# Performance Analysis of MUSIC and LMS Algorithms for Smart Antenna Systems

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2 272 nternational Journal of Electronics Engineering desired users arriving at directions θ.θ as shown in Fig. 2. The array also receives narrow band source signals S i (t) from undesired (or interference) users arriving at directions θ.θ. At a particular instant of time t =, 2. where is the total number of snapshots taken. The desired user signal vector x (t) can be defined as [ ] T S (t) = S ( t ) S 2 ( t )... S ( t )... (6) The undesired (or interference) user signal vector X (t) as X (t) = A i (t)... (7) Where A is the N matrix of the undesired users signal direction vectors and is given by A = a ( θ ), a ( θ ),... a ( θ )]... (8) [ 2 And i (t) is the undesired (or interference) users source waveform vector defined as [ ] T i (t) = i ( t) i2 ( t)... i ( t)... (9) The overall received signal vector X (t) can be written as X (t) = X ( t) + n ( t) X ( t)... (0) + Fig. 2: Geometry of a Uniform Linear Array X ( t) D = a ( θm ) Sm ( t)... () m = where a ( θ ) is the N array steering vector which represents the array response at direction θ m is given by T m a ( θ m ) = [exp ( j ( n ) ϕ ] ; n N... (2) Where [(.)] T is the transposition operator, and ϕ m represents the electrical phase shift from element to element along the array. This can be defined by d 2... (3) λ ϕ m = π sin ( θm ) where d is the inter-element spacing and λ is the wavelength of the received signal. The desired users signal vector X (t) of () can be written as X (t) = A S (t)... (4) Where A is the N matrix of the desired users signal direction vectors and is given by A = a ( θ ), a ( θ ),... a ( θ )]... (5) [ 2 And S (t) is the desired users source waveform vector defined as where n (t) represents white Gaussian noise. The conventional estimate of the correlation matrix defined as R = E { X ( t) X ( t)}... () where E {.} represents the ensemble average; and (.) is the ermitian operator. The above equation can be approximated by applying temporal averaging over snapshots (samples) taken from the signals incident on the sensor array. This leads to forming a spatial correlation matrix R given by [5]; R = k = X ( k) X ( k) Substituting for X (t) from (0) in (2) gives R = ss A R A + n ( k) n ( k) + A R ii A... (2)... (3) where R ss = E {s (t) s (t)} is an desired users source waveform correlation matrix; R ii = E {i (t) i (t)} is an undesired users source waveform correlation matrix. Finally, Eq. (3) can be rewritten as 2 R = A [ S ( k) S ( k)] A + σ + k = k = A [ i ( k) i ( k)] A... (4) where σ 2 is the noise variance, and is an identity matrix of size N N.

4 274 nternational Journal of Electronics Engineering Fig. 3: Simulation Results (a) Normalized USC Spectrum for Arrival Angles 20, 40, and 60 (d = 0.5 lamda). (b) Normalized USC Spectrum for Arrival Angles 20, 40, and 60 ( = 8). (c) Array Factor Pattern for Arrival Angles 20, 40, and 60 and nterferer Angle 0 (d = 0.5 lamda). (d) Array Factor Pattern for Arrival Angles 20, 40, 60 and nterferer Angle 0 (N = 8). (e) Resulting Weights agnitude Versus teration Number. (f) ean Square Error e 2 Versus teration Number. (g) Desired Signal and Array Output. 4. CONCLUSON This paper presented the performance analysis of two popular algorithms for direction of arrival based beamforming smart antenna system. USC, DOA estimation and LS, adaptive beamforming algorithms are analyzed through simulations using ATLAB. Sharper peaks in the USC angular spectrum indicate locations of desired users. Peaks of LS are formed in the same desired direction and deep null in the direction of the undesired interference. Results obtained verify the improved resolution when the number of elements and spacing between elements are more. This analysis is useful in implementation of direction of arrival based smart antenna system.

5 Performance Analysis of USC and LS Algorithms for Smart Antenna Systems 275 REFERENCES [] Ogawa Y. and Ohgane T., Adaptive Antennas for Future obile Radio, Computer Journal of ECE Transaction Fundamentals, 79 (7), pp , 996. [2] Ogawa Y., Ohmiya. and toh., An Adaptive Array System for igh-speed obile Communications, 75 (5), pp , 992. [3] Raed. Shubair, ohmoud A., Al-Qutayri and Jassim. Samhan, A Set up for the Evaluation of USC and LS Algorithms for a Smart Antenna System, 2 (4), pp. 7 77, [4] Godara L.C., Application of Antenna Arrays to obile Communications Part-: Beamforming and Direction-of- Arrival Consideration, n proceedings of EEE, 85 (8), pp , [5] S. aykin, Adaptive Filter Theory, Prantice-all, 4Th Edition, [6] Frank Gross, Smart Antennas for Wireless Communications with atlab, cgraw ill, New-York, [7] Andrew night, Basics of ATLAB and Beyond, CRC Press, 2000.

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