# Smart Antenna Direction Arrival Estimation Adaptive Computer Science Essay

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This paper presents a simulation study of a smart antenna system based on direction-of-arrival estimation is based on the MUltiple SIgnal Classification (MUSIC) algorithm for finding the Position Location (PL) of the desired user. The beamformer steer the main beam towards the desired user and nullify all other interferer, through adaptive beamforming using Least Mean Square (LMS) algorithm. This simulation results revealed the sharper peaks in the MUSIC angular spectrum and deep nulls in the LMS beam pattern. Also, this paper deals with DOA estimation and adaptive beamforming for the static case based on SA. Eigen decomposing fined the PL of the desired user using MUSIC algorithm and steer the beam toward this user using compute the weight vectors like Least Mean Square (LMS) algorithm.

There is an ever increasing demand on mobile wireless operators to provide voice and high speed data services. At the same time, these operators want to support more users per base station to reduce overall network cost and make the services affordable to subscribers. As a result, wireless systems that enable higher data rates and higher capabilities are pressing need. Unfortunately because the available broadcast spectrum is limited, attempts to increase traffic within a fixed bandwidth create more interference in the system and degrade the signal quality. When omni-directional antennas are used at the base station, the transmission and reception of each users signal becomes a

source of interference to other users located in the same cell, making the overall system interference limited.

The demand for wireless services has risen dramatically from few years. Wireless communication systems are evolving from the second generation systems to the third and fourth generation systems, which will provide high data rate multimedia services as video transmission. New value added services such as the position location (PL) services for emerging calls, the fraud detection, intelligent transportation systems, and so fourth are also coming in to reality[1,2,3].

The smart antenna systems can generally be classified as either switched beam or adaptive array systems. In a switched beam systems can generally be classified as either switched beam or adaptive array systems. In a switched beam system multiple fixed beams in predetermined directions are used to serve the users. in this approach the base station switches between several beams that gives the best performance as the mobile user moves through he cell. Adaptive beam forming uses antenna arrays backed by strong signal process capability to automatically change the beam pattern in accordance with the changing signal environment. 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. The adaptation achieved by multiplying the incoming signal with complex weights and then summing them together to obtain the desired radiation pattern. These weights are computed adaptively to adapt to the changes in the signal environment. The complex weight computation based on different criteria and incorporated in the signal processor in the form of software algorithms like Least Mean Square. [7]

A smart antenna technology can achieve a number benefits like increase the system capacity, greatly reduce interference, increase power efficiency [4, 5]. In the following section, we implement the simulation study of DOA estimation using MUSIC algorithm and adapts the beam towards the desired user and nullify all other interference signal through LMS algorithm.

## II. SYSTEM IMPLEMENTATION

The MUSIC, Multiple signal classification is a popular high resolution technique for estimating the DOA of multiple plane waves in noisy environment, using an array of multiple sensors. This algorithm involves Eigen decomposition of the covariance matrix derived from the input data model. The Eigen values of the covariance matrix are further divided into two sets called signal and noise subspaces. The signal subspace consists of vectors correspond to signals received at an array and vectors of noise subspace are completely orthogonal to the signal subspace.

This algorithm can be summarized as, Estimate the spatial covariance matrix and compute the eigenvectors in signal and noise. After computing the eigenvectors find the steering vector, incoming signal vector and noise vectors.

Element M

Element 2

y(t)

e(t)=d(t) - y(t)

## +

d(t)

## Î‡ Î‡ Î‡

## ×ƒ

## ×ƒ

Element 1

wM

w1

w2

Adaptive Signal Processing Unit

Radio Unit

## ïƒ¥

Antenna Arrays

## ×ƒ

## ×ƒ

Fig.1. Smart Antenna System

Figure1, shows the LMS adaptive beamforming network, it consist of antenna arrays, signal processing unit, radio unit and adaptive weights. Consider a Uniform Linear Array (ULA) with M isotropic elements, which forms the integral part of the adaptive beamforming system as shown in the figure above. In short, the beam forming is done digitally, the beam forming and signal processing units normally be integrated in the same unit. For the DOA estimation and beamforming the antenna array and signal processing unit etc are the common.

## III. SIMULATION AND RESULTS

As per reciprocity theory for radiation patterns, the received signals can be models as with reference to the data model equation

(1)

Where,

A(q) = steering vector corresponding to signal direction.

s(t) = incident waves with the amplitude and phase in the

azimuth plane

n(t) = Additive White Gaussian Noise (AWGN)

(2)

Then the signal correlation matrix at the antenna output is Rxx

(3)

Where 'X' is the data matrix, H denotes Hermitian Transpose. The Eigenstructure method, Multiple Signal Classification (MUSIC) algorithm are implement for direction source.

In short, by using this Eigen decomposing find the Position Location of the Desire user. To implement this, MUSIC algorithm is used.

If S0 is the steering vector associated with the desired signal of interest and Si is the steering vector associated with interfering signal then

WH S0 = 1 ; if user signal direction (4)

WH Si = 0 ; if interferer (5)

i = 1.2,3 ….k

And the output of the antenna array x(t) is given by,

(6)

s(t) denotes the desired signal arriving at angle θ0 and ui(t) denotes interfering signals arriving at angle of incidences θi respectively. a(θ0) and a(θi) represent the steering vectors for the desired signal and interfering signals respectively. Therefore it is required to construct the desired signal from the received signal amid the interfering signal and additional noise n(t)

The LMS algorithm can be summarized in following equations.

Output, (7)

Error, (8)

Weight, (9)

The above data model, Eigenvector decomposition for Direction of Arrival Estimation using MUSIC algorithm and the parameters/results for beamforming through LMS algorithm has been simulated on MATLAB.

For this simulation, assign a different parameters and universal constants as

Parameter

Constant to be Assigned

Value

Speed of Light

C

3x108 m/s

Signal to Noise Ratio

(SNR)

SNR

20dB

Number of Elements

in antenna array

M

6

Number of Time

Steps

N

100,500 etc

Length of Time Step

dt

1.0000e-004 (1E-4)

Number of Incoming

Signals

L

5

Incoming Signal

Frequency

f0

1x109 Hz (1E9)

Lambda

Lambda

0.3000 (c/f0)

Step Size

mu_0

0.02

Table.1 Constants to be used for Simulation

And the simulation results on MATLAB are as:

Fig.2 shows the MUSIC spectrum for DOA Estimation, here the desired user at an angle of 1000 and the four interferers at the different location at angle of 35, 65, 125 and 150 degree. And by using this simulation method, find the Position Location (PL) of the desired user.

Fig. 2 Angle of Arrival Vs Magnitude in Degree (MUSIC

Here the desired angle is arriving at 100 degrees and there are four interfering signals arriving at angles 65, 35, 125 and 150 degrees respectively. The array factor plot in Fig.3 shows that the LMS algorithm is able to iteratively update the weights to force deep nulls at the direction of the interferers and achieve maximum in the direction of the desired signal. It can be seen that nulls are deep at around 20dB level below the maximum. In figure 4, the null steering beamformer in which the desired signal at an angle of 100 degree and all other interferer are nullify. The LMS error plot in fig.5 shows that the LMS algorithm converges. In this case the LMS error is almost 0.025 at around 500 samples.

Fig 3. Position Location Vs Normalize Array Factor

Fig 4. Null Steering Beamformer

Fig. 5 Samples (Time) Vs Least Mean Square Error

## IV. CONCLUSION

Here the simulation for the DOA estimation, compute a spatial spectrum then estimate DOA's using MUSIC algorithm. These methods apply weights to each element in the array so as to steer the antenna pattern towards a known look direction. And the capability to resolve multiple targets with separation angles smaller the main lobe beam width of the array. Once a DOA is estimated, the beamformer adapts the antenna pattern to steer the main beam towards the desired user and place nulls in the unwanted direction through LMS algorithm.

It is easy to identify the transfer function of the unknown system, also its ability to perform in a system, which is heavily corrupted with noise and the stability of its results.