# Smart Antenna Smi Algorithm Computer Science Essay

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Smart Antenna considerably improves the wireless system performance and economics for a variety of users. Smart antennas are applicable to all wireless protocol and standards. There are still several challenges to be resolved before the full potential of smart antennas can be realized. These are the aspects related to both modern implementation as well as algorithms for beam forming. This paper discusses the main concept of Smart Antenna and SMI Algorithm. The last section disusses the MATLAB program to simulate the Smart Antenna System using SMI Algorithm on a BTS receiver (Uplink).

In mobile communication systems, capacity and performance are usually limited by two major impairments. They are multipath and co-channel interference. Multipath is a condition which arises when a transmitted signal undergoes reflection from various obstacles in the propagation environment. This gives rise to multiple signals arriving from different directions. Since the multipath signals follow different paths, they have different phases when they are arrive at the receiver. The result is degradation in signal quality when they are combined at the receiver due to the phase mismatch. Co-channel interference is the interference between two signals that operate at the same frequency. In cellular communication the interference is usually caused by a signal from a different cell occupying the same frequency band.

Smart antenna is one of the most promising technologies that will enable a higher capacity in wireless networks by effectively reducing multipath and co-channel interference. This is achieved by focusing the radiation only in the desired direction and adjusting itself to changing traffic conditions or signal environments. Smart antennas employ a set of radiating elements arranged in the form of an array. The signals from these elements are combined to form a movable or switchable beam pattern that follows the desired user. In a Smart antenna system the arrays by themselves are not smart, it is the digital signal processing that makes them smart. The process of combining the signals and then focusing the radiation in a particular direction is often referred to as digital beam forming [1].

The technology of smart antennas for mobile communication systems has received much interest in the last couple of years. The smart antenna system needs to differentiate the desired signal from the co-channel interferences and normally requires either the knowledge of a reference signal (or training signal), or the direction of the desired signal source. There exists a range of schemes to estimate the direction of sources with conflicting demands of accuracy and processing power.

Similarly, there are many methods and algorithms to update the array weights, each with its speed of convergence and required processing time. For the smart antenna systems, there is an SDMA scheme (space division multiple access), which uses an array of antennas to provide control of space by providing virtual channels in an angle domain. Using this scheme, simultaneous calls in different (adjacent) cells or in the same cell can be established at the same carrier frequency. The scheme allows a transmission to take place in one cell, without disturbing the transmission in another cell. Using space diversity, the shape of a cell may be changed dynamically to reflect the user movement [2]. Figure 1 clearly explains this concept. Thus the spatial dimension can be exploited as a hybrid multiple access technique in complement with one of the three basic schemes.

(a) Moment ta (b) Moment tb

Figure 1: Simultaneous calls in the same cell

Since interference suppression was a feature in this system, this technology was borrowed to apply to personal wireless communications where interference was limiting the number of users that a network could handle. It is a major challenge to apply smart antenna technology to personal wireless communications since the traffic is denser. Also, the time available for complex computations is limited. However, the advent of powerful, low-cost, digital processing components and the development of software-based techniques has made smart antenna systems a practical reality for cellular communications systems.

## Basic Mechanism

A smart antenna system can perform the following functions: first the direction of arrival of all the incoming signals including the interfering signals and the multipath signals are estimated using the Direction of Arrival algorithms. Secondly, the desired user signal is identified and separated from the rest of the unwanted incoming signals. Lastly, a beam forming algorithm is created in which a beam is steered in the direction of the desired signal and the user is tracked as he moves while placing nulls at interfering signal directions by constantly updating the complex weights.

Therefore, it is quite evident that the direction of radiation of the main beam in an array depends upon the phase difference between the elements of the array. Therefore it is possible to continuously steer the main beam in any direction by adjusting the progressive phase difference β between the elements. The same concept forms the basis in adaptive array systems in which the phase is adjusted to achieve maximum radiation in the desired direction. To have a better understanding of how an adaptive array system works, let us consider a typical adaptive digital beam-forming network shown below in Figure 2.

Figure 2: Block diagram of an Adaptive Array System

In a beam-forming network, the signals incidents at the individual elements are combined intelligently to form a single desired beamformed output. Before the incoming signals are weighted they are brought down to baseband or intermediate frequencies (IF's). The receivers provided at the output of each element perform the necessary frequency down conversion. Adaptive antenna array systems use digital signal processors (DSP's) to weight the incoming signal. Therefore it is required that the down-converted signal be converted into digital format before they are processed by the DSP. Analog-to-digital converters (ADC's) are provided for this purpose. For accurate performance, they are required to provide accurate translation of the RF signal from the analog to the digital domain. The digital signal processor forms the heart of the system, which accepts the IF signal in digital format and the processing of the digital data is driven by software. The processor interprets the incoming data information, determines the 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 algorithms based on different criteria for updating and computing the optimum weights.

## Antenna Array

An Antenna Array is a configuration of individual radiating elements that are arranged in space and can be used to produce a directional radiation pattern. Single-element antennas have radiation patterns that are broad and hence have a low directivity that is not suitable for long distance communications. A high directivity can be still be achieved with single-element antennas by increasing the electrical dimensions (in terms of wavelength) and hence the physical size of the antenna. Antenna arrays come in various geometrical configurations, the most common being; linear arrays (1D). Arrays usually employ identical antenna elements. The radiating pattern of the array depends on the configuration, the distance between the elements, the amplitude and phase excitation of the elements, and also the radiation pattern of individual elements. Some of the antenna parameters before are discussed below.

## Parameters of Antenna

Although the parameters of an antenna may be interrelated, however an antenna is chosen for its operation in a particular application according to its physical and electrical characteristics.

Furthermore, the antenna must perform in a required mode for the particular measurement system.

Typically, antenna characteristics are measured in two principal planes and they are known as the azimuth and elevation planes, which can also be considered as the horizontal and vertical planes respectively, for land-based antennas. Conventionally, the angle in the azimuth plane is denoted by the Greek letter phi, , while the Greek letter theta, , represents the angle in the elevation plane. Some characteristics such as beam width and side lobes are the same in both planes for the symmetrical antennas such as circular waveguide horns and reflector.

Other characteristics such as the gain on bore sight (i.e., where the azimuth and elevation planes intersect) can only have a single value. In general, for unsymmetrical antennas the characteristics are different in the two principal planes, with a gradual transition in the intervening region between these two planes.

An antenna can be characterized by the following elements, not all of which may apply to all the antenna types:

Radiation Power Density

Radiation Power density gives a measure of the average power radiated by the antenna in a particular direction and is obtained by time-averaging the Poynting vector.

(watts/m2) (4.1)

where, E is the electric field intensity; His the magnetic field intensity, and η is the intrinsic impedance.

Radiation Intensity

Radiation intensity U in a given direction is the power radiated by the antenna per unit solid angle. It is given by the product of the radiation density and the square of the distance r.

(Watts/unit solid angle) (4.2)

Total power radiated

The total power radiated by the antenna in all the directions is given by:

(4.3)

(4.4)

Directivity

The Directive gain is the ratio of the radiation intensity in a given direction to the radiation intensity in all the directions:

(4.5)

The Directivity is the maximum value of the directive gain i.e. for a given direction is:

(4.6)

where the maximum radiation intensity.

## Types of Smart Antenna Systems

There are basically two approaches to implement antennas that dynamically change their antenna pattern to mitigate interference and multipath affects while increasing coverage and range [3]. They are as follows:

• Switched beam

• Adaptive Arrays

## Switched Beam Systems

The Switched beam approach is simpler compared to the fully adaptive approach. It provides a considerable increase in network capacity when compared to traditional omnidirectional antenna systems or sector-based systems. In this approach, an antenna array generates overlapping beams that cover the surrounding area as shown in Figure 3.

Figure 3: Block diagram of Switched Beam Systems

## Adaptive Array Systems

The Adaptive array system is the smarter of the two approaches. This system tracks the mobile user continuously by steering the main beam towards the user and at the same time forming nulls in the directions of the interfering signal as shown in Figure 1.6. Like switched beam systems, they also incorporate arrays. Typically, the received signal from each of the spatially distributed antenna elements is multiplied by a weight. The weights are complex in nature and adjust the amplitude and phase. These signals are combined to yield the array output.

These complex weights are computed by a complicated adaptive algorithm, which is pre-programmed into the digital signal-processing unit that manages the signal radiated by the base station.

Figure 1.6: Beam-forming for adaptive array antenna system

The adaptive array systems are really intelligent in the true sense and can actually be referred to as smart antennas. The smartness in these systems comes from the intelligent digital processor that is incorporated in the system. The processing is mainly governed by complex computationally intensive algorithms.

## 1.5 Adaptive Algorithms

The adaptive algorithms can be classified into categories based on the following approaches:

## 1. Algorithms based on adaptations:-

Continuous adaptation:

In this approach, the algorithm adjusts the weights as the incoming data is sampled and keep updating it such that it converges to an optimal solution. This approach is suitable when the signal statistics are time varying.

Examples: The Least Mean Square (LMS) algorithm and the Recursive Least square (RLS) algorithm.

Block adaptation:

In this approach, the algorithm compute the weights based on the estimates obtained from a temporal block of data. This method can be used in a non-stationary environment provided the weights are computed periodically.

Example: The Sample Matrix Inversion (SMI) algorithm.

## 2. Algorithms based on information required:-

Reference signal based algorithms:

These types of algorithms are based on minimization of the mean square error between the received signal and the reference signal. Therefore it is required that a reference signal be available which has high correlation with the desired signal.

Examples: The Least Mean Square (LMS) algorithm, The Recursive Least square (RLS) algorithm and the Sample Matrix Inversion (SMI) algorithm.

Blind adaptive algorithms:

These algorithms do not require any reference signal information. They themselves generate the required reference signal from the received signal to get the desired signal.

Examples: The Constant Modulus Algorithm (CMA), The Cyclostationary algorithm, and the Decision-Directed algorithm.

## SAMPLE MATRIX INVERSION (SMI) ALGORITHM

A smart antenna combines antenna arrays with digital signal processing units in order to improve reception and emission radiation patterns dynamically in response to the signal environment to steer multiple beams to track many mobiles, compensate aperture distortion or reduce multipath fading and co-channel interference. Of course, such a system is much complex as it includes very powerful numeric processors. However, even with the most powerful signal processors available today it is a very challenging task because the computational complexity of the operations involved becomes very large if the number of array elements increases. There will be a growing need for developing efficient algorithms. One such algorithm is the Sample Matrix Inversion (SMI), which provides good performance in a discontinuous traffic. However, it requires that the number of interferers and their positions remain constant during the duration of the block acquisition.

Figure 4: Block diagram of Sample Matrix Inversion (SMI) Algorithm

The Sample Matrix Inversion is a time average estimate of the array correlation, matrix using K-time samples. If the random process is ergodic in the correlation, the time average estimate will equal the actual correlation matrix. As the LMS algorithm is a continuously adaptive algorithm and has a slow convergence when the eigen values of the covariance matrix are widespread. When the transmission is discontinuous, a block adaptive approach such as SMI would give a better performance than a continuous approach.

## 2.1 SMI Formulation

The SMI algorithm has a faster convergence rate since it employs direct inversion of the covariance matrix R. Let us recall the equations for the covariance matrix R and the correlation matrix r.

(6.1)

(6.2)

If prior information about the desired and the interfering signals is known, then the optimum weights can be calculated directly by using the Weiner solution:

(6.3)

However, in practice signals are not known and the signal environment keeps changing. Therefore optimal weights can be computed by obtaining the estimates of the covariance matrix R and the correlation matrix r, by time averaging from the block of input data. The estimates of the matrices over a block size N1 - N2 are given by:

(6.4)

(6.5)

And, the weight vector can now be estimated by the following equation:

(6.6)

Based on the above discussion the weights will be updated for each incoming block. There is always a residual error in the SMI algorithm since it is based on estimation. This error is usually greater when compared to the LMS error. The error due to estimates can be computed by the following equation:

(6.7)

The stability of the SMI algorithm depends on the ability to invert the large covariance matrix. In order to avoid a singularity of the covariance matrix, a zero- mean white Gaussian noise is added to the array response vector. It creates a strong additive component to the diagonal of the matrix. In the absence of noise in the system, a singularity occurs when the number of signals to be resolved is less than the number of elements in the array. Since SMI employs direct matrix inversion, therefore the convergence of this algorithm is much faster compared to the LMS algorithm. However, huge matrix inversions lead to computational complexities that cannot be easily overcome.

## 2.3 Weight Adaptation Techniques

Weight adaptation in the SMI algorithm can be achieved in different ways [4] as shown below:

## Block adaptation:

The above-mentioned block adaptive approach, where the adaptation is carried over disjoint intervals of time, is the most common type. This is well suited for a highly time varying signal environment as in mobile communications

## Overlapping block adaptation:

This approach is computational intensive as adaptation intervals are not disjoint but overlapping. It provides better performance but has an increased number of inversions when compared to the above method.

## Block adaptation 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. It works better when the signal environment is stationary.

## EVALUATION

In this section MATLAB program is developed to simulate the Smart Antenna System using Sample Matrix Inversion (SMI) Algorithm on a BTS receiver (Uplink) to evaluate the performance of the Spatial Beamformer. This MATLAB simulation is divided into two stages: Angle of Arrival Estimation and Spatial Beamforming.

## Simulation Result

Figure 5: Plot of Radiation Pattern of a Spatial Beamformer

For simulation purposes, the SMI algorithm here uses the block adaptation approach, the size of the block being equal to 10 time samples. A 4-element linear array is used with its individual elements spaced at half-wavelength distance.

With the values of The Channel Signal to Noise Ratio = 2, The Signal Arrival Phase Angle = 60 Degrees and The Signal Arrival Phase Angle = 60 Degrees, we get the above plot for radiation pattern of a spatial beamformer. Assumptions made for this program that the presence of narrow band signals and 2 users are served in the presence of Additive White Gaussian Noise only.

As the Arriving Phase Angle is 60 degrees, so it can be seen in Figue 5 that at every 60 degree there is a null value in the beam formation. These null points lead to lower bandwidth and efficeincy of the signal. The null points should be absent in order to achieve a maximum gain in the direction of the desired signal of the user. More the number of null points mean more handoffs.

## CONCLUSIONS

The smart antennas are applicable to all major wireless protocols and standards. There are still several challenges to be resolved before the full potential of smart antennas can be realized. These are the aspects related to both modern implementation as well as algorithms for beam forming. The Sample Matrix Inversion (SMI) Smart Antenna Algorithm design should be able to update the weights blockwise to force deep nulls in the direction of the interferers and achieve a maximum in the direction of the desired signal.