Adaptive Beamforming for OFDMA Using Positioning Information

Shahid Mumtaz1, Joaquim Bastos2, Jonathan Rodriguez3, Christos Verikoukis4

1, 2, 3 Institute of Telecommunications, 2, 4Universitat de Barcelona Aveiro, 3810078, Portugal.

Tel: +351 234 377900, Fax: +351 234 3779 Email: 1smumtaz@av.it.pt

Abstract— In this paper a downlink location based adaptive beamforming algorithm (LBA) for OFDMA network is proposed. Conventional beamforming algorithms use SINR for determining the weights vector, whereas the proposed LBA profits from available positioning information, which reduces the convergence time of the weights vector determination. From the simulation results we see that a location-based algorithm reduces significantly the amount of necessary iterations in order to achieve the appropriate weights vector that maximizes SINR at a specific mobile terminal (MT). Ultimately this reduction has a clear impact on the overall performance of a cellular communication system.

Keywords—Adaptive beamforming, SINR, Weight Vector, Mobile terminal.

1. Introduction

In the past decade, a great effort has been made to build the future generation mobile communication systems. It is expected to provide high-speed and high quality information services. Adaptive Beamforming has numerous applications in array signal processing, radar, sonar, astronomy, medical imaging and wireless communications. Beamforming is a key technology in the smart antenna systems so that many different adaptive Beamforming algorithms have been the subject of active research.

A wireless cellular network consists of a large number of cells, base stations and a number of mobile terminals (MTs) with various movement patterns (position, speed and direction). With current technology, it is now possible to implement very sophisticated and computationally intensive digital signal processing algorithms for practical cellular communications. For that, it has been demonstrated that adaptive or self-adjusted antenna array beamformers hold great potential for improving signal to interference plus noise ratio (SINR) and hence achieving higher cell capacities [1].The spatial selectivity is achieved by using fixed or adaptive receive, or transmit, beampatterns. Its concept is based on an array of antenna elements that are sufficiently close together in order to make possible to exploit the associated strong spatial correlation of the received, or transmitted, signals through that antenna array.

In a conventional adaptive beamforming algorithm, an antenna array is exploited to achieve maximum transmission in a specified direction by manipulating the signal emanating from base station, towards a desired

direction of an MT while transmission towards other directions is mitigated. This is achieved by varying the weights of each of the antenna elements in the array used at the base station. This spatial separation is exploited to prevent the transmitted signal to interfere with other MTs, and reach mainly the desired MT. The optimum weights are iteratively computed in adaptive beamforming using adaptive filter algorithms. In this study we consider only LMS (Least Mean square) [3] as adaptive filter algorithm. LMS algorithm can be considered as the most common adaptive algorithm for continuous adaptation. It uses the steepest descent method and recursively computes and updates the weight vector. In this paper we propose adaptive beamforming algorithm based on LMS that exploits the available positioning information regarding BS and MTs’ locations. In the proposed algorithm the whole system setup is considered to be identical to the conventional adaptive beamforming one, with the exception of the SINR feedback, coming from the MT for the weights vector optimization to maximize the SINR at the MT. Proposed algorithm assumes that there is updated positioning information distribution in the considered system.

The rest of the paper is arranged as follows. Section 2 explains the adaptive beamforming. Section 3 explains the system model. Section 4 explains the location assisted beamforming. Section 5 presents the simulation scenario and results follow by conclusion in section 6.

2. Downlink Adaptive Beamforming

Switched beamforming and adaptive beamforming are the two main approaches usually considered, although element-space beamforming and beam-space beamforming techniques can also be considered [3] and [4]. Switched beamforming algorithms are less efficient than adaptive algorithms. The performance measurements are made through simulation study of array factor, error estimation over time change, angle of arrival, steering angles, and BER (Bit Error Rate) vs. SINR. In DL beamforming the radiation pattern of the transmitting antenna can be shaped by the array of elemental radiators, which define namely the main beam lobe of the antenna, increasing or decreasing its directivity. As the directivity of the antenna increases, it also increases its gain. For time varying signal propagation environments, statistics change with time as the mobile target and interferers move around the cell. Due to the mobility effect, the additive

2011 Wireless Advanced

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Gaussian channel model is not practical, and hence the wireless channel to consider for the mobile cellular network is a fading channel. The fast fading effect is more serious than the path loss, in mobile communications. For this, at the BS, a recursive update of the beamformer’s weight vector is necessary to track a moving MT. Adaptive beamforming algorithms are used in mobile communication systems to determine dynamically the optimal weight vector for the antenna array at the BS, based on different performance criteria, such as Mean Square Error (MSE), Maximum Likelihood (ML), or maximum SINR. The weighting coefficients are in function of the signal’s direction of arrival and the antenna array geometry. The optimum weighting coefficients are obtained from the Wiener solution [1]

3. System Model

We are considering one OFDM base station (BS) with one Mobile users (MS) case only for downlink direction. In a BS, we consider an antenna array with ´mth´ element. It is assumed that the BS is equipped with an antenna array to receive and transmit signals from and to MS. Two antenna arrays are assumed for MS, other simulation parameters are shown in table 1. The beamforming structure to be used for DL transmission from a base station is depicted in Figure 1.

∑

Figure 1: Beamforming structure for DL transmission from BS

The m-th sample of an OFDM symbol at the output of an OFDM transmitter can be written as

1

0

2exp , 0 m N-1,N

m nn

mnx X jN

−

=

Π⎧ ⎫= ≤ ≤⎨ ⎬⎩ ⎭

∑ (1)

Where N is the number of subcarriers and Xn is the data symbol on the nth subcarrier. We assume that each OFDM symbol is transmitted (BS) through multipath channel with L discrete paths towards the receiver (MS). BS deploys a uniformly spaced liner array consist of K elements. Using the narrowband model assumption, the mth sampled at the

kth antenna elements can be written as sample of an OFDM symbol at the output transmitter can be written as.

1

, , , ,0

2exp ( ( 1) sin 0 -1m

L

m k m l x m kl

r h j k d n m Nθλ

−

=

Π⎧ ⎫= − − + ≤ ≤⎨ ⎬⎩ ⎭

∑ (2)

Where d is the antenna spacing, λ is the wavelength of the carrier,θ is the AOA with respect to the ray normal, , , mm l xh is the complex random variable for the l-th path of the channel impulse response at time m, and , ,m kn is the AWGN at the kth antenna element at time m. If we let w ( )k θ be the phase shift of the received signal at the kth antenna element with respect to the received signal at the reference antenna element, then equcation1 can be written as

{ }1

, , , , ,0

exp ( ) + 0 m N-1m

L

m k m l x k m kl

r h j w nθ−

=

= − ≤ ≤∑

Where 2 ( 1) sinkw k dθ θλΠ= −

We assume that the guard time is longer than the delay spread so that ISI can be completely eliminated. The demodulated symbol on the n-th subcarrier at the output of FFT at the k-th antenna element can be written as [14]

1 1

, ,0 0

1

0

1 1

,0, 0

, , ,

2( ) exp ( ) ( )

2 (0)exp ( ) ( )

2 + ( )exp ( ) ( )

, 0 n N-1,

N L

n k m l k n km l

L

l k nl

N L

m l k n km m n l

n k n n k n k

mlY X H n m j w NN

nlH j w XN

mlX H n m j w NN

X N

θ

θ

θ

α β

− −

= =

−

=

− −

= ≠ =

Π⎧ ⎫= − − + +⎨ ⎬⎩ ⎭

⎡ Π ⎤⎧ ⎫= − +⎨ ⎬⎢ ⎥⎩ ⎭⎣ ⎦Π⎧ ⎫− − + +⎨ ⎬

⎩ ⎭= + + ≤ ≤

∑∑

∑

∑ ∑

(3) where ,n kN is the AWGN on the n-th subcarrier at the k-th

antenna element, ,n kα is the multiplicative distortion caused by the channel at the desired subcarrier at the k-th antenna element, ,n kβ is the ICI term, and ( )lH n m− is

the FFT of a time-variant multipath channel ,m lh , which is defined as follows:

1

,0

1 2 ( )( ) exp ( )N

l m lk

k n mH n m h jN N

−

=

Π −⎧ ⎫− = −⎨ ⎬⎩ ⎭

∑ (4)

8

If we assume the multipath channel is time-invariant over one OFDM symbol duration, ( )lH n m− in equation 4

becomes zero and thus there is no ICI and , ,n kβ is also zero in equation 3. After the FFT operation on each antenna element, demodulated symbols on each subcarrier are passed to the corresponding beamformers. The output of the n-th beamformers can be written as

*,,

1

0 1K

n n kn kk

p Y n Nw=

= ≤ ≤ −∑

where ,n kW is the weight on the k-th antenna element for

the n-th beamformers and ,n kY is the demodulated symbol on the n-subcarrier at the k-th antenna element defined in equation 3. The eventual lack of direct measurement of DL channel responses at the BS is an issue that afflicts the downlink beamforming problem. A simple method for DL channel estimation is the probing-feedback approach [5]. The direction of arrival (DoA) of the uplink signals can also be used to overcome this problem [6]. Actually, downlink and uplink signals propagate, reflecting and refracting on the same scatters which are in the BS and MTs surroundings, meaning that the uplink signals’ DoA should be the only constant parameters which can be used for DL channel estimation. The DoA associated with the desired user can be determined using the received uplink signals, after which the DL channel responses can be determined using known relations between UL and DL steering vectors. Another problem with DL beamforming weights determination is that the associated algorithms are not that efficient even when DL channel responses are provided. The MRC (maximum ratio combining) method uses a straightforward approach based on setting the DL channel responses as the DL beamforming weights, which corresponds to keep the main lobe of the DL radiation pattern towards the desired MT. A virtual uplink beamforming and power control technique (V-UBPCT) is proposed in [7] where DL beamforming weights are generated through simple computations as in real UL beamforming. It is considered that the maximum achievable capacity in the DL is the maximum number of users for which the desired SINR is achievable. The algorithm determines a set of transmit beamforming weights and also DL transmit power allocations which assure that the required SINR at each MT is higher than a specific value, minimizing the total transmitted power. The base station can transmit to distinct mobile terminals, using different beamforming weight vectors, denoted here by wi regarding MTi. The received signal at each MT is given by

( ) ( ) ( ) ( ) ( )0 1

k LH l l

i i i l i i i i i in l

y t G g t nT Ps n n tθ ρ α τ= =

= − − +∑∑w a

(5)

where k=|t/T|, T is the symbol duration, ai(θl) is the response to the signal coming from MTi at direction θl, s is the signal transmitted by the BS, ni(t) is the thermal noise at MTi, P is the signal power before the beamformer, ρi models the log-normal shadow fading, αi

l and Gi are the lth path fading and path loss from the base station to the MTi, respectively, and gi(t) models the effect of the pulse-shaping function of the modulation scheme.

Channel Model

The channel response in the beamforming scheme is of critical importance for the determination of the relevant beamforming weights. In order to evaluate the performance of multiple antennas structures, the 3GPP-3GPP2 Spatial Channel Ad hoc group has developed SCM for three different scenarios (Suburban Macro, Urban Macro, and Urban Micro). The parameters and methods generating the channel coefficients, which reflect power delay profiles, angle spreads, dependencies between parameters, antenna arrangements and fading, are described in the 3GPP document [8]. In there, for an N element linear BS array and an M element linear MS array, the channel coefficients for one of L multipath components are given by a M x N matrix of complex amplitudes. We denote the channel matrix for the lth multipath component (l = 1, …, L) as Hl(t). The (m,n)th component (n = 1, …, N; m = 1, …, M ) of Hl(t) is given by

( ) ( ) ( )

( ) ( ) ( )( )

, , , ,, ,

1

, , , , , , ,

exp sin

exp sin exp cos

UBS l u AoD n l u AoDl SF

m n lu

l u MS l u AoA m l u AoA l u AoA v

G jkdPh t

U

G jkd jk v t

θ θσ

θ θ θ θ

=

⎛ ⎞⎜ ⎟=⎜ ⎟⎝ ⎠

+Φ −

∑

(6)

The definitions and generating procedures of parameters in (4) are defined in [8].Assuming a single antenna element at the mobile stations, following the notation in (3), we can model our channel by a discrete impulse response

( ) ( ) ( )1

Ll l

i i l i i i il

n G r nθ ρ α=

=∑h a (7)

where ril(n) takes into account the effects of the receiver

matched filter, wave shaping function and transmitter filter.

LMS algorithm The Least Mean Squares (LMS) algorithm can be considered as the most common adaptive algorithm for continuous adaptation. It uses the steepest descent method and recursively computes and updates the weight vector. Due to the steepest descent 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 LMS algorithm is simple to implement, but the dynamic range over which it operates is quite limited, therefore a normalized LMS algorithm can be used to overcome the dynamic range limitation. The

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following derivation for the LMS algorithm is found in [Lit96]. The MSE is defined by

22 *( ) ( ) ( )Hk d k w x kε ⎡ ⎤= −⎣ ⎦ where d*(k) is the complex conjugate of the desired signal. The signal x(k) is the signal to be transmitted by the antenna elements, and wHx(k) is the output of the beamformer antenna, where H stands for the Hermitian operator. The expected value of both sides leads to [9, 3]

{ } { }2 2( ) ( ) 2 H HE k E d k w r w Rwε = − + In this relation, r and R are defined as [12, 13]

{ }*( ) ( )r E d k x k=

{ }( ) ( )HR E x k x k= where R is referred to as the covariance matrix and r is the cross-correlation. If the gradient of the weight vector w is zero, the MSE is at its minimum [3]. This leads to

{ }( )2 ( ) 2 2 0w E k r Rwε∇ = − + = (8)

The solution of the above equation is called the Wiener-Hopf equation for the optimum Wiener solution

1optw R r−=

The LMS algorithm converges to this optimum Wiener solution, for which the basic iteration is based on the following simple recursive relation [10, 3]

{ }( )( )2( 1) ( )2

w k w k Eμ ε+ = − ∇ (9)

where μ is the step size. Combining (8) with (9) gives:

( )( 1) ( ) ( )w k w k r Rw kμ+ = + − (10)

Since the measurement of the gradient vector is not possible, the instantaneous estimate is used as defined by

*ˆ( ) ( ) ( )r k d k x k=

ˆ ( ) ( ) ( )HR k x k x k=

By rewriting (10) using the instantaneous estimates, the LMS algorithm can be written in its final form as

( )* *ˆ ˆ ˆ ˆ( 1) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )Hw k w k x k d k x k w k w k x k kμ μ ε+ = + − = +One of the issues regarding 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 LMS algorithm can be the best choice for antenna array systems with a relatively small number of elements.

LMS algorithm.

4. Location-Assisted Beamforming

In order to assess the expected advantage of using positioning information in adaptive beamforming, an implementation of a conventional algorithm was carried out in our study. Its performance can therefore be used as a reference or benchmark.

In a conventional adaptive beamforming algorithm, an antenna array is exploited to achieve maximum transmission in a specified direction by manipulating the signal emanating from base station, towards a desired direction of an MT while transmission towards other directions is mitigated. This is achieved by varying the weights of each of the antenna elements in the array used at the base station. This spatial separation is exploited to prevent the transmitted signal to interfere with other MTs, and reach mainly the desired MT. In our adaptive beamforming implementation the optimum weights are iteratively computed using LMS towards the maximization of the signal to interference plus noise ratio at the desired mobile terminal, according with the analytical expressions in section, regarding the LMS algorithm. A straightforward representation of the algorithm is shown in Figure 2.

Figure 2: Conventional adaptive beamforming.

Trained adaptive beamforming algorithms, such as the LMS, use a finite set of training symbols to adapt the weights of the array and maximize the SINR in the direction of the desired mobile terminal. First, a training

Base Station

Mobile Terminal

Maximize SINR in the direction

SINR Weights iterative update based on SINR

10

signal, which is known to both the BS and MT, is transmitted by the BS. The beamformer at the BS uses the information of the training signal coming from the MT to determine the optimal weights vector. After the training period, data is sent to the MT, for which the beamformer in the BS uses the weight vector computed previously, to process the signal to be transmitted to that desired MT.

For the proposed beamforming algorithm exploiting the available positioning information regarding BS and MTs’ locations, we assume this information is available to the BS without any error (perfect positioning info), and that it is always up-to-date (updated in real-time). In this proposed algorithm the whole system setup is considered to be identical to the conventional adaptive beamforming one, with the exception of the SINR feedback, coming from the MT for the weights vector optimization to maximize the SINR at the MT, which doesn’t exist here. The MT SINR info feedback is here replaced by an estimation of its value, calculated directly at the BS, by using the positioning information to determine the distance between BS and MT(s), and also between the latter and eventual interferers, distances which are used afterwards for the SINR estimation. With this approach, there is an upfront clear advantage for not requiring the necessary feedback as in the conventional algorithm, which represents a drawback in terms of the extra utilization of transmission time at the MTs and wastage of bandwidth. On the other hand, proposed algorithm assumes that there is updated positioning info distribution in the considered system. A simplistic representation of the algorithm is shown below in Figure 3.

Considering a cell in which we have a base station and a mobile terminal, assuming only downlink communication, and that positioning information is available regarding the location of the BS, at (x1, y1), and the MT, at (x2, y2), it is possible to determine the distance between the two according to the expression.

Figure 3: Location-assisted adaptive beamforming.

( ) ( )2 21 2 1 2BS MTd x x y y− = − + −

Once this distance is determined it is possible to estimate SNR based on the learned value. When interfering signals exist at the MT, from other sources like other nearby base stations, the beamformer needs to take them into account, as long as their positions are available, computing the weights vector solution that statistically maximizes the SINR at the MT. For this it is required the knowledge of the desired signal and also the interference correlation matrix.

int( ) ( ) ( ) ( )signal erference noisex k x k x k x k= + + The slot is the basic resource unit in a WiMAX based system. The SINR is computed over the subcarriers of a slot in the downlink, considering distributed subcarrier permutation PUSC. The physical abstraction model used for this purpose was the Mean Instantaneous Capacity (MIC) [11]. In the considered system there are 1024 subcarriers (720 for data), which implies calculating the SINR for each subcarrier, therefore

(0) (0), , , (0)

( ) ( ) ( )0 , , , ( )1

n Tx n Sh n FF

nB b b b

Sc n Tx n Sh n FF nbb

KP a adSINR

KN W P a ad

α

α δ=

=+∑

where Pn.Tx is the transmit power per subcarrier, a (0)

n,Sh and a (0)

n,FF represent the shadowing (log-normal) and fast fading (Rician) factors for the received signal, coming from the BS, respectively. WSc is the subcarrier frequency spacing and N0 is the thermal noise density. B is the number of interfering base stations, K is the path loss constant, α is the path loss exponent and d(0) is the distance between MT and considered BS. The terms with superscript b are related to the interfering base stations, and δ(b)

n is equal to 1 if the interfering BS is transmitting on the nth subcarrier and 0 otherwise.

The relation between the SINR and BER in an adaptive antenna array system is given in [3] as,

( )3 sBER Q N SINR=

( )2

2 31 1 1 , 02 2 2 22

ts

x

N SINRxQ x e dt erfc erfc xπ

−∞ ⎛ ⎞⎛ ⎞= = = ≥⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠∫

where Ns is the number of subcarriers.

5. Simulation Scenario and Results

A four element antenna array is considered for transmission at the base station of an IEEE 802.16e (Mobile WiMAX) cell, and a two element antenna is assumed at the mobile terminal for reception. These antennas setup involve therefore a multiple input multiple output (MIMO) channel configuration, which in our work was modelled according with the 3GPP spatial channel model [8]. The service area

Base Station

Mobile Terminal

Maximize SINR in the direction

Positioning MT SINR = f (distances)

Weights iterative update based on SINR

11

of the cellular network is assumed to be covered by many identical regular hexagonal cells, and MTs are uniformly distributed in each cell with a random speed v, which has a probability density function (pdf) fv(v). Mobile terminals move randomly in any direction with equal probability over [0, 2π] for the angle of arrival. In mobile cellular systems implementing beamforming, it is assumed that the bandwidth separation is θb, which is further assumed as the minimum separation angle between two consecutive MTs using the same physical channel. In our study we considered a uniform linear array with two elements with array element spacing λ/2. The produced radiation patterns for the considered combination between the number of elements and the spacing between each other are represented in Figure 4.

Figure 4: Radiation patterns : a) N=2, d=λ/2

For our work, according with the produced radiation patterns, and a reasonable trade-off between performance, complexity and cost. The antennas inter-elements spacing d is considered to be half of the signal wavelength, λ/2, on BS’s transmitter and MTs’ receiver. The two beamforming algorithms were implemented and included in a simulation platform made in MATLAB code, reproducing a WiMAX transmission chain. The simulation code core stands essentially in the necessary loops to update the weights vector that is used to approximate the desired signal by the beamforming algorithms, and also actually on its computation. Some of the most important parameters used in the performed simulations are the number of the antenna array elements at the BS, its antenna noise figure (BS system noise), the antenna elements spacing (d), and the LMS algorithm step size (μ). The efficiency of the evaluated beamforming algorithms is quite dependent on the selected values for these parameters. In addition to these parameters there are others which are fixed with constant values. The considered interference signals are Gaussian white noise, with zero mean and unitary standard deviation. Perfect channel estimation was always assumed. The most important simulation parameters and setup details are shown below in Table 1. In this work the proposed algorithm performance is compared against the performance of a conventional adaptive beamforming implementation. This comparison focuses essentially on the time, or number of iterations, necessary for the weights vector to be determined with negligible error, and also on the BER achieved by the system when the mobile terminal is moving with a determined speed.

Parameters ValuesSystem channel bandwidth 10 MHz Sampling frequency 11.2 MHz FFT size 1024 Subcarrier frequency spacing 10.94 kHz Useful symbol time (T

b= 1/f) 91.4 µs

Guard time (Tg=T

b/8) 11.4 µs

OFDMA symbol duration (Ts= T

b+T

g) 102.9 µs

Modulation scheme 64-QAM Coding rate 3/4 Frame duration 5 ms Number of OFDMA Symbols 48 Data OFDM Symbols 44

DL PUSC Null subcarriers 184 Pilot subcarriers 120 Data subcarriers 720

Beamforming

Number of elements 4 Inter-element spacing λ/2 Step size 0.01 System noise 0.1 Number of interferers 2 AoD 20º

Steering angle for nulls -82º, -40º, -19º, 0º, 40º, 82º

Table 1 : Setup and simulation parameters.

For this evaluation, the mobile terminal is considered to be in line of sight (LoS) in the direction of 20º, relative to the BS, and other MTs are assumed to be in the directions of the nulls specified in Table 1. A representation of the radiation pattern is shown below in Figure 5.

Figure 5: BS Antenna amplitude response pattern.

Weights Iterations In mobile environments, the convergence rate of any adaptive algorithm is quite important, since the achieved solution is most useful before the channel conditions change. Therefore one of the performance evaluations that was accessed in this work is the convergence speed of the algorithms, in terms of mean square error according with the number of iterations performed in the algorithms. This comparison is shown in Figure 6.

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Figure 6: Algorithm’s MSE vs. iteration number.

It is visible that the proposed location-based algorithm can reach a negligible MSE value roughly twice as fast as the conventional version of the algorithm, with much less fluctuation. This evaluation shows that the location-based algorithm reaches the optimum solution for the complex weights vector in half of the number of iterations required by the conventional one, which can enhance significantly the overall performance of the communication system due to its faster response to changing environments.

In Figure 7 is represented the actual convergence in terms of magnitude of the signal computed by each of the algorithms, which can be seen converging towards the normalized desired signal magnitude (unitary dashed line), coherent with the algorithms’ MSE convergence rates, and complementing the visualisation of the performance of the algorithms in terms of convergence rate.

Static and dynamic performance In order to be able to assess the actual impact of the two adaptive beamforming algorithms in the overall mobile system performance, a bit error rate evaluation was carried out considering the mobile terminal moved with a constant speed, in the normal direction of the base station. In Figure 8 the performance of both algorithms is represented in terms of the achieved BER considering both static and moving MT.

Figure 7: Magnitude of normalized desired signal.

Figure 8: BER performance against mobile terminal speed.

-25 -20 -15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SINR

Mea

n sq

uare

Err

or

Empirical CDF

Proposed

Conventioal

Figure 9: SINR performance

The advantage brought by the location-based algorithm in terms of faster determination of the appropriate weights vector that maximize SINR at the MT as shown in Figure 9 is only actually useful once the mobile terminal moves above pedestrian speed values, and decreases above vehicular speed figures of approximately 50km/h, as expected. In the static MT case this happens because once the weights vector is determined it will be used and will provide maximum performance on both systems. For MT speeds above roughly 70 km/h the performance edge offered by the location-assisted algorithm becomes not so attractive since both algorithms are not able to respond as well to the faster changing channel conditions.

6. Conclusion

In this paper our main focus is on a beamforming algorithm that profits from available positioning information, based on the reduction of the convergence time of weights vector determination. This was clearly achieved with the proposed location-based algorithm, which reduces significantly the amount of necessary iterations in order to achieve the appropriate weight vector that maximizes SINR at a specific MT .The proposed location-assisted algorithm has the advantage of not being as dependent on the mobile terminal as the conventional version, since it doesn’t require feedback information from the MT regarding SINR. Both algorithms depend strongly on the channel state

13

information for the complex weight vector determination. Also, convenient distribution of positioning information is fundamental for the proposed beamforming algorithm, which should include both information on line of sight and non-line of sight regarding base station and mobile terminals.

Acknowledgment This work has been performed in the framework of the ICT projects ICT-248894 WHERE2 which are partly funded by the European Union.

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