CH.RAGHAVENDRA et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 6, Issue No. 1, 035 - 040

Adaptive Beam Forming using DMI and CMA Algorithms

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CH.RAGHAVENDRA Dr.A.Jhansi Rani Dr. K. SRI RAMA KRISHNA Lecturer Professor Professor & Head Department of Electronics & Communication Engineering V R Siddhartha Engineering College Vijayawada, A.P-520007 raghi.2u@gmail.com jhansi9rani@gmail.com srk_kalva@yahoo.com

ABSTRACT:

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The main objective

INTRODUCTION :

is to analyze adaptive

beam forming approach based on smart antenna. Several algorithms have been developed based

on different criteria to compute the complex

weights. They have their own disadvantages and advantages as far as complexity, convergence,

speed and other aspects are concerned. In this

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paper the comparison of the performance of algorithms namely Direct matrix Inversion algorithm

(DMI)

and

Constant

algorithm (CMA) are presented.

modulus

The main

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advantage of these algorithms is its simplicity with a minimal loss of accuracy.

This paper

describes the design of an adaptive antenna array after receiving the signals from the desired and interfering directions. Then the weight vector is evaluated to minimize the error that provides an appropriate beam pattern to each subscriber. For these two algorithms the mean square error and Array factor are evaluated and compared. Keywords : Antenna Arrays, Adaptive Algorithms, Beam forming, Interference, Smart antenna

ISSN: 2230-7818

In the past, different algorithms are implemented in smart antennas. Those algorithms tracks the signal received from the user. The radiation pattern is adjusted to place nulls in the Direction of Interferers and Maxima in the direction of the desired user so, that algorithms has low computation complexity and poor convergence In order to avoid those problems two methods has to be developed. They are constant modulus algorithm and direct matrix inversion algorithms. This algorithms has improve the computation complexity and better convergence. This paper discusses algorithms developed for smart antenna applications. The Direct Matrix Inversion Algorithm and RLS algorithms are the two adaptive beam forming algorithms used in smart antennas. The Simulation results show that convergence is faster in the DMI algorithm than in the CMA algorithm. Adaptive modulation is a technique that varies some transmission parameters to take advantage of favorable channel conditions. Under bad channel conditions, a robust signal

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CH.RAGHAVENDRA et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 6, Issue No. 1, 035 - 040

A smart antenna usually involves spatial processing and adaptive filtering techniques. The field of application is very large, ranging from signal to noise improvement to the user capacity enlargement of the mobile network. A typical application will involve an adaptive algorithm to create a beam to track a user or to eliminate noise sources and therefore the smart antenna is also referred to as adaptive array or adaptive beam former. This paper descrides four algorithms, the Least Mean Square algorithm and the Constant Modulus algorithm. The smart antenna is basically a set of receiving antennas in a certain topology. The received signals are multiplied with a factor, adjusting phase and amplitude. Summing up the weighted signals, results in the Output signal. The concept of a transmitting smart antenna is rather the same, by splitting up the signal between multiple antennas and then multiplying these signals with a factor, which adjusts the phase and amplitude. Figure 1 represents the concept of the smart antenna. The signals and weight factors are complex

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While, in good channel, spectrally efficient mode that offer higher throughput is applied. This mechanism ensures the most efficient mode is always used based on certain criteria and constraint. The varying parameters can be the symbol transmission rate, transmitted power level, constellation size, BER, code rate or scheme, any combination of these parameters [1]. Compared to the fixed system, which was designed specifically for the worst case channel conditions, this adaptive modulation offers higher spectral efficiency, higher throughput and remarkable capacity enhancement without sacrificing BER or wasting power [2]. Research on applications of adaptive antenna arrays have been an interesting subject over past 40 years [3] contributing to the invention of adaptive beam forming method. By taking advantage of the fact that users collocated in frequency domain are typically separated in spatial domain, the beam former is used to direct the antenna beams toward the desired user while canceling signal from other users [4]. The beam former electronically steer a phased array by weighting the amplitude and phase of signal. .At each array element in response to changes in the propagation environment. Capacity improvement is achieved by effective co-channel interference cancellation and multipath fading mitigation. Theoretically proven impressive performance, coupled with enabling signal processing technologies has attracted researchers to focus on better utilization of the methods discussed. This paper will outline a few approaches

of adaptive modulation and adaptive beam forming techniques and highlight some of the recent works that employ these techniques. SMARTANTENNA

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transmission mode will be applied to ensure reliable data exchange.

ISSN: 2230-7818

Fig.1,Adaptive diagram

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beam-forming

block

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CH.RAGHAVENDRA et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 6, Issue No. 1, 035 - 040

Least Mean Square Algorithm: This algorithm uses a steepest decent method [8] and computes the weight vector recursively using the equation. W(n+1)=W(n)+μX(n)[d*(n)−XH(n) W(n)..................................................] (4) where µ is a gain constant and control the rate of adaptation. The least mean squar algorithm(LMS) is important because of its simplicity and ease of computation, and because it does not require off-line gradient estimations or repetition of data. If adaptive system is a adaptive linear combiner and if the input vector and desired response are available at each iteration, The LMS algorithm is generally the best choice for many different applications of adaptive signal processing.

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The digital signal processor interprets the incoming data information and it determines. This paper describes complex weights.(amplification and phase information) and multiplies the weights to each element output to optimize the array pattern. The optimization is based on a particular criterion, which minimizes the contribution from noise and interference while producing maximum beam gain at the desired direction. There are several Adaptive beam-forming [6] algorithms varying in complexity based on different criteria for updating and computing the optimum weights.Block implementation of the adaptive beam-former uses a block of data to estimate the adaptive beam-forming weight vector and is known as “sample matrix inversion (SMI)” [7]. The sample-by-sample method updates the adaptive beamforming weight vector with each sample. The SMI adaptive beam-former uses a block of code to get optimum weight; therefore it is not suitable for non stationary environment . Since the sample-by-sample adaptive beam-former [7] alters its weight with each new sample, it can dynamically update its response for such a changing scenario. Another important distinction between sample and block adaptive method is the inclusion of the signal of interest in each sample and thus in the correlation matrix.Therefore, for sample adaptive method, we can not use signal free version of the correlation matrix, that is, the interference plus noise correlation matrix, but rather must use the whole correlation matrix inclusion of the signal in the correlation matrix has profound effect on the robustness of the

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ADAPTIVE BEAM FORMING ALGORITHMS

adaptive beam-former in the case of signal mismatch. In these paper performed simulationus sample-by sample adaptive beam-former using least mean square (LMS) algorithm, constant modulus algorithm (CMA) and recursive least square (RLS) algorithm. The weight vector W is calculated using the statistics of signal x(t) arriving from the antenna array. An adaptive processor will minimize the error e(t) between a desired signal d(t) and the array output y(t).

ISSN: 2230-7818

Constant Modulus Algorithm: The configuration of CMA adaptive beam forming [7] is the same as that of the Sample Matrix Inversion system except that it requires no reference signal. It is a gradient-based algorithm that works on the theory that the existence of interference causes changes in the amplitude of the transmitted signal, which otherwise has

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of inversions required are more when compared to block adaptation method. Another block adaptation technique is the block adaptation technique with memory. This method utilizes the matrix estimates computed in the previous blocks. This approach provides faster convergence for spatial channels that are highly time correlated. This technique works better when the signal environment is stationary SIMULATION AND RESULTS:

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a constant envelope (modulus)..The weight is updated by the equation W(n1)=W(n)U(n)e*(n)](5) where µ is the step-size parameter(n) is the input vector,and e(n)=y(n)(R2=|Y(n)|2).................(6) R2=E[|X(n)|4]/[|x(n|2]........................(7) Y(n) is the array output after the nth iteration. One severe disadvantage of the CMA is slow convergence time. The slow converges limits the usefulness of the algorithm in the dynamic environment where the signal must be Captured quickly.

desired signal 10 degrees interferers -10 and -40 degrees

phase(rad)

0

ISSN: 2230-7818

-2

0

50

100

150

phase(d) phase(y)

200

250

samples

phase(rad)

desired signalresponse 10 degrees interferers -10 Fig.2. Phase ofand -40 degrees constant 2 modulus algorithm for phase(d)N=5

The fig2 shows the phase(y) phase 0 constant for for CMA algorithm for N=5 here N Indicates the no of antennas the graph -2 drawn between samples along x0 50 along 100 y-axis 150 200 250 axis and phase amplitude

2 |d| |y|

1.5 1 0.5

0

50

Fig.3.

100

150

200

250

samples

1 amplitude

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Recursive Least Square Algorithm In recursive least-square algorithm[9] the weights are updated by the following equation. W(n) =W(n −1) + K(n)ξ * (n), n =1,2,................................................ (8) Where, K(n) is referred to as the gain vector and ξ (n) is a priori estimation error which is given by the equation ξ (n)=d(n)-wh(n1)u(n)..........................(9) The RLS algorithm does not require any matrix inversion computations as the inverse correlation matrix is computed directly. It requires reference signal and correlation matrix information. Weight adaptation in the DMI algorithm: Weight adaptation in the DMI algorithm can be achieved by using block adaptation technique where the adaptation is carried over disjoint intervals of time is the most common type. This block adaptation technique is suitable for mobile communications where the signal environment is highly time varying. The overlapping block adaptation technique is computational intensive as adaptation intervals are not disjoint but overlapping. This technique gives better performance but the number

2

Amplitude

response

|error| of

constant modulus algorithm for N=5 0.5

The fig3 shows the amplitude response for CMA algorithm for n=5 the 0 20 40 between 60 80 100 samples 120 140 160 along 180 200 xgraph0 drawn axis and amplitudesample(index) along y-axis

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ampl

1

0.5

0

50

100

150

200

250 amplitude response antenne, desired signal: 10 degrees, interferers: -10 and -40 degrees 10 N=5 N=8 5 N=20

|er or|

0 -5

(dB)

amplitude

1

0.5

-10 -15 -20 -25 -30

Error

response

modulus algorithm

of

-40

-20 0 20 angle(degrees)

40

60

80

factor of constant modulus algorithm

constant

for

-60

Fig.6. comparison the Normalize array

0 20 40 60 80 100 120 140 160 180 200 sample(index)

Fig.4.

-80

N=5

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The fig.4 shows the error response for CMA algorithm for n=5 the graph drawn between samples along xaxis and amplitude along y-axis

The fig.6 shows the comparing the normalize array factor of CMA algorithm for n=5 the graph drawn between samples along x-axis and amplitude along y-axis

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0

amplitude response antenne, desired signal: 10 degrees, interferers: -10 and -40 degrees 10 DMI CMD 5 0

amplitude response antenne, desired signal: 10 degrees, interferers: -10 and -40 degrees 10

(dB)

-5

5

-10 -15 -20

0

A

-25

(dB)

-5 -10 -15

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-20 -25 -30

-80

-60

-40

-20 0 20 angle(degrees)

40

60

80

Fig.5.Normalize array factor of constant modulus algorithm for N=5

The fig.5 shows the normalize array factor of CMA algorithm for n=5 the graph drawn between samples along x-axis and amplitude along y-axis

ISSN: 2230-7818

-30

-80

-60

-40

-20 0 20 angle(degrees)

40

60

80

Fig7. Comparison plots between DMI and

CMA

algorithms when N = 5

The fig.7 shows the comparision plots CMA and DMI algorithm for n=5 the graph drawn between samples along x-axis and amplitude along y-axis

CONCLUSION:

In this paper direct matrix inversion and constant modulus algorithm are used to update the combining weights of adaptive antenna array. However, its fast convergence presents an acquisition compare to LMS algorithm. These algorithms are good

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REFERENCES

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Beamforming and Network Throughput” IEEE Antenna's and Propagation Magazine, Vol. 44, NO. 4, August 2002. [6] Dimitris G. Manolakis, Vinay K.Ingle,Stephen M. Kogon ,“Statistical and Adaptive Signal Processing”, Mc. Graw Hill Publication, 2005. [7] Frank Gross, “Smart Antenna For Wireless Communication” Mcgraw-hill, September 14, 2005 [8] Symon Haykin, “Adaptive filter theory”, Forth edition, Pearson Education, Asia, 2002. [9] Bernard Widrow, Samuel D. Stearns, “Adaptive Signal Processing”, Pearson Education Asia, Second Indian Reprint, 2002. [10] Agee, B, “The Least-Square CMA: A New Technique for Rapid Correction of Constant Modulus Signal” IEEE International Conference on ICASSP’86, Vol. 11, pp. 953-956, April 1986

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computation complexity. Smart antennas technology suggested in this present work offers a significantly improved solution to reduce interference levels and improve the system capacity. With this novel approach, each user’s signal is transmitted and received by the base station only in the direction of that particular user. This drastically reduces the overall interference in the system. Further through adaptive beam forming, the base station can form narrower beams towards the desired user and nulls towards interfering users, considerably improving the signal-to-interferenceplus noise ratio.

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[1] Carl B. Dietrich, Jr., Warren L. Stutzman, Byung-Ki Kim, and Kai Dietze, “Smart Antennas in Wireless Communications: Base-Station Diversity and Handset Beam forming” lEEE Antennas and Propagation Magazine, Vol. 42, No. 5, October 2000. [2] Michael Chryssomallis, “Smart Antennas” lEEE Antennas and Propagation Magazine, Vol. 42, No. 3, June 2000. [3] Liu, J.; Jing Xia; Gang Wang; ’’ A Dual-Band Micro strip-Fed Bow-Tie Antenna for GSM/CDMA and 3G/WLAN’’,Microwaveantenna, propagation and EMC Technologies for WirelessCommunication,2007 [4] Lal C. Godara, “Application of Antenna Arrays to Mobile Communications ,Part П: beam-forming and direction-of-arrival considerations”, Proceeding of the IEEE, Vol. 85, No. 8, pp. 1195- 1234, August 19 [5] Salvatore Bellofiore, Jeffrey Foutz, Constantine A Balanis, and Andreas S. Spanias, “Smart-Antenna System for Mobile Communication Networks Part2:

ISSN: 2230-7818

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