinging rom dierent angles θi, i = 1, 2,, M, impinging into a uniorm linear array (ULA) o equi-spaced sensors, as shown in Figure 1. Figure1.Uniorm linear array antenna In narrowband array processing, when n signals arrive at an m-element array, the linear data model y(t)=a(φ)x(t)+n(t) (1) is commonly used, where the m*n spatial matrix A=[a 1, a 2,...a n ] represents the mixing matrix or the steering matrix. In direction inding problems, we require A to have a known structure, and each column o A corresponds to a single arrival and carries a clear bearing. a(φ) is an 1 vector reerred to as the array response to that source or array steering vector or that direction. It is given by: a(φ) = [1 e... e ] T (2) where T is the transposition operator, and φ represents the electrical phase shit rom element to element along the array. This can be deined by: φ = (2π /λ )d cosθ (3) where d is the element spacing and λ is the wavelength o the received signal. Due to the mixture o the signals at each antenna, the elements o the m 1 data vector y(t) are multicomponent signals. Whereas each source signal x(t) o the n 1 signal vector, x(t) is oten a monocomponent signal. n(t) is an additive noise vector whose elements are modeled as stationary, spatially and temporally white, zero mean complex random processes that are independent o the source signals. That is E[n (t+г) n (t)]=σδ(τ)i E[n (t+г) n T (t)]=0, or any τ (4) Where δ(τ) is the delta unction, I denotes the identity matrix, σ is the noise power at each antenna element, superscripts and T, respectively, denote conjugate transpose and transpose and E(.) is the statistical expectation operator. In (1), it is assumed that the number o receiving antenna element is larger than the number o sources, i.e., m>n. Further, matrix A is ull column rank, which implies that the steering vectors corresponding to n dierent angles o arrival are linearly independent. We urther assume that the correlation matrix R E [ y( t) y ( t) ] yy = (5) is nonsingular and that the observation period consists o snapshots with >m. Under the above assumptions, the correlation matrix is given by R yy [( y(t)y (t))] = AR A + σi Where R xx = E[(x(t)x (t))] is the source correlation matrix. = E (6) xx

3 Let λ 1 > λ 2 > λ 3... λ n = λ n+1 =... λ m = σ denote the eigen values o R yy. It is assumed that Λ i, i=1, 2, 3.n are distinct. The unit norm Eigen vectors associated with the columns o matrix S= [s 1 s 2..s n ], and those corresponding to λ n +1.λ m make up matrix G=[g 1.g m-n ]. Since the columns o matrix A and S span the same subspace, then A G=0; In practice R yy is unknown and, thereore, should be estimated rom the available data samples y(i), i= The estimated correlation matrix is given by R = yy 1 / ( y ( t ) y ( t )) n = 1 Let { s 1, s 2,... s n,...g m-n } denote the unit norm eigen vectors o R yy that are arranged in descending order o the associated eigen values respectively. The statistical properties o the eigen vectors o the sample covariance matrix R yy or the signals modeled as independent processes with additive white Gaussian noise are given in [9]. (7) The MIMO received signal data model is given by II. MIMO SIGAL MODEL y l ( t ) α l (k) x mk (t) + n l (t) (8) = K k = 1 Where α l (k) = α(k)a k (Φ); a k (Φ) is the antenna response vector. Where x mk (t) is the signal transmitted by k th user o m th signal, α l (k) is the ading coeicient or the path connecting user k to the l th antenna, n l (t) is circularly symmetric complex Gaussian noise. ere we examine two basic channel models [4]. In the irst case, ading process or each user is assumed to be constant across the ace o the antenna array and we can associate a DOA to the signal. This is called coherent wave ront ading. In coherent wave ront ading channel the ading parameters or each user is modeled as α l (k) = α(k)a k (Φ), where α(k) is a constant complex ading parameter across the array, Φ k is the DOA o the k th user s signal relative to the array geometry, and a k (Φ) is the response o the l th antenna element to a narrow band signal arriving rom Φ k. The signal model is represented in vector orm as y = K l α l (k) g mk (k) + n l (9) 1 k = ere g mk is a vector containing the k th user s m k th signal. The second model we consider is non-coherent element- to- element ading channel on which each antenna receives a copy o the transmitted signal with a dierent ading parameter. In this case, the dependency o the array response on the DOA or each user cannot be separated rom the ading process, so that no DOA can be exploited or conventional beam orming. III. ALGORITMS A. MUSIC MUSIC is a method or estimating the individual requencies o multiple times harmonic signals. MUSIC is now applied to estimate the arrival angle o the particular user [1],[2]. The structure o the exact covariance matrix with the spatial white noise assumption implies that its spectral decomposition is expressed as R 2 = APA = U SAU S + σ U n U n (10) Where assuming APA to be the ull rank, the diagonal matrix Us contains the M largest Eigen values. Since the Eigen vectors in Un (the noise Eigen vectors) are orthogonal to A. U a( φ ) = 0, where φ { ϕ φ,... φ } (11) n 1, 2 To allow or unique DOA estimates, the array is usually assumed to be unambiguous; that is, any collection o steering vectors corresponding to distinct DOAs Φm orms a linearly independent set { a Φ1,..a Φm }.I a(.) satisies these conditions and P has ull rank, then APA is also ull rank. The above equation is very helpul to locate the DOAs in accurate manner. Let {s 1...s n, g 1.g m-n } denote a unit norm eigenvectors o R, arranged in the descending order o the associated Eigen values, and let Š and Ĝ denote the matrices S and G made o {s I } and {g I } respectively. The Eigen vectors are separated in to the signal and noise Eigen vectors. The orthogonal projector onto the noise subspace is estimated. And the MUSIC spatial spectrum is then deined as ( φ) = ) ) * * [ a ( φ)gg a( φ) ] m (12)

4 * * [ a ( φ)i [ SS] a( φ) ] ( φ ) = (13) The MUSIC estimates o {Φ i} are obtained by picking the n values o Φ or which (Φ) is minimized. To conclude, or uncorrelated signals, MUSIC estimator has an excellent perormance or reasonably large values o, m and SR. I the signals are highly correlated, then the MUSIC estimator may be very ineicient even or large values o, m, and SR. Figure 2: Perormance comparison o MUSIC B. Cyclic MUSIC We assume that m α sources emit cyclostationary signals with cycle requency α (m α m). In the ollowing, we consider that x(t) contains only the m α signals that exhibit cycle requency α, and all o the remaining m-m α signals that have not the cycle requency α. Cyclic autocorrelation matrix and cyclic conjugate autocorrelation matrix at cycle requency α or some lag parameter τ are then nonzero and can be estimated by Ryyα ( τ) = y(tn + τ/2) y n= 1 (tn τ/2) e j2παt n * T j2παtn Ryy α( τ) = y (tn /2)y (tn /2) e + τ τ (15) n= 1 where is the number o samples. Contrary to the covariance matrix exploited by the MUSIC algorithm [1], the Cyclic MUSIC method [8] is generally not hermitian. Then, instead o using the Eigen Value decomposition (EVD), Cyclic MUSIC uses the Singular value decomposition (SVD) o the cyclic correlation matrix. For inite number o time samples, the algorithm can be implemented as ollows: Estimate the matrix R α yy ( τ) by using (15) or R α yy* ( τ) by using (16). Compute SVD (14) (16) Where [Us Un ] and [ Vs Vn] are unitary, and the diagonal elements o the diagonal matrices s and n are arranged in the decreasing order. n tends to zero as the number o time samples becomes large. Find the minima o Un a(φ) 2 or the max o Us a(φ) 2

5 Figure 3: Perormance comparison o Cyclic MUSIC IV. EW APPROAC OF DOA ESTIMATIO A signal subspace based DOA estimation perormance is aected by the two actors o an accurate array maniold modeling and a spatial covariance matrix o a received array signal. A higher SR signal or a target source is required or an accurate estimation rom inite received signal samples. But the DOA estimation perormance is limited by the lower SR rom intererence signals and environmental noise. For the perormance improvement o DOA estimation, this paper proposed a preprocessing technique o time-requency conversion methodology or signal iltering. This method includes a time-requency conversion technique with a signal OBW (Occupied Bandwidth) measurement based on wavelet de-noising method as shown in Fig. 1. This is a DOA method or SR improvement based on time-requency conversion approach. The improvement o a DOA estimation perormance was veriied by the simulation. Figure4.Proposed Model or MUSIC

6 Figure5:.Proposed Model or CYCLIC MUSIC This is proposed to overcome the limitation o existing DOA estimation techniques based on only time domain analysis. The more eective estimation is expected by the improvement o SR rom the proposed pre-processing techniques o requency domain analysis. The proposed method collects a time sampled signal y(t) rom an array antenna as shown in Fig. 1. The upper and lower 99% - OBW limits L and o a signal are determined rom y(), which is the DFT result o a received signal y(t). The iltered covariance matrix R[L; ] can be obtained rom the estimated signal energy, y[l; L+1; : : : ; ] with an improved SR. And the more exact OBW measurement is expected through the proposed wavelet de-noising method based on time-requency analysis. The proposed OBW limits are deined as ollowing measurement concepts o Equations (9) ~ (12). This process can eectively eliminate small intererence noises rom the target signal streams by the requency domain analysis [15, 16]. Where Px is a power o each spectrum requency elements { 1,.., }. The 99% OBW is calculated rom the upper limit and the lower limit L o 0.5% OBW point rom each spectrum boundary. P p = rel Py i i= 1 β / 2 = Prel β / ( ) (17) 2 [%] ( β = 1 or 99% OBW analysis) L L = 1 (18) = arg min Py( ) Pβ (19) L = 1 L / 2 = arg min Py( ) Pβ (20) An improved DOA estimation is expected rom the iltered covariance matrix and Eigen-decomposition processing at particularly low SR signal conditions. By the proposed pre-processing, it can eectively reject adjacent intererences at low SR conditions. Moreover, it can acquire the signal spectrum with an improved DOA estimation spectrum simultaneously without additional computation. This improved signal spectrum is important results or radio surveillance procedure. The signal de-noising is achieved by the discrete wavelet transorm-based thresholding to the resulting coeicients, and suppressing those / 2

7 coeicients smaller than certain amplitude. An appropriate transorm can project a signal to the domain where the signal energy is concentrated in a small number o coeicients. The proposed Wavelet de-noising process get a de-noised version o input signal obtained by thresholding the wavelet coeicients. In this paper, the wavelet procedure applied the heuristic sot thresholding o wavelet decomposition at level one. This de-noising processing model is depicted as ollowing simple model. S( n) = ( n) + σe( n), n=0,.,-1 (21) In this simplest model, e(n) is a Gaussian white noise o independent normal random variable (0; 1) and the noise level is supposed to be equal to 1. Using this model, it ollows the objectives o noise removal by reconstruct the original signal. It can be assumed that the higher coeicients are result rom the signal and the lower coeicients are result rom the noise. The noise eliminated signal is obtained by transorming back into the original time domain using these wavelet coeicients. Data Speciication V. SIMULATIO AD PERFORMACE COMPARISO Signal speciication: Data Model: QPSK Input bit duration T Sampling interval t = 0.5µsec = T/10; Antenna Array Model: Type: Uniorm Linear array antenna o. o array Elements = 16 Free space velocity c = 3*10 8 Centre requency c = 2.4Gz Wavelength λ = c / c Inter element Spacing d = λ/2 Angle o arrival in degrees θ = -5 to 20 Figure6. DOA estimation spectrum

8 Figure7. Comparison o spurious peak In this section, we present some simulation results, to show the behavior o the three methods and to compare the perormance with the analytically obtained Root Mean Squared Error (RMSE). We consider here a linear uniormly spaced array with 16- antenna elements spaced λ/2 apart. Incoming QPSK signals are generated with additive white Gaussian noise with signal to noise ratio 10dB, the bit rate o the QPSK signal o interest is 2Mb/s and other QPSK modulated signals with data rate 1Mb/s are considered as intererence. MUSIC is simulated using the speciied parameters. The Cyclic MUSIC algorithm is also simulated with some cyclic requency o 4Mz and some lag parameter o 2. One QPSK signals arrived at 20 degree and an intererer at 5 degree DOA. RMSE Vs SR plots or the two methods as shown in igure 2and 3. This section presents Mont Carlo computer simulation results to illustrate the perormance o the proposed algorithms or synchronous system. Each Monte Carlo experiment involved a total o 1000 runs, and each estimation algorithm is presented with exactly the same data intern. It is interesting to note that QPSK signal perorms better than FM signal. So that bandwidth requirement is as low as possible or QPSK signals as FM signals. It is interesting to note that the conventional MUSIC would require more data samples than Cyclic MUSIC to achieve the same RMSE. Form the simulation results, the proposed method improves the DOA estimation perormance o accuracy and spurious peak o spatial spectrum especially or lower SR signals. Figure 6 and 7 show the comparison results o DOA estimation perormance or low SR signals with intererence and noise. The DOA estimation perormance was compared by the spurious peak o DOA estimation spectrums which increase a measurement ambiguity and probability o successul DOA estimation. The proposed method improves the spurious peak characteristic more than 10 db at less than -10 db SR signal condition by applying MUSIC and cyclic MUSIC estimation. VI. COCLUSIO Unlike MUSIC, Cyclic MUSIC does not suer rom the drawback o requiring a higher number o antenna elements than sources. Good signal selective capability and high resolution is achieved in Cyclic MUSIC than MUSIC. This algorithm exploits cyclostationarity, which improves the signal Direction o Arrival estimation over the ading channel. The proposed method shows an improved ability o DOA resolution and estimation error at the noise and intererence conditions. These are the measurement limits at on-air environment. REFERECES [1] Maximum likelihood methods in radar signal processing by A.LEE Swindlehurst, member, IEEE, and Peter Stoica, Fellow,IEEE eb-1998 [2] Two decades o array signal processing Research by amid Krim and Mats Viberg, IEEE signal processing magazine,july [3] Michael L,McCloud, K.Varanasi, Beamorming, Diversity,and Intererence Rejection or Multiuser communication over ading channels with a receive antenna array,ieee Trans on Comm,vol.51,Jan-03 [4] R.Kumaresan and D.W.Tuts, Estimating the angles arrival o multiple plane waves, IEEE Trans Aerosp, Electron. Syst.vol AES -19,Jan-1983 [5] K.C.Sharman and T.S. Durrani, Maximum Likelihood parameter estimation by simulated anneling in Proc IEEE Int Con Acoust SpeechProcessing Apr-88

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