SIMULATION AND COMPARISON OF ADAPTIVE ALGORITHMS FOR OPTIMAL WEIGHTING OF ARRAY ELEMENTS IN SMART ANTENNAS.
The most important task of an antenna is producing an appropriate radiation pattern in order to construct optimal communication channel between base station and user. Processing of received signal in various elements of antenna array may results in access to different data in identification of massage and user position as well as received direction and/or angle of transmitted signal toward antenna. In this paper, several algorithms, including RLS, LMS, and CMA, are proposed in order to obtain optimum weighting of appropriate radiation pattern. Furthermore, LMS simulation is carried out and the obtained results are compared with that of RLS and CMA algorithms. By increasing sample number of received signals, the estimated values approach real values and weights reach the optimum weights.
Keywords: Constant Modulus Algorithm (CMA), Least Mean Square (LMS), Recursive Least Square (RLS), Smart antenna.
The task of a smart/array antenna is to produce specific pattern in order to receive optimum signal and eliminate interference. The interference can be brought out by other user or multi-path routes. Various methods are exists to form beam, each of which is used considering the desired aspect as well as radiated signal characteristics to the array.
With this antenna architecture, the weights of the antennas are adapted to point the main beam in the desired direction and place nulls in the interference directions. Different algorithms are used to adjust the weights in Smart Antenna Systems .
An adaptive antenna array combines the outputs of antenna elements but controls the directional gain of the antenna by adjusting both phase and amplitude of the signal at each individual element [2,3]. The combined relative amplitude and phase shift for each antenna is called a complex weight. These weights are calculated using different algorithms [4-9]. The weighted signals are summed and the output is fed to a controller that adjusts the weights to satisfy an optimization criterion.
Adaptive antennas have the ability of separating automatically the desired signal from the noise and the interference signals and continuously update the element weights to ensure that the best possible signal is delivered in the look direction. It not only directs maximum radiation in the direction of the desired mobile user but also introduces nulls at interfering directions while tracking the desired mobile user at the same time [10,11].
2. CONSTRUCTION OF BEAM AND ADAPTIVE ALGORITHMS
Array coefficients are usually obtained by direct solving of the equation related to the correlation matrix. Instead of solving direct equation, adaptive algorithms can be utilized which obtain weights in several iterations. The noticeable advantage of these algorithms is their application in noisyenvironment. Since these algorithms utilize previous weights they reduce noise impact in order to update weights. A comparison of Least Mean Square (LMS) and Recursive
2.2 RLS Algorithm
LMS algorithm convergence is related to eigenvalues of correlation matrix. LMS algorithm convergence is less in environments where eigenvalues of correlation matrix is high. This problem is solved in RLS algorithm where inverse of correlation matrix is used instead of step size, . Thus, update relation of weights is demonstrated by Eq. 8.
2.3 CMA Algorithm
CMA algorithm is another algorithm based on gradient calculation. It is assumed in this algorithm that the interference signals change signals level. Weights are achieved through minimizing fitness function as:
3. ANALYSIS AND SIMULATION RESULTS
For simulation purposes, a linear array of concentric elements is considered. The distance between the elements is half of the wavelength. In addition, a sequence signal, up to 5000 samples with binary values of 1 and -1, is sampled and used as the input. Although 5000 instantaneous samples are exists, the obtained results reveal that the system converges up to 150 samples. The parameter is 0.008. Moreover, in order to reach real results, in particular for more than one multi-pad, significant impact on system, while the latter has no effect on it.
Figure 1 depicts diagram obtained by LMS algorithm. As can be seen, weak beams are generated in the path of interference. Figures 2 and 3 show array pattern diagram when elements distance is 1/4 and 1/8 of wavelength, respectively. Obviously, simulations prove that the optimal value between the elements is half of the wavelength.
4. COMPARISON OF SIMULATION RESULTS OBTAINED BY LMS, CMA, and RLS ALGORITHMS
In a wide comparison among adaptive algorithms, parameters of antenna pattern, amplitude response, error diagram and BER are studied. LMS algorithm importance in constructing the best main lobe in the direction of user cannot be ignored. However, it is not completely satisfactory in neutralizing interference signals.
CMA algorithm has the highest error. However, it leads to reliable solutions compared to LMS and RLS algorithm in elimination of interferences. Obtained results by simulations in Figure 5 indicate that inserting zero in interference routes, in the CMA algorithm, actually results in interference signal omission. Whereas in the case the signal receiving angle of user and interference is very close to each other, BER in this algorithm is higher than that of array elements signals.
RLS algorithm is more computationally complex than LMS. RLS algorithm convergence is higher than that of LMS. RLS has the minimum error signal and minimum BER.
In this paper, various algorithms, including LMS, RLS, and CMA, producing adaptive beam in smart antennas were addressed. Convergence speed of LMS algorithm is dependent on eigenvalues of array correlation matrix. In environment where eigenvalues expansion of correlation matrix is high, the algorithm expands with low convergence speed. This problem is resolved in LMS algorithm by substituting inversion of matrix R with gradient step size of . Simulation results provide better understanding of convergence, stability, and adaptability method of algorithm. The obtained results by simulations indicate that LMS algorithm has low speed compared with RLS algorithm. However, LMS put forward less computation on system processor in the case it converges in load channel conditions. While its convergence speed id high, RLS algorithm needs initial estimation of inversion of matrix R. In addition, it is much more complicated than LMS algorithm in terms of computations.
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