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1. INTRODUCTION

Current and future demands in mobile communication for various

high speed multimedia data services entail a robust, high data rate

transmission system. Increasing numbers of users amid limited

spectrum motivate research on technology to expand the capacity and

increase spectral efficiency. At the same time, some detrimental

effects in randomly varying mobile communication environment like

multipath fading, co-channel interference and Doppler effects need to

be addressed. Adaptive beam forming are part of recent methods that

known to offer the solution for the abovementioned problems.

Adaptive modulation is a technique that varies some

transmission parameters to take advantage of favorable channel

conditions. Under bad channel conditions, a robust signal transmission

mode will be applied to ensure reliable data exchange. 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 constraints. The varying parameters

can be the symbol transmission rate, transmitted power level,

constellation size, BER, code rate or scheme, any combination of theseparameters [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

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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. Two important improvements on the CMA

performance are the dithered signed-error CMA (DSE-CMA) and the

pre-whitened CMA (PW-CMA). The DSE-CMA is an approach to reduce

the computational complexity of the CMA while retaining its robustness

and the PW-CMA aims at improving the convergence rate of the CMA in

case of channels exhibiting large frequency response deviations. In this

paper we review the two approaches and propose a new scheme

combining the virtues of the two. The combined scheme is

computationally simpler than the PW-CMA and provides better

convergence than the DSE-CMA. It is particularly suited for thesituations where ill-convergence needs to be treated with minimum

additional complexity and without loss of robustness.

In this work provides a review of Constant modulus algorithm

and direct inversion matrix methods used in mobile communication

systems. A comprehensive review includes some performance

comparisons, advantages and drawbacks of each method.

1.1. Problem outline

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

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Interferers and Maxima in the direction of the desired user.so, that

algorithms has low computation complexity and poor convergence.

1.2.Objective

In order to avoid those problems two methods has to be

developed.They are conjugate gradient method and music algorithm.

This algorithms has improve the computation complexity and better

convergence.

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2. SMART ANTENNA FUNDAMENTALS

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 chapter discusses two algorithms, the

Least Mean Square algorithm and the Constant Modulus algorithm.

2.1. Smart antenna basics

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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The following mathematical foundations on the smart antenna concept

can be found in [5]. If the wave front arrives at the array antenna as

shown in Figure 2, the wave front will be earlier on antenna element

k+1 than element k. The difference in length between the paths is

dsin. If the arriving signal is a harmonic signal or frequency, then the

signal arriving at antenna k+1 is leading in phase compared with

antenna k. The signal that arrives at antenna element zero is

considered to have a phase lead of zero. The signal that arrives at

antenna k, leads in phase with kdsin, where =2/ and is thewavelength.

The weight vector is defined by:

W=[w0,w1,w2,--wk-1 ]T ----------- (1)

Now the array factor is defined by:

[ W1 W2 W3 WK ]

X1

X2

X3

XK

Y

Figure 1, smart antenna concept for a receiving antenna

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F=wTv ----------------------- (2)

Where

V=[1 ej dsin e2j dsin---ej(k-1) dsin]------(3)

Here

K=no. of antennas

Wk=weight vector of antenna k

V=Array propagation vector

2.2. Adaptive beam forming

Popularly referred as smart antenna, adaptive beamforming is

one of antenna arrays application in mobile communication. With the

ability to adaptively directing the beam in specific directions it is

known to be an effective technique in canceling co-channel

interference. Some of the invaluable references that thoroughly

outlined all the methods and algorithms include [4] [26] [27] [28]

Adaptive beam forming can be done in many ways. Many

algorithms exist for many applications varying in complexity. Most of

the algorithms are concerned with the maximization of the signal to

noise ratio. A generic adaptive beam former is shown in Figure 3. The

weight vector w is calculated using the statistics of signal x (t) arrivingfrom the antenna array. An adaptive processor will minimize the error

e between a desired signal d(t) and the array output y(t).

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One of the simplest algorithms for adaptive processing is based

on the Least Mean Square (LMS) error. Although the complexity of the

algorithm is very low, its results are satisfying in many cases. The

algorithm is very stable and it needs few computations, which is

important for system implementation. The computational power of

many systems is limited and should be managed wisely.

The algorithm is based on knowledge of the arriving signal. The

knowledge of the received signal eliminates the need for beam

forming, but the reference can also be a vector that is partly known, orcorrelated with the received signal. For example, the training sequence

in the GSM standard, intended for channel equalization, could be used

for beam forming. The rest of the signal is unknown, and beam forming

using LMS can only be performed on the known training sequence.

When the adaptive algorithm is not using this knowledge, but statistic

[ W1 W2 W3 WK ]

X1

X2

X3

XK

Y

Figure.2. Smart antenna concept for a beam forming

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information of the signal, it is called blind beam forming. There are

several algorithms for blind beam forming. For example the Constant

Modulus algorithm (CMA) uses the knowledge that the modulus of the

signal is constant. There are many modulation schemes where the

modulus is kept constant. CMA is one of the simplest blind beam

forming algorithms.

J. Litva and K. Y. Lo in Chapter 3 of [4] explained in detail the

basic concept of adaptive beamforming starting from the used of two

elements array to suppress interference. The fundamental method in

adaptive beamforming is to choose the weights of array elements in

order to optimize the beamformer response to fulfill certain criterion.

The criterion includes Minimum Mean-Square Error, Maximum Signal-

to-Interference Ratio and Minimum Variance was discussed in the

book. The choice of criteria is not critically important since they are

closely related to each other. The more important part is the adaptive

algorithms, which will determine the speed of convergence and

hardware complexity required. The algorithms include Least Mean

Squares algorithm (LMS), Direct Sample Covarince Matrix Inversion

(SMI), Recursive Least Squares Algorithms (RLS) and Neural Networks.The notion of partially adaptivity then explained which is the

alternative technique when the number of array elements becomes

very large until it is difficult to implement full adaptivity. Another

important component in adaptive beamforming is the reference

signals, also known as the prior knowledge of the signal of interest,

which is needed to decrease the complexity, improve accuracy and

achieve faster convergence. Two known types are temporal reference

and spatial reference.

Some benefits of using adaptive antennas in mobile

communication were listed. The performance improvement in terms of

BER and co-channel interference reduction was shown using a few

simulation results from some established literatures. Since spatial

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channel information available on the uplink and most of the research

done on it, the discussion was focused on this type of application. An

optimum criterion, which was explained in chapter 3 is directly

applicable here. Some adaptive algorithms that suitable in mobile

communication with their implementation issues then were briefly

discussed. This includes LMS algorithm, SMI technique, RLS algorithm

touching on the pro and cons of each of them. Other algorithms that

proposed to overcome shortcomings or improve the performance of

the three basic algorithms such as conjugate gradient method,

eigenanlysis algorithm, rotational invariance method, linear least

square error (LSSE) algorithm, and Hopfield neural network with

respective references are listed.

The estimation technique of spatial reference signals referred as

Angle of Arrival (AOA) of the desired signal was categorized into two

groups. The first group named as wavenumber estimation is based on

decomposition of a covariance matrix whose terms consist of

estimates of the correlation between the signals at the elements of an

array antenna. The techniques include Multiple signal classification

(MUSIC), modified forward-backward linear prediction (FBLP), PrincipalEigenvector Gram-Schmidt (PEGS), Estimation of Signal Parameters by

Rotational Invariance Techniques (ESPRIT). The second group is

parametric estimation cover a variety of maximum likelihood

estimation (MLE) techniques, which require a high computational

complexity. It is noted that the main drawback of AOA approaches is

requirement for array calibration and extra processing load. The

temporal reference may be a pilot signal that is correlated with the

wanted signal, or known PN code in CDMA. The alternative techniques

in case of unavailability of explicit reference signal called blind

adaptive beamforming were briefly described. They are Constant

Modulus Algorithm, Decision Directed Algorithm and Cyclostationary

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Algorithms. Finally, some implementation issues for downlink

application were discussed.

An earlier literature by B. D. V. Veen and K. M. Buckley [16]

introduced beamforming as a versatile form of spatial filtering. Started

with the basic concept, associated the explanation with FIR filtering.

Beamformer was classified into data independent and statistically

optimum beamformer. Independent of the received data, the first class

of beamformer chose a fixed antenna arrays weights. The later class

use statistical information of received data to select the weights.

Adaptive beamforming comes into picture for the fact that the data

statistics are often unknown and varying over time. Two basic adaptive

approaches, block adaptation and continuous adaptation were

discussed. In block adaptation, the statistics are estimated from

temporal block of array data while continuous adaptation the weights

are adjusted as the data is sampled. Two basics adaptive algorithms,

LMS and RLS also introduced. Partial adaptivity was highlighted.

Lal. C. Godara [17][18] contributed a thorough study on antenna

arrays application in mobile communication. Part I gave a briefoverview of mobile communications, antenna array terminology, the

usage of antenna arrays in mobile communication systems, the

advantages and improvements that it brings, design issues, and the

feasibility in implementation. Part II presented a detail depiction of

various beam-forming schemes, adaptive algorithms, DOA estimation

methods, and some issues on error sensitivities. Relevant details and

references were provided for further research on each topic.

The important comparison of different approach in beamforming

may be compared based on type of adaptive algorithm it used. Many

researches were done on each algorithm and some comparisons were

highlighted in [4] [18]. Simplicity of Least Mean Square (LMS)

algorithm makes it widely been used for tap coefficient adaptations of

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an adaptive processor in antenna array. However, this continuous

adaptation approach algorithm causes signal acquisition and tracking

problems due to its slow convergence in multipath fading channel. This

is not suitable for mobile communication and some other measures

need to be taken if this algorithm is to be used such as power control

or normalized LMS algorithm. Converging faster than LMS algorithm,

SMI has attracted to be applied in mobile communication. However,

implementation difficulties need to be considered since its complexity

requires advance hardware capability and the use of finite precision

arithmetic may cause numerical instability. RLS can be seen as the

solution for the slow convergence of LMS and high complexity of SMI.

This is provided that SNR is high and setting of a fading rate dependent

forgotten factor is correct [4]. Computer simulation results for mobile

communication application shown that RLS outperform LMS and SMI in

flat fading channels. Another algorithm, conjugate gradient method

was studied to mitigate multipath fading effect in mobile

communication and shown a better BER performance than RLS [28].

2.3. kalman based on LMS algorithm

The LMS algorithm can be considered to be the most commonadaptive algorithm for continues adaptation. It uses the steepest-

descent method and recursively computes and updates the weight

vector. Due to the steepest-descend the updated vector will propagate

to the vector which causes the least mean square error (MSE) between

the beamformer output and the reference signal. The following

derivation for the LMS algorithm is found in [1]. The MSE is defined by:

e2(t) =[d*(t)-wHx(t)]2-------(4)

where

d*(t) = complex conjugate of the desired signal.

X(t)=received signal from the antenna elements.

wH=output of the beam form antenna.

(.)H = Hermetian operator.

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The LMS algorithm converges to this optimum Wiener solution. The

basic iteration is based on the following simple recursive relation:

W(n+1)=w(n)+1/2(-(E(e2)))-------(5)

Or

W(n+1)=w(n)+x(n)e(n)------(6)

One of the issues on the use of the instantaneous error is concerned

with the gradient vector, which is not the true error gradient. The

gradient is stochastic and therefore the estimated vector will never be

the optimum solution. The steady state solution is noisy; it will

fluctuate around the optimum solution. By decreasing the precision

will improve but it will decrease the adaptation rate. An adaptive

could solve this issue by starting with a large and decrease the factor

when the vector converges.

An adaptive array is simulated in MATLAB by using the LMS algorithm.

When an array of 4 antennas is used, there is a maximum of 3 nulls

that can eliminate the interferer. Figure shows the convergence of the

array for 2 interferers as shown in results. The minimum error is a

result of the extra system noise that is added to all antennas. The

interference signals are Gaussian white noise, zero mean with a sigmaof 1. The extra system noise to all antennas is white noise with zero

mean and a sigma of 0.1. The received signals are MSK signals with an

oversampling of 4 and have amplitude of 1 in the simulations. The

true array output y(t) is converging to the desired signal d(t). After 40

samples the signal is at its minimum due to the system noise. The LMS

cannot filter the system noise, as it is not correlated for all four

antennas.The interferers are cancelled by placing nulls in the direction

of the interferers. The received signal arrives at an angle of 25 degrees

and the array response is 0 dB. The LMS algorithm clearly works

sufficient as the strong interferers are reduced.

2.4. Constant Modulus Algorithm

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The CM algorithm is used for blind equalization of signals that

have a constant modulus. The MSK signal, for example, is a signal that

has the property of a constant modulus. The algorithm that updates

the weight Coefficients are exactly the same as for the LMS algorithm.

2.5. Direct matrix inversion

The Direct matrix inversion is a computationally intensive

process. Various algorithms can be applied for direction of arrival

estimation and tracking problems, such as blind algorithms that use

the temporal constant modulus structure of the signal (without training

signal) or algorithms that use the spatial properties of received signals

or training signal method [Godara97]. The main Disadvantage of the

training signal method is the slower convergence rate. It can be

applied to 3G Communication systems because a pilot signal is

presented in the structure of the uplink CDMA frame of UMTS/ITM2000

physical channel. The reason for a dedicated pilot instead of a common

pilot is to support the use of adaptive antenna arrays.

2.6. Adaptive modulation

With the main objective to maximize the spectral efficiency,many approaches of adaptive modulation have been proposed in

literature. An early work includes in Chapter 13 of [15], where W.T.

Webb and L. Hanzo introduce variable rate QAM. The transmitter varies

the signal constellation size from 1bit/symbol corresponding to BPSK to

6bits/symbol star 64-QAM. In a good quality channel, the constellation

size is increased, and as the channel quality become worst, i.e. as the

receiver enters a deep fade, the constellation size is decreased to a

value, which provides an acceptable BER. Two choices of

implementation can be applied where to keep constant of one

parameter and varying the other parameter. Specifying a required BER

value leads to varying data throughput and vise versa. The chapter

also highlights two different types of switching criteria to control the

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modulation modes, Received Signal Strength Indicator (RSSI) system

and error detector switching system. RSSI system use SNR values

corresponding to the BER of interest as the switching thresholds while

the later system use the channel coder to monitor the channel quality.

Simulation results showed the performance improvement over fixed

modulation and comparisons of the two switching systems. It is

observed that RSSI typically offering a slightly higher number of

bits/sym at low SNRs for some BERs. This is due to the RSSI switching

systems ability to select a lower number of levels before any errors

occurred. RSSI is also more attractive in term of implementation

complexity because no additional BCH codec is needed.

Another literature [2] indicated the above switching system as

the channel state information (CSI) which specified the channel quality.

SNR based CSI corresponding to RSSI system was compared with error-

based CSI corresponding to error detector switching system. SNR

based CSI adapts with a faster rate, but relies on the computation of

adaptation or switching thresholds that may be inaccurate. Accuracy of

the threshold mechanism increases by taking into account higher order

statistics of SNR than just the mean.Studies on varying combination of parameters also attract a

great interest. In [16], A. J. Goldsmith and S.G. Chua proposed a

variable-rate and variable-power MQAM modulation scheme for fading

channels. The transmission rate and power is both optimized to

maximize spectral efficiency, while satisfying average power and BER

constraints. Spectral efficiency of the proposed technique was derived

and compared with Shannons capacity limit. A comparison in terms of

spectral efficiency between the proposed method and two fixed-rate

variable-power schemes also performed. One of the compared scheme,

using channel inversion method adapts the transmit power to maintain

a constant received SNR. The main drawback of this technique is it

suffers a large power penalty since it use most of it power to

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compensate for deep fades. The other method, called truncated

channel inversion maintains a constant received SNR unless the

channel fading falls below a given threshold point. It is acknowledged

this technique can achieve almost the same spectral efficiency as the

proposed method. However, the outage probability can be quite high.

A question raised on power adaptation of whether or not power

adaptation actually provides substantial performance gains over

constant power system. Goldsmith showed theoretically in [17] that

Shannon capacity can be achieved by varying both rate and power.

However, as stressed in [1], Shannon capacity assumes that BER is

arbitrarily small, coding schemes are random and of unbounded length

and complexity, and there is no delay constraint. Therefore, the

capacity results do not necessarily shown insight of practical system.

Moreover, [17] also highlights that varying both power and rate

achieve negligibly increase in channel capacity compared to varying

rate only. The results shown in [1] prove that constraining power or

rate to be constant causes only little lost in spectral efficiency. They

also concluded that spectral efficiency of adaptive modulation isrelatively insensitive to which degrees of freedom are adapted.

Realizing that previous work only deals with uncoded

modulation, Goldsmith and S.G. Chua [18] propose adaptive coded

modulation for fading channels. They applied coset codes since the

code design are separable from modulation design, which is well suited

to be combined with adaptive modulation system. Special cases of

coset codes, trellis and lattice codes were first applied to general class

adaptive modulation. Combination of trellis code with spectrally

efficient adaptive M-ary quadrature amplitude modulation (M-QAM)

introduced in [16] produce trellis-coded adaptive MQAM. Analytical and

simulation results shown that the new simple 4-state trellis-coded

adaptive MQAM achieves 3-dB effective coding gain relative to

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uncoded adaptive M-QAM and 3.6 dB for 8-state trellis. Compared with

traditional trellis codes and fixed-rate modulation, the new scheme

shown more than 20 dB power savings.

K. J. Hole, Henrik Holm [19] introduced a general variable-rate

constant-power Trellis Coded Modulation (TCM) scheme for frequency-

flat, slowly varying Nakagami Fading (NMF) channel. Their main

contribution is the development of a general technique to determine

the average spectral efficiency of the coding scheme for any set of 2L-

dimensional (2L-D) trellis codes. The paper concentrates on code sets

that can be generated by the same encoder and decoded by the same

decoder to avoid hardware complexity. It is assumed that the perfect

channel state estimation (CSI) is available at the decoder and reliable

feedback channel available between the encoder and decoder.

Considering channel estimation accuracy and feedback delay

problem, D. L. Goeckel [20] propose an adaptive trellis-coded

modulation schemes, which is proved to gain higher bandwidth

efficiency over their non-adaptive counterparts on time-varying

channels. The scheme was designed using only a single outdated

fading estimate when neither the Doppler frequency nor exact shapeof autocorrelation function of the channel fading process is known. This

issue concerning channel estimation errors and outdated feedback

have become one of critical issue in ensure the effectiveness of

adaptive modulation. Some works on this includes [21] [22]

Another way of categorizing adaptive modulation is based on the

adaptation algorithms used, including the constraints and the

objectives. Some typical constraints are upper bound BER, fixed

throughput and average transmitted power [23]. For some application

that required low delay such as speech and real-time video

communication, fixed throughput adaptive transmission is favored.

However, for data transmission systems, which can tolerate for higher

delay the variable throughput, maximum BER is usually utilized [24].

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Aiming to maximize the throughput, some works done on deriving the

optimum switching mode thresholds subject to the average BER

constraints [22] [25].

3. BENEFITS OF SMART ANTENNA

Multipath propagation, defined as the creation of multiple signal

paths between the transmitter and the receiver due to the reflection of

the transmitted signal by physical obstacles is one of the major

problems of mobile communications [6]. It is well known that the delay

spread and resulting intersymbol interference (ISI) due to multiple

signal paths arriving at the receiver at different times have a critical

impact on communication link quality. On the other hand, co-channel

interference is a major limiting factor on the capacity of wireless

systems, resulting from the reuse of the available network resources

(e.g., frequency, time) by a number of users. Smart antenna systems

can improve link quality by combating the effects of multipath

propagation or constructively exploiting the different paths, and

increase capacity by mitigating interference and allowing transmission

of different data streams from different antennas. More specifically,

the benefits of smart antennas can

be summarized as follows [6]:

3.1. Increased range/coverage:

The array or beam forming gain is the average increase in signalpower at the receiver due to a coherent combination of the signals

received at all antenna elements. It is proportional to the number of

receive antennas and also allows for lower battery life.Lower power

requirements and/or cost reduction: Optimizing transmission toward

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the wanted user (transmit beam forming gain) achieves lower power

consumption and amplifier costs.

3.2. Improved link quality/reliability:

Diversity gain is obtained by receiving independent replicas of

the signal through independently fading signal components. Based on

the fact that it is highly probable that at least one or more of these

signal components will not be in a deep fade, the availability of

multiple independent dimensions reduces the effective fluctuations of

the signal. Forms of diversity include temporal, frequency, code, and

spatial diversity obtained when sampling the spatial domain with smart

antennas. The maximum spatial diversity order of a non-frequency-

selective fading MIMO channel is equal to the product of the number of

receives and transmits antennas. Transmit diversity with multiple

transmit antennas can be exploited via special modulation and coding

schemes [6], whereas receive diversity relies on the combination of

independently fading signal dimensions.

3.3. Increased spectral efficiency:

Precise control of the transmitted and received power and

exploitation of the knowledge of training sequence and/or otherproperties of the received signal (e.g., constant envelope, finite

alphabet, cyclostationarity) allows for interference reduction/mitigation

and increased numbers of users sharing the same available resources

(e.g., time, frequency, codes) and/or reuse of these resources by users

served by the same base station/access point. The latter introduces a

new multiple access scheme that exploits the space domain, space-

division multiple access (SDMA). Moreover, increased data rates and

therefore increased spectral efficiency can be achieved by exploiting

the spatial multiplexing gain, that is, the possibility to simultaneously

transmit multiple data streams, exploiting the multiple independent

dimensions, the so called spatial signatures or MIMO channel

eigenmodes. It was shown [7] that in uncorrelated Raleigh fading the

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MIMO channel capacity limit grows linearly with min (M, N), where M

and N denote the number of transmit and receive antennas,

respectively.

Traditionally, smart antenna systems have been designed

focusing on maximization of one of the above-mentioned gains (beam

forming diversity, and multiplexing gains). Nevertheless the trade-offs

between these gains have been recently studied [8], and smart

antenna approaches have been proposed that combine the resulting

benefits [9].

4. SMART ANTENNA MODELS

In this work, we are interested more in adaptive array

antennas that can independently steer their main beam and nulls

to arbitrary directions. This process is generally called beam

forming. Their main difference from simple directional antennas

(and hence their smartness) is the following: Instead of just

directing the main beam towards the direction specified (e.g. by the

application), smart antennas can automatically adapt their

radiation pattern, in order to track the intended

receiver/transmitter and minimize transmission/reception gain (i.e.

create nulls) towards unintended receivers/transmitters .A large

number of alternative beamforming designs (e.g. digital,

microwave, aerial beamforming) and algorithms (e.g. Least Mean

Square, Constant Modulus Algorithm, etc.) have been proposed in

literature, a detailed tutorial of which can be found in [10]. Until

recently, adaptive array antennas had only been considered for

the use on base station in cellular systems, due to their large size, highcost, considerable power consumption, and complexity of design.

However, recently there have been proposed simple, analog, smart

antenna designs [11] [12] that are low cost and energy-efficient

enough to be used on wireless terminals. Theyre based on the

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concept of aerial beamforming and prototype antennas have been built

and tested [13].

5. CONJUGATE GRADIENT METHOD

The Conjugate Gradient method is an effective method for

symmetric positive definite systems. The method proceeds by

generating vector sequences of iterates, residuals corresponding to the

iterates, and search directions used in updating the iterates and

residuals.

The unpreconditioned conjugate gradient method constructs the thk

iterate kx as an element of },,{0100

rArspanxk+ so that )()(

xxAxx kTk

is minimized, where

x is the exact solution of Ax=b. This minimum is

guaranteed to exist in general only if A is symmetric positive definite.

The conjugate gradient iterates converge to the solution of Ax=b in no

more than n steps, where n is the size of the matrix.

In every iteration of the method, two inner products are performed in

order to compute update scalars that are defined to make the

sequences satisfy certain orthogonal conditions. On a symmetric

positive definite linear system these conditions imply that the distance

to the true solution is minimized in some norm.

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The iterates kx are updated in each iteration by a multiple k of the

search direction vector kp :

kkkk pxx += 1

Correspondingly the residuals kk Axbr = are updated as

kkk Aprr = 1

The choice kkkk ApprrTT

/11 = minimizes kk rArT 1

The search directions are updated using the residuals 11 += kkkk prp

where the choice 11/ = kkkkk rrrrTT

ensures that kr and 1kr are

orthogonal.

The following is parallel code fragment which performs the conjugate

gradient algorithm for solving Ax=b.

r_local = b_local

rho = Allreduce (r_local* r_local)

for k=1:itermax

if k=1

p_local=r_local

else

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beta=rho/oldrho

p_local = r_local + beta* p_local

end

p=Gather(p_local)

v_local=A_local*p

alpha = rho/ Allreduce(p_local*v_local)

x_local = x_local + alpha*p_local

r_local = r_local alpha*v_local

oldrho = rho

rho = Allreduce (r_local*r_local)

end

The algorithm is the same as that in serial computer. All matrices and

vectors, however, have distributed: various dot products are performed

by collecting partial results (using Gather) and Sum them up (using

Allreduce(SUM)).

Example 1

Assume A be a 57600x57600 sparse matrix,

=

TI

I

I

IT

A

,

=

51

1

1

15

T

CG method convergent in 8 iterations.

Result:

No of processor

used 1 2 4

Time used 0.95 1.13 1.12

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(1) In Network of work-stations, since the time used in both algorithm

are almost the same. The difference between them is when one

processor is used, the time recorded is just used in calculation. When

four processors are used, the time mainly used in message passing.

(2) In cluster, if we dont including the time used in showing x, the time

used in both algorithms are almost the same.

No of processor 1 2 4

Total time - Time showing

x1.17-0.65

= 0.52

4.52 -

3.86 =

0.66

3.48 -

2.68 =

0.8

The time used in message passing becomes longer if more processors

are used. Ex. When 2 and 4 processors are used, it used 0.17s and

0.37s to transfer message respectively.

Since this matrix is too fast to convergent, there is just 8 iteration

steps and the time used in calculation is not obvious in this program.

Example 2

In this example, I will let smaller number in diagonal, so it need more

iterates to convergent.

Assume A be a 57600x57600 sparse matrix,

=

TI

I

I

IT

A

,

=

41

1

1

14

T

Since A is still a symmetric and positive definite matrix, we can solve

the equations by conjugate gradient method.

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The solution convergent in 296 iterations.

Result:

No of processor

used 1 2 4 8

Time used 6.4 6.73 5.8 5.41

(1) In network, from the profile report, the time used in calculation is

shorted. But when 2 processors are used, we need to add up the time

used in calculation and message passing. We find that the total time

used is almost the same as that when one processor is used.When 4 and 8 processors are used, the speedup of parallel algorithm is

1034.18.5

4.6

4==S , 1830.1

41.5

4.68 ==S

The efficiency is

2759.04

1034.1

4==E , 1479.0

8

1830.18 ==E

(2) In cluster, comparing with example 7, we find that if it needs more

iteration to convergent, the time used in message passing increased.

No of processor 1 2 4 8

Time used in calculation 6.24 5.52 5.38 4.26

Time used in message

passing ~ 6.2 6.08 6.62

Although the time used in calculation decrease continually, the range

is too close. Ex. When 2 processors are used, the calculations time is

5.52s, it just only increased about 11%. In addition, the time used in

transferring message is around 6s. So there is no speedup.

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Advantage:

The cgmprovides good performance in a discontinuous traffic

when the number of interferers and their positions remain

constant during the duration of the block acquisition.

The main advantage of cgm is the good conversation.

The block diagram of direct matrix inversion algorithm as shown below

The above diagram is the smart antenna concept for a receiving

antenna. In this diagram, contains k anntenas and their correspondingweighted vectors are w1, w2, w3, ---, wk. y is the summation of the all

reference signal with vectors.

[ W1 W2 W3 WK ]

X1

X2

X3

XK

Y

Figure 3, smart antenna CGM concept

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The covariance matrix of the input vector X for a finite sample size is

defined as the maximum likelihood estimation of matrix R and can be

calculate as

R(N)=1/N*X.XH------------------(17)

Here

K=no.of antennas


wH=output of the beam form antenna.

(.)H = Hermetian operator.

The optimum weight vector that correspond to the estimated matrix

Rk for any i-th channel is given by

W=R-1V------------------------------ (18)

Where

V=[1 ej dsin e2j dsin---ej(k-1) dsin]------(19)

Here

K=no. of antennas

W=weight vector

V=Array propagation vector.

The Direct Matrix Inversion Algorithm provides good performance in adiscontinuous traffic when the number of interferers and their positions

remain constant during the duration of the block acquisition. The DMI

algorithm employs direct inversion of the co-variance matrix R and

therefore it has faster convergence rate. The equation for co-variance

matrix R is given by

R=E[x(t).xH(t)] ----------------------------------(20)

The equation for correlation matrix r is given by equation

r=E[d(t).x(t)]----------------------------------(21)

The error e due to estimation can be computed by the equation

e=Rw-r-------------------------------------- (22)

or

e=x(n)-y(n)

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where

x(n)=reference signal

y(n)=received signal

Then to calculate the array factor by using following equation

Arrayfactor=w(n)*ejksin---------------------------(23)

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 numbers 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.When an array of 4 antennas is used, there is a maximum of 3 nulls




interference signals are Gaussian white noise, zero mean with a sigma

of 1. The extra system noise to all antennas is white noise with zero


over sampling of 4 and have amplitude of 1 in the simulations. The

true array output y(t) is converging to the desired signal d(t). After 40

samples the signal is at its minimum due to the system noise. The LMS



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5.1. FLOWCHART

The flowchart of direct matrix inversion as shown below. By using

flowchart to implement the mat lab code easily.

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star

t

Assign k,

W=1/k*[1 e-jsin e-j2sin -----e-j(k-1) sin]

Noise=sin+j cos

nan =signal_n1 * e-j(k) sin

x(n)=noise+n1+n

2+x

Yan =w*x(an)

Error= x(an)- Yan

W=w+.error.x(an)

Arrayfactor=w* e-j(k) sin

En

d

Fig 4. Direct matrix inversion algorithm flowchart

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5.2. Algorithm of conjugate gradient algorithm

Define the of k, %k=no. of antennas,=angle

W=1/k*[1 e-jsin

e-j2sin

-----e-j(k-1) sin

] %weighted vector

Noise=sin+j cos % system noise for every antenna

X=noise

For an=1:k

nan =noise * e-j(k) sin %received signal from noise source an(i.e antenna an)

end

x(n)=noise+n1+n2+x %total signal(i.e all antenna signals)

For an=1:k

Yan =w*x(an) % received signal

Error= x(an)- Yan

W=w+.error.x(an)

End

Arrayfactor=w* e-j(k) sin

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6. RLS ALGORITHM

As was mentioned in the previous section, the SMI technique has

several drawbacks. Even though the SMI method is faster than the

LMS algorithm, the computational burden and potentialsingularities can cause problems. However, we can recursively

calculate the required correlation matrix and the required

correlation vector. Recall that in Eqs. (8.60) and (8.61) the estimate

of the correlation matrix and vector was taken as the sum of the

terms divided by the block length K. When we calculate the weights

in Eq. (8.66), the division by K is cancelled by the product xx

(k)r(k). Thus, we can rewrite the correlation matrix and thecorrelation vector omitting K as

where k is the block length and last time sample k and Rxx (k),r (k)

is

the correlation estimates ending at time sample k. Both summations

(Eqs. (8.67) and (8.68)) use rectangular windows, thus they equallyconsider all previous time samples. Since the signal sources can

change or slowly move with time, we might want to deemphasize the

earliest data samples and emphasize the most recent ones. This can be

accomplished by modifying Eqs. (8.67) and (8.68) such that we forget

the earliest time samples. This is called a weighted estimate.

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where is the forgetting factor.

The forgetting factor is also sometimes referred to as the exponential

weighting factor [37]. is a positive constant such that 0

1. When = 1, we restore the ordinary least squares algorithm.

= 1 also indicates infinite memory. Let us break up the summation in

Eqs. (8.69) and (8.70) into two terms: the summation for values up

to i = k1 and last term for i = k.

Example 6.1 For an M = 4-element array, d = /2, one signal

arrives at 45, and S(k) = cos(2(k 1)/( K 1)). Calculate the

array correlation for a block of length K = 200 using the standard

SMI algorithm and the recursion algorithm with = 1. Plot the

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trace of the SMI correlation matrix for K data

points and the trace of the recursion correlation matrix vs. block

length k where 1 < k < K. Solution Using MATLAB, we can

construct the array steering vector for the angle of arrival of 45.

After multiplying the steering vector by the signal S(k) we can then

find the correlation matrix to start the recursion relationship in Eq.

(8.71). After K iterations, we can superimpose the traces of both

correlation matrices. It can be seen that the recursion formula

oscillates for different block lengths and that it matches the SMI

solution when k = K. The recursion formula always gives a

correlation matrix estimate for any block length k but only

matches SMI when the forgetting factor is 1. The advantage of the

recursion approach is that one need not calculate the correlation

for an entire block of length K. Rather, each update only requires

one a block of length 1 and the previous correlation matrix. Not

only can we recursively calculate the most recent correlation

estimates, we can also use Eq. (8.71) to derive a recursion

relationship for the inverse of the correlation matrix. The next

steps follow the derivation in [37]. We can invoke the ShermanMorrison-Woodbury (SMW) theorem [38] to find the inverse of Eq.

(8.71). Repeating the SMW theorem Example 6.2:Use the RLS

method to solve for the array weights and plot the resulting

pattern. Let the array be an M = 8-element array with

spacingd= .5withareceivedsignalarrivingattheangle0 =

30,aninterferer at 1 = 60. Use MATLAB to write an RLS

routine to solve for the desired weights. Use Eqs. (8.71), (8.78),

and (8.81). Assume that the desired received signal vector is

defined by xs(k) =a0s(k) where s(k) =

cos(2*pi*t(k)/T);withT=1ms.LettherebeK=50timesamplessuc

hthatt=(0:K1)*T/().Assume that the interfering signal vector

is defined byxi(k) = a1i(k) where i(k) = sin(pi*t(k)/T);. Let the

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desired signal d(k) = s(k). In order to keep the correlation matrix

inverse from becoming singular, add noise to the system with

variance n =.01.Beginwiththeassumptionthatallarrayweights are

zero such that w(1) = [0000 0 000]T . Set the forgetting factor

Advantages The advantage of the RLS algorithm over SMI is that it is no

longer necessary to invert a large correlation matrix. The

recursive equations allow for easy updates of the inverse of

the correlation matrix.

The RLS algorithm also converges much more quickly than the

LMS algorithm.

Interference is low Less noise

7. LMS ALGORITHM

The LMS algorithm can be considered to be the most common

adaptive algorithm for continues adaptation. It uses the steepest-

descent method and recursively computes and updates the weight

vector. Due to the steepest-descend the updated vector will propagate

to the vector which causes the least mean square error (MSE) between

the beamformer output and the reference signal. The following

derivation for the LMS algorithm is found in [1]. The MSE is defined by:

e2(t) =[d*(t)-wHx(t)]2-------(4)

where

d*(t) = complex conjugate of the desired signal.


wH

=output of the beam form antenna.(.)H = Hermetian operator.

The LMS algorithm converges to this optimum Wiener solution. The

basic iteration is based on the following simple recursive relation:

W(n+1)=w(n)+1/2(-(E(e2)))-------(5)

Or

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W(n+1)=w(n)+x(n)e(n)------(6)

One of the issues on the use of the instantaneous error is concerned

with the gradient vector, which is not the true error gradient. The

gradient is stochastic and therefore the estimated vector will never be

the optimum solution. The steady state solution is noisy; it will

fluctuate around the optimum solution. By decreasing the precision

will improve but it will decrease the adaptation rate. An adaptive

could solve this issue by starting with a large and decrease the factor

when the vector converges.

An adaptive array is simulated in MATLAB by using the LMS algorithm.

When an array of 4 antennas is used, there is a maximum of 3 nulls




interference signals are Gaussian white noise, zero mean with a sigma

of 1. The extra system noise to all antennas is white noise with zero


oversampling of 4 and have amplitude of 1 in the simulations. The

true array output y(t) is converging to the desired signal d(t). After 40samples the signal is at its minimum due to the system noise. The LMS






Disadvantages

The disadvantage of the LMS algorithm is difficulty for easy

updates of the inverse of the correlation matrix.

The LMS algorithm converges much slower.

Interference is high

high noise

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7. RESULTS

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0- 2

0

2

p

h

a

s

e

(ra

d

)

d e s i re d s i g n a l 1 0 d e g r e e s i n t e r fe r e r s - 1 0 a n d - 4 0 d e g r e e s

p h a s e ( d )p h a s e ( y )

Fig.6 .Phase response of LMS algorithm when N=5

0 5 0 1 0 0 1 5 0 2 0 0 2 5 00 . 5

1

1 . 5

2

a

m

pl

itu

d

e

| d |

| y |

.

| |Fig.7. Amplitude response of LMS algorithm when N=5

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li

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 00

0 . 5

1

s a m p le ( i n d e x )

am

plitude

| e r r o r |

Fig.8. Error response of LMS algorithm When N=5

-80 -60 -40 -20 0 20 40 60 80-30

-25

-20

-15

-10

-5

0

5

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

(dB)

angle(degrees)

Fig.9.Normalize array factor of LMS algorithm when N=5

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0 5 0 1 0 0 1 5 0 2 0 0 2 5 0-2

0

2

phase(rad)

d e s ire d s ig n a l 1 0 d e g re e s in te rfe re rs -1 0 a n d -4 0 d e g re e s

p h a s e (d )

p h a s e (y )

li

l i

li

Fig .10.Phase response of LMS algorithm when N=8

0 50 100 150 200 250-2

0

2

phase(ra

desiredsignal 10degrees interferers -10and-40degrees

phase(d)

phase(y)

0 50 100 150 200 2500.5

1

1.5

amplitude

|d|

|y|

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

sample(index)

amplitude

|error|

Fig.11. Amplitude response of LMS algorithm when N=8

0 50 100 150 200 250-2

0

2

phase(rad desiredsignal 10degrees interferers -10and-40degrees

phase(d)

phase(y)

0 50 100 150 200 2500.5

1

1.5

amplitude

|d|

|y|

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

sample(index)

amplitude

|error|

Fig.12. Normalize array factor of LMS algorithm when N=8

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-80 -60 -40 -20 0 20 40 60 80-30

-25

-20

-15

-10

-5

0

5


(dB)

angle(degrees)


0 5 0 1 0 0 1 5 0 2 0 0 2 5 0-2

0

2

phase(rad)

d e s ire d s ig n a l 1 0 d e g re e s in te rfe re rs -1 0 a n d -4 0 d e g re e s

p h a s e (d )

p h a s e (y )

li

| |

| |

i

| |

Fig .14.Phase response of LMS algorithm when N=20

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0 50 100 150 200 250-2

0

2

phase(rad) desiredsignal 10degrees interferers -10 and -40degrees

phase(d)

phase(y)

0 50 100 150 200 2500.8

1

1.2

amplitude

|d|

|y|

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

sample(index)

amplitude

|error|

Fig.15. Amplitude response of LMS algorithm when N=20

0 50 100 150 200 250-2

0

2

phase(ra

desiredsignal 10degrees interferers -10and-40degrees

phase(d)

phase(y)

0 50 100 150 200 2500.8

1

1.2

amplitude

|d|

|y|

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

sample(index)

amplitude

|error|


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-80 -60 -40 -20 0 20 40 60 80-30

-25

-20

-15

-10

-5

0

5


(dB)

angle(degrees)


-80 -60 -40 -20 0 20 40 60 80-30

-25

-20

-15

-10

-5

0

5


(dB

)

angle(degrees)

N=5

N=8

N=20

Fig.18. comparison the Normalize array factor of LMS algorithm

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0 50 100 150 200 250-2

0

2

phase(ra

desiredsignal 25degrees interferers 0and-40degrees

phase(d)

phase(y)

0 50 100 150 200 2500.5

1

1.5

amplitude

|d|

|y|

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

sample(index)

amplitude

|error|

Fig .19.Phase response of direct matrix inversion algorithm when N=5

l

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0

0 . 5

1

1 . 5

a

m

p

litu

d

e

| d |

| y |

.

l

l

| |

Fig.20 .Amplitude response of direct matrix inversion algorithm when N=5

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.

li

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 00

0 . 5

1

s a m p le ( in d e x )

a

m

p

litu

d

e

|e r r o r |

Fig .21.error response of direct matrix inversion algorithm when N=5

-80 -60 -40 -20 0 20 40 60 80-20

-15

-10

-5

0

5

amplitude response antenne pattern

(dB)

angle(degrees)

Fig.22. Normalize array factor of Direct matrix inversion algorithm when N=5

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0 5 0 1 0 0 1 5 0 2 0 0 2 5 0- 2

0

2

phase(rad)

d e s i r e d s ig n a l 2 5 d e g re e s in t e r fe re rs 0 a n d -4 0 d e g re e s

p h a s e (d )

p h a s e (y )

li

| |

| |

l i

li

| |

Fig.23 .Phase response of direct matrix inversion algorithm when N=8

0 5 0 1 0 0 1 5 0 2 0 0 2 5 00 . 5

1

1 . 5

a

m

p

litu

d

e

| d |

| y |

.

| |Fig .24.Amplitude response of direct matrix inversion algorithm when N=8

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0 5 0 1 0 0 1 5 0 2 0 0 2 5 00 . 5

1

1 . 5

a

m

p

litu

d

e

| d |

| y |

.

l

l

| |

Fig .25.Amplitude response of direct matrix inversion algorithm when N=8

-80 -60 -40 -20 0 20 40 60 80-20

-15

-10

-5

0

5


(

dB)

angle(degrees)


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0 5 0 1 0 0 1 5 0 2 0 0 2 5 0- 2 0

0

2 0

4 0

p

h

a

s

e

(ra

d

)

d e s ir e d s ig n a l 2 5 d e g r e e s in t e r fe r e r s 0 a n d - 4 0 d e g r e e s

p h a s e ( d )

p h a s e ( y )

li

| |

| |

.

l i

li

| |

Fig.27 .Phase response of direct matrix inversion algorithm when N=20

i i l i

0 5 0 1 0 0 1 5 0 2 0 0 2 5 00

5

1 0x 1 0

1 7

am

p

litude

| d |

| y |

l i

li

| |Fig .28.Amplitude response of direct matrix inversion algorithm when N=20

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0 50 100 150 200 250-20

0

20

40

phase(rad)

desired signal 25 degrees interferers 0 and -40 degrees

phase(d)

phase(y)

0 50 100 150 200 2500

5

10x 10

17

amplitude

|d|

|y|

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

sample(index)

amplitude

|error|

Fig .29.error response of direct matrix inversion algorithm when N=20

-80 -60 -40 -20 0 20 40 60 80-20

-15

-10

-5

0

5


(dB)

angle(degrees)


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-80 -60 -40 -20 0 20 40 60 80-20

-15

-10

-5

0

5


(dB)

angle(degrees)

N=5

N=8

N=20

Fig.31. comparison the Normalize array factor of direct matrix inversion algorithm

-80 -60 -40 -20 0 20 40 60 80-30

-25

-20

-15

-10

-5

0

5


(dB)

angle(degrees)

DMI

CMD

Fig.32. Comparison plots between DMI and CMA algorithms when N=5

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-80 -60 -40 -20 0 20 40 60 80-20

-15

-10

-5

0

5


(dB)

angle(degrees)

CMD

DMI


-80 -60 -40 -20 0 20 40 60 80-20

-15

-10

-5

0

5


(dB)

angle(degrees)

CMD

DMI


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-80 -60 -40 -20 0 20 40 60 80-30

-25

-20

-15

-10

-5

0

5

10amplitude response antenne pattern

(dB)

l

Fig.35. Normalize array factor of CM algorithm when N=5

-80 -60 -40 -20 0 20 40 60 80-30

-25

-20

-15

-10

-5

0

5

10


(dB)

angle(degrees)


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-200 -150 -100 -50 0 50 100 150 200435

440

445

450

455

460

465

470

475

480

485amplitude response antenne pattern

(dB)

angle(degrees)


8. CONCLUSION

In this work,direct matrix inversion and constant modulus

algorithm are used to update the combining weights of adaptiveantenna array. However, its fast convergence presents an acquisition

compare to LMS algorithm.These algorithms are good 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

users 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-interference-plus noise ratio.

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9. REFERENCES

[1] S.T. Chung, A.J. Goldsmith, Degrees of Freedom in Adaptive

Modulation: A Unified View, IEEE Trans. Commun., vol. 49, pp.

1561-1571, Sept. 2001

[2] S. Catreux, V. Erceg, D. Gesbert, and R.W. Health, Jr., Adaptive

Modulation and MIMO Coding for Broadband Wireless Data

Networks, IEEE Commun Mag, pp. 108-115, June 2002

[3] S. Applebaum, Adaptive arrays, Technical Report SPL TR-66-

001, Syracuse Univ. Rec., Corp. Report, 1965

[4] J. Litva, T. K. Lo, Digital Beamforming in Wireless

Communications, Artech House, Norwood, 1996.

[5] J. Litva, Digital Beamforming in wireless communications, 1996

[6] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-

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Time Wireless Communications, Cambridge Univ.Press,

2003.

[7] G. J. Foschini and M. J. Gans, On Limits of Wireless

Communications in a Fading Environment when Using

Multiple Antennas, Wireless Pers. Commun., vol. 6,

Kluwer, 1998, pp. 31135.

[8] L. Zheng and D. N. C. Tse, Diversity and Multiplexing:

A

Fundamental Trade-Off In Multiple Antenna Channels,

IEEE Trans. Info. Theory, vol. 49, no. 5, May 2003, pp.107396.

[9] V. Tarokh et al. , Combined Array Processing and

Space-Time Coding, IEEE Trans. Info. Theory, vol. 45,

May 1999, pp. 112128.

[10] W. F. Gabriel, Adaptive Processing Array Systems, in

Proceedings of IEEE, Vol. 80, Issue 1, Jan 1992.

[11] T. Ohira, Analog smart antennas: an overview, The

13th IEEE International Symposium on Personal, Indoor and

Mobile Radio Communications, 2002, Volume: 4, 2002, Page(s):

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