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-1- Investigation of Uplink and Downlink Performance of Investigation of Uplink and Downlink Performance of Investigation of Uplink and Downlink Performance of Investigation of Uplink and Downlink Performance of Directivity Directivity Directivity Directivity Controlled Constrained Beamforming Algorithms for Controlled Constrained Beamforming Algorithms for Controlled Constrained Beamforming Algorithms for Controlled Constrained Beamforming Algorithms for CDMA-Based Systems CDMA-Based Systems CDMA-Based Systems CDMA-Based Systems Holger Boche and Martin Schubert Holger Boche and Martin Schubert Holger Boche and Martin Schubert Holger Boche and Martin Schubert Heinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbH Heinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbH Heinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbH Heinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbH Broadband Mobile Communication Networks Broadband Mobile Communication Networks Broadband Mobile Communication Networks Broadband Mobile Communication Networks Einsteinufer 37, D-10587 Berlin/Germany Einsteinufer 37, D-10587 Berlin/Germany Einsteinufer 37, D-10587 Berlin/Germany Einsteinufer 37, D-10587 Berlin/Germany E-mail: [email protected], [email protected] / Tel: +49 (0)30-31002-399 E-mail: [email protected], [email protected] / Tel: +49 (0)30-31002-399 E-mail: [email protected], [email protected] / Tel: +49 (0)30-31002-399 E-mail: [email protected], [email protected] / Tel: +49 (0)30-31002-399 Abstract Abstract Abstract Abstract This paper investigates the applicability of the blind DoA-based maximum This paper investigates the applicability of the blind DoA-based maximum This paper investigates the applicability of the blind DoA-based maximum This paper investigates the applicability of the blind DoA-based maximum directivity (MD) beamformer to CDMA-based systems in up- and downlink. Our directivity (MD) beamformer to CDMA-based systems in up- and downlink. Our directivity (MD) beamformer to CDMA-based systems in up- and downlink. Our directivity (MD) beamformer to CDMA-based systems in up- and downlink. Our approach is based on DoA estimation and consequently does not require any pilot approach is based on DoA estimation and consequently does not require any pilot approach is based on DoA estimation and consequently does not require any pilot approach is based on DoA estimation and consequently does not require any pilot signal or training sequence. It is shown how knowledge of the DoA can be used signal or training sequence. It is shown how knowledge of the DoA can be used signal or training sequence. It is shown how knowledge of the DoA can be used signal or training sequence. It is shown how knowledge of the DoA can be used to generate a most robust beam pattern in order to perform spatial filtering of to generate a most robust beam pattern in order to perform spatial filtering of to generate a most robust beam pattern in order to perform spatial filtering of to generate a most robust beam pattern in order to perform spatial filtering of multipath components in up- and downlink. Robustness is achieved by multipath components in up- and downlink. Robustness is achieved by multipath components in up- and downlink. Robustness is achieved by multipath components in up- and downlink. Robustness is achieved by maximising the directivity of the beam pattern as well as by generating broad maximising the directivity of the beam pattern as well as by generating broad maximising the directivity of the beam pattern as well as by generating broad maximising the directivity of the beam pattern as well as by generating broad nulls. Analytical results are presented and different aspects of directivity nulls. Analytical results are presented and different aspects of directivity nulls. Analytical results are presented and different aspects of directivity nulls. Analytical results are presented and different aspects of directivity controlled beamforming are discussed. controlled beamforming are discussed. controlled beamforming are discussed. controlled beamforming are discussed. I INTRODUCTION I INTRODUCTION I INTRODUCTION I INTRODUCTION Wireless cellular communication based on DS-CDMA has experienced tremendous growth in markets, technology and range of services throughout the last decade. However, radio spectrum is a limited resource. The resulting challenge is to develop enhanced transmission techniques in order to realise emerging broadband services and applications. One promising way to significantly increase the spectral efficiency is the deployment of antenna arrays at the base station in order to perform space-time processing (STP) [1, 2, 3] . While the deployment of antenna arrays in 3 rd generation systems is still optional, they will be an essential part of future systems [4] .

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Investigation of Uplink and Downlink Performance ofInvestigation of Uplink and Downlink Performance ofInvestigation of Uplink and Downlink Performance ofInvestigation of Uplink and Downlink Performance of

DirectivityDirectivityDirectivityDirectivity

Controlled Constrained Beamforming Algorithms forControlled Constrained Beamforming Algorithms forControlled Constrained Beamforming Algorithms forControlled Constrained Beamforming Algorithms for

CDMA-Based SystemsCDMA-Based SystemsCDMA-Based SystemsCDMA-Based Systems

Holger Boche and Martin SchubertHolger Boche and Martin SchubertHolger Boche and Martin SchubertHolger Boche and Martin Schubert

Heinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbHHeinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbHHeinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbHHeinrich-Hertz-Institut für Nachrichtentechnik Berlin GmbH

Broadband Mobile Communication NetworksBroadband Mobile Communication NetworksBroadband Mobile Communication NetworksBroadband Mobile Communication Networks

Einsteinufer 37, D-10587 Berlin/GermanyEinsteinufer 37, D-10587 Berlin/GermanyEinsteinufer 37, D-10587 Berlin/GermanyEinsteinufer 37, D-10587 Berlin/Germany

E-mail: [email protected], [email protected] / Tel: +49 (0)30-31002-399E-mail: [email protected], [email protected] / Tel: +49 (0)30-31002-399E-mail: [email protected], [email protected] / Tel: +49 (0)30-31002-399E-mail: [email protected], [email protected] / Tel: +49 (0)30-31002-399

AbstractAbstractAbstractAbstract

This paper investigates the applicability of the blind DoA-based maximumThis paper investigates the applicability of the blind DoA-based maximumThis paper investigates the applicability of the blind DoA-based maximumThis paper investigates the applicability of the blind DoA-based maximum

directivity (MD) beamformer to CDMA-based systems in up- and downlink. Ourdirectivity (MD) beamformer to CDMA-based systems in up- and downlink. Ourdirectivity (MD) beamformer to CDMA-based systems in up- and downlink. Ourdirectivity (MD) beamformer to CDMA-based systems in up- and downlink. Our

approach is based on DoA estimation and consequently does not require any pilotapproach is based on DoA estimation and consequently does not require any pilotapproach is based on DoA estimation and consequently does not require any pilotapproach is based on DoA estimation and consequently does not require any pilot

signal or training sequence. It is shown how knowledge of the DoA can be usedsignal or training sequence. It is shown how knowledge of the DoA can be usedsignal or training sequence. It is shown how knowledge of the DoA can be usedsignal or training sequence. It is shown how knowledge of the DoA can be used

to generate a most robust beam pattern in order to perform spatial filtering ofto generate a most robust beam pattern in order to perform spatial filtering ofto generate a most robust beam pattern in order to perform spatial filtering ofto generate a most robust beam pattern in order to perform spatial filtering of

multipath components in up- and downlink. Robustness is achieved bymultipath components in up- and downlink. Robustness is achieved bymultipath components in up- and downlink. Robustness is achieved bymultipath components in up- and downlink. Robustness is achieved by

maximising the directivity of the beam pattern as well as by generating broadmaximising the directivity of the beam pattern as well as by generating broadmaximising the directivity of the beam pattern as well as by generating broadmaximising the directivity of the beam pattern as well as by generating broad

nulls. Analytical results are presented and different aspects of directivitynulls. Analytical results are presented and different aspects of directivitynulls. Analytical results are presented and different aspects of directivitynulls. Analytical results are presented and different aspects of directivity

controlled beamforming are discussed.controlled beamforming are discussed.controlled beamforming are discussed.controlled beamforming are discussed.

I INTRODUCTIONI INTRODUCTIONI INTRODUCTIONI INTRODUCTION

Wireless cellular communication based on DS-CDMA has experienced tremendous

growth in markets, technology and range of services throughout the last decade.

However, radio spectrum is a limited resource. The resulting challenge is to develop

enhanced transmission techniques in order to realise emerging broadband services and

applications. One promising way to significantly increase the spectral efficiency is the

deployment of antenna arrays at the base station in order to perform space-time

processing (STP)[1, 2, 3]

. While the deployment of antenna arrays in 3rdgeneration

systems is still optional, they will be an essential part of future systems[4].

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Exploitation of the spatial dimension can be used to reduce co-channel interference

(CCI) and inter-symbol interference (ISI), while improving resistance to fading and

thermal noise. Reducing intra- and inter-cell CCI can be traded for improved coverage,

capacity or quality. Thus, spatial filtering, also referred to as beamforming[5], will play

an important role in future broadband wireless networks.

In this paper, we focus on so-called blind DoA-based beamforming techniques, assuming

that the direction-of-arrival (DoA) of the dominant transmission paths are known. Blind

techniques do not need any training sequence or pilot signal. Thus, they consume no

additional spectrum resource (note that in GSM 20% of the bits are dedicated for

training). This makes them promising candidates for various types of wireless networks.

DoA estimates can be obtained with second order statistics of the communication

signals[6], which are assumed to be stationary within the coherence time of the channel.

Improvement can be achieved by mobility models, which help predicting the movement

of the mobile unit by considering the slowly time varying nature of the user location.

However, the wireless radio channel poses a great challenge as a medium for reliable

high speed communications and accurate DoA-estimation is difficult to realize. First field

trials [7, 8] have shown that DoA-based methods are very sensitive to error effects.

Consequently, DoA-based beamforming must take into account a DoA mismatch of

several degrees. Conventional DoA-based beamforming has been shown to perform poor

in this case. This is mostly due to beam pattern distortion caused by hyper-sensitive

algorithms in presence of DoA errors. Thus, the deployment of DoA-based beamforming

in mobile environments demands for more robust techniques being able to cope with

numerous error effects like inter-cell CCI, scattering effects or DoA estimation errors.

Consequently, the investigation of the beam pattern is an important aspect and new

performance parameters are needed to assess the quality of the beam pattern.

In this paper we will focus on the impact of directivity and broad nulls on STP

architectures for CDMA-based systems. It will be shown how these parameters can be

used to generate a beam pattern having maximum directivity. Robust beam pattern

control is envisaged which must compensate for DoA errors, angle spread and CCI.

We assume a single cell scenario without inter-cell CCI, where all users are separated

by quasi-orthogonal spreading codes. The cell is divided in three sectors of 120°. For

each sector a uniform linear antenna array(ULA) is deployed at the base station. Linear

arrays have been developed vigorously during the last decades mainly for radar and

sonar signal environments in military applications. Its application to mobile

communications is subject of ongoing world wide research and development activity [1, 2].

The paper is organised as follows. In Section II we will briefly introduce the underlying

vector channel model and discuss the angle spread of dominant transmission paths.

Next, in Section III we discuss different aspects of directivity controlled beamforming

and broad nulls with respect to space-time processing. The maximum directivity (MD)

beamformer is presented and its application up- and downlink processing is discussed.

Finally, we conclude with a summary in Section IV.

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Some notational conventions are: scalars in lower case, matrices in upper case and

vectors in boldface lowercase. The expectation operator is written as E[ ]. The complexㆍ

conjugate and the complex conjugate transpose are given by ( )ㆍ and ( )ㆍH, respectively.

II SIGNAL AND CHANNEL MODELII SIGNAL AND CHANNEL MODELII SIGNAL AND CHANNEL MODELII SIGNAL AND CHANNEL MODEL

Consider a narrowband signal s(t) = u(t)ㆍejw 0t, where u(t) denotes the complex

baseband envelope and w0 the carrier frequency. The signal source is assumed to

lie in in the far field of a ULA consisting of M isotropic antenna elements with half

wavelength element spacing. In this case, a plane wave front crosses the array with

the angle of incidence array elements with the azimuth angle θ, as depicted in Fig.

1. For convenience it is assumed that all users and the array lie in a horizontal

plane, but all results can be extended by the elevation angle.

Fig. 1: Plane wave front crossing a ULAFig. 1: Plane wave front crossing a ULAFig. 1: Plane wave front crossing a ULAFig. 1: Plane wave front crossing a ULA

If the ratio of the array aperture to the velocity of light is much smaller than the

inverse of the bandwidth of the signal, then u(t) can be regarded as constant during the

propagation time across the array (narrowband assumption). Investigations on the impact

of non-zero bandwidth signals can be found in[9].

Choosing the first element x1 as the reference point, the output signal of the l-th

element

is simply a phase-shifted version of the reference signal x1(t) = s(t). The propagation

delay between these two elements is denoted as тl. Introducing the spatial frequency μ =

- sinπ θ, equation (1) can be rewritten

Given the common structure of a narrowband beam-forming network, as depicted in Fig.

2, the array output signal y(t) is the weighted sum of all all antenna outputs xl, 1 ≤ l

≤ M:

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Fig. 2: Narrowband DoA-based beamforming schemeFig. 2: Narrowband DoA-based beamforming schemeFig. 2: Narrowband DoA-based beamforming schemeFig. 2: Narrowband DoA-based beamforming scheme

where

is the so-called beam pattern function describing the array gain for spatial frequencies μ

[- , ). It is dependent on the complex array weightsπ π∈ w1,...,wM which can be adjusted

in order to steer beams and nulls towards desired directions. The beam pattern of an

M-element ULA has the form of a degree M - 1 polynomial. Thus, a maximum

number of K = M - 1 nulls of the beam pattern can be placed, no matter what kind of

beamforming algorithm is used. We will look in more detail at the special needs of

beamforming algorithms in the following section.

Next we will shortly discuss the underlying outdoor propagation model. The vector

impulse response seen by the k-th user is commonly written as

where δ(t) is the Dirac delta, тk,l the path delay of the l-th path of the k-th user, βk,l

the corresponding complex path attenuation and

the complex array response. The so-called steering vector a(θ) contains the phase shifts

of all antenna elements for a certain transmission path from direction θ.

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All channel models assume the existence of local scatterers in the vicinity of the mobile

and the base station. Local scattering gives rise to angle and delay spread of the

dominant transmission path. If the antenna location is high, the scattering is limited to

the mobile. This is the case that we assume in this paper. Measurements suggest that

typical angle spreads for macrocell environments with a Tx-Rx separation of 1km are

approximately two to six degrees[10].

Among the various models which have been described in literature[10], the Lee model is

a first approach to the problem. It assumes scatterers which are evenly spaced on a

circular ring about the mobile as shown in Fig. 3. This model has been useful for

predicting the correlation between any pair of elements in the array. However, it fails to

include phenomenas like delay spread or angle spread of the incoming paths[10].

Fig. 3: Lee model for local scatterersFig. 3: Lee model for local scatterersFig. 3: Lee model for local scatterersFig. 3: Lee model for local scatterers

The angle spread poses a great challenge on the beam pattern of the array and must be

taken into account for the design of reliable STP schemes, otherwise the performance

may degrade quickly in real radio environments. This has been the result of field trials

performed by[8].

Realistic modelling of the pdf of the angle spread requires new vector channel models.

Oue approach is the geometrically based single-bounce model (GBSM) presented by [11].

It assumes uniformly distributed local scatterers within a circle around the mobile, as

shown in Fig. 4. This offers more realistic modelling of the distribution of the angle

spread.

Fig. 4: Uplink GBSM modelFig. 4: Uplink GBSM modelFig. 4: Uplink GBSM modelFig. 4: Uplink GBSM model

In addition to the local scatterers around the mobile, there are dominant remote

reflectors such as large buildings, hills and other structures. They give rise to multipath

propagation between the basestation and the mobile (see Fig. 5). The multipaths also

experience angle and delay spread due to remote scatterers[3].

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Fig. 5: Uplink multi-path modelFig. 5: Uplink multi-path modelFig. 5: Uplink multi-path modelFig. 5: Uplink multi-path model

Consequently, angle spread has to be taken into account for each propagation path, not

only for the LoS.

III DIRECTIVITY- CONTROLLED SPACE-TIME PROCESSINGIII DIRECTIVITY- CONTROLLED SPACE-TIME PROCESSINGIII DIRECTIVITY- CONTROLLED SPACE-TIME PROCESSINGIII DIRECTIVITY- CONTROLLED SPACE-TIME PROCESSING

We will now see how the above beam pattern function (4) can be exploited by

DoA-based beamforming schemes in order to perform directivity-controlled space-time

processing.

Both, uplink and downlink STP relies on the spatial information which can be extracted

from the array covariance matrix. This information includes the DoA of resolvable

signal paths that are received at the base station. With an M-element ULA at

maximum M different paths can be detected, where in practise an array with more than

eight elements seems to be cost inefficient. However, the propagation medium is often

rich in multipath signals from different users. Nevertheless, DoA estimation becomes

feasible if it is performed after de-spreading. Then, only the signal paths of the

intended user are detected while all others can be regarded as noise. In the following

we assume that the DoA of the dominant paths of a single user can be estimated and

are a priori known.

A Classical DoA-Based BeamformingA Classical DoA-Based BeamformingA Classical DoA-Based BeamformingA Classical DoA-Based Beamforming

Next, we will shortly review classical DoA-based beamforming schemes as described in

the literature[2]. We start with the phased array solution

where μ* is the intended look direction.

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Fig. 6: Phased array: insufficient suppression of undesired propagation pathsFig. 6: Phased array: insufficient suppression of undesired propagation pathsFig. 6: Phased array: insufficient suppression of undesired propagation pathsFig. 6: Phased array: insufficient suppression of undesired propagation paths

The phased array allows steering of one single main beam. Its principal disadvantage is,

that no nulls of the beam pattern can be steered towards unwanted transmission paths,

as shown in Fig. 6. This is needed if strong directional interferences occur which may

considerably decrease the signal-to-noise-and-interference-ratio (SNIR).

Another processor is the constrained beamformer(nullsteering beamformer)[5]. It allows

steering of K = M - 1 nulls μ1,...,μK by solving the following set of equations

The term "constrained" refers to the requirement that the beam pattern function of the

array is constrained to the values given by (8).

The corresponding array weight vector wwww = [w1,...,wM]Tis given by

A beam pattern solving these equations is given by

where

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With (10) we have a closed form expression only depending on the DoA μ*, μ1,..., μK.

Thus, a fast convergence rate is guaranteed. The constrained beamformer is able to

suppress the maximum number of interfering paths by nulls of the beam pattern.

However, steering of M - 1 nulls is not reasonable if less than M - 1 interference

paths are present. Furthermore, in certain situations the nullsteering beamformer has

been shown to suffer from performance degradation due to Direction-of-Arrival (DoA)

errors, noise, angular spread and CCI. The algorithm only leads reliable results if the

look direction μ* is sufficiently spaced from the nulls μl. There is no control of beam

pattern besides the given constraints.

In the remainder of this section we will show how directivity and broad nulls can be

used as additional performance parameters to generate a beam pattern which is more

robust to angle spread and background noise.

B DirectivityB DirectivityB DirectivityB Directivity

The directivity

is inversely proportional to the surface under the beam pattern (4). It provides a

measure for the amplification of the spatially white background noise including both

thermal noise and interference. The directivity D(Hc) of the constrained beamformer (8)

is a function of the constraints μ* and μl, 1 ≤ l ≤ K. Once they are fixed, D can only

be affected by additional antenna elements.

A possible way of controlling the behaviour of the constrained beamformer (10) with the

directivity has already been investigated in[12], where a best possible upper bound

on the directivity of the constrained beamformer has been found. It gives a measure for

the separability of two signals in space and can be used to perform computationally

inexpensive spatial channel assignment in space division multiple access (SDMA)

systems.

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1. Improvement of SNR1. Improvement of SNR1. Improvement of SNR1. Improvement of SNR

Next we will show that the directivity is an important measure for the quality of the

beam pattern. Consider an additive white Gaussian noise (AWGN) channel where no

multipath interference occurs. The desired user signal s*(t) is assumed to have a spatial

frequency μ*. Furthermore, there are M - 1 multiple access interferers (MAI) with

spatial frequencies μl, 2 ≤ l ≤ M, which are supposed to be nulled out by the beam

pattern. Then, the array output signal can be written as

where a(μ) is the array response vector for a certain spatial frequency μ and nnnn(t) =

[n1(t), ,‥‥ nM(t)]Tis the error vector containing additive white Gaussian noise signals

nl(t) for each antenna element. With the constraints defined in (8) equation (14) becomes

That is, the signal s* can be separated except an error wwwwHnnnn(t). In appendix A it is

shown that the error variance is

This means that in case of an AWGN channel with given noise variance σn2 the error

E[│wwwwHnnnn(t)│2] only depends on the directivity D. The SNR becomes

where σs2is the variance of s*. Obviously, D must be maximised to avoid amplification

of uncorrelated background noise. The maximum achievable directivity equals the

number of antenna elements, but may easily be deteriorated, as has been shown above.

Figure 7 illustrates the deterioration of the directivity when an interferer approaches the

look direction.

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Fig. 7: Constrained beamformer: decreasing directivity ofFig. 7: Constrained beamformer: decreasing directivity ofFig. 7: Constrained beamformer: decreasing directivity ofFig. 7: Constrained beamformer: decreasing directivity of

the beam pattern forthe beam pattern forthe beam pattern forthe beam pattern for μμμμ**** approachingapproachingapproachingapproaching μμμμ3333

2. Impact on Asynchronous CDMA2. Impact on Asynchronous CDMA2. Impact on Asynchronous CDMA2. Impact on Asynchronous CDMA

The impact of the directivity can also be shown for an asynchronous CDMA system

using pseudo-noise sequences, as presented by Liberti/Rappaport[13]. Consider the uplink

of a single cell system without multipath propagation and a large number of K users,

which are uniformly distributed in space. Then the central limit theorem may be applied

and interferences can be regarded as Gaussian-distributed random variables. The

resulting bit-error-rate (BER) may be approximated by

where N is the spreading factor and

yields the probability that >ξ x, with assumed to be a Gaussian distributed,ξ

zero-mean, unit variance random variable. The resulting BER is illustrated in Fig 8.

The Liberti/Rappaport model is based on earlier work on the BER in CDMA-based

systems published by[14]and

[15]. It only holds for the assumption of single cell systems

with optimum power control, where no CCI occurs and no space-time processing is

considered. Nevertheless, it provides useful insight into the impact of the directivity on

the system performance. By optimising the directivity, the amount of noise introduced

by uniformly distributed interferers can be reduced.

Steering nulls towards interferers also reduces interference power, but deteriorates the

directivity of the beam pattern. The optimum BER shall be a tradeoff between the

directivity D and the number of cancelled interferers. As a first approximation, (18) may

be applied to more general systems[13]. It can also be extended to multiple cell systems.

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Fig. 8: Impact of the directivity D on the approximated BER ofFig. 8: Impact of the directivity D on the approximated BER ofFig. 8: Impact of the directivity D on the approximated BER ofFig. 8: Impact of the directivity D on the approximated BER of

an asynchronous CDMA system (Liberti/Rappaport model)an asynchronous CDMA system (Liberti/Rappaport model)an asynchronous CDMA system (Liberti/Rappaport model)an asynchronous CDMA system (Liberti/Rappaport model)

C Broad NullsC Broad NullsC Broad NullsC Broad Nulls

The interference power introduced by all sub-paths of the l-th dominant path from a

certain direction θl at the array output can be written as

where fp(θ) is the azimuth power density function and Pl is the radiated power of the

l-th path. The distribution fp(θ) has been measured in[16]. It has been shown that for

rural environments it can be modelled by the Laplacian function.

Assume that the path from direction θl shall be suppressed by a null of the beam

pattern (4). With θ [∈ θl - θmax, θl + θmax] denoting the direction for which H(e-j sinπ θ

)

becomes maximum, (20) can be upper bounded by

For sufficiently small θmax it can be assumed that θ = θmax holds. Thus, the expression

│H(e-j sinπ θ)│

2is dependent on the maximum angle spread θmax as well as on the

behaviour of the function H(e-j sinπ θ) within the interval [θl - θmax, θl + θmax]. Thus, in

order to obtain efficient azimuth spread suppression, │H(e-j sinπ θ)│2 must be minimised.

This can be achieved by broad nulls of the beam pattern, as depicted in Fig. 9.

The broadness of the nulls is dependent on both the interference tolerance and the angle

spread θmax, which in turn depends on the channel characteristics. We have

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where R is the cluster radius and D the distance between base station and the mobile

(see Fig. 4). For R 《 D the approximation holds.

Broad nulls mitigate the consequence of DoA errors and angular spread, which are both

unavoidable in real mobile environments. They can be achieved by placing multiple nulls

in the wanted directions. For example, a beam pattern with a double null in the

direction μ1 is given by the following equation:

where λ0 is a scaling factor such that H( ejμ *) = 1 holds. The same result can be

achieved by derivative constraints, i.e.,

Fig. 9: Broad null generated by simple (Fig. 9: Broad null generated by simple (Fig. 9: Broad null generated by simple (Fig. 9: Broad null generated by simple (solidsolidsolidsolid), double(), double(), double(), double(dasheddasheddasheddashed))))

and triple (and triple (and triple (and triple (dotteddotteddotteddotted) zeros of the beam pattern function) zeros of the beam pattern function) zeros of the beam pattern function) zeros of the beam pattern function

Placing broad nulls always requires additional degrees of freedom, i.e. antenna elements.

If the beam pattern is flattened in the vicinity of the nulls, the dynamics of the beam

pattern will be worsened for all other directions, as shown in Fig. 9.

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A further method to generate broad nulls is the steering of several, closely spaced nulls

in the direction of interest. This is quite similar to the above method and also takes

additional elements. Likewise, all disadvantages of the null-steering technique have to be

taken into account. Another approach has been reported in[8].

In order to obtain an expression for the broadness of a null, we can apply the mean

value theorem. With (8) we have

where θo is a number in the closed interval [-θmax ,-θmax] With (23) we have

where C1 is the first derivative in the vicinity of the null. If C1 becomes small, than we

have a broad null.

D Maximum Directivity BeamformingD Maximum Directivity BeamformingD Maximum Directivity BeamformingD Maximum Directivity Beamforming

Next we will present a solution to the equations (9) providing the maximum directivity.

This solution is referred to as the maximum directivity (MD) beamformer1 [17].

Assuming additional antenna elements M > K + 1, we can exploit the additional

degrees of freedom to maximise the directivity, i.e.

subject to the constraints (8). Defining a function

the optimum MD beam pattern is given by

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where the look direction is denoted as μK+1. The coefficients al, 1 ≤ l ≤ K + 1, are the

solutions of the linear set of equations

where BBBB = {bk,l}, 1 ≤ k,l ≤ K+1 and bk,l = Ω (ej (μ k - μ l ) ). This set of equations has

a unique solution if det{B} 0 holds.≠

Theorem 1Theorem 1Theorem 1Theorem 1 Let μ1,...,μK+1 be arbitrary spatial frequencies with μl ≠ μk, l ≠ k, then

det{BBBB} 0≠ holds.

The proof of theorem 1 is given in[18].

With (28) the MD beam pattern can be rewritten as

Comparing (31) with (4), it can be seen that the antenna weights are given by

The beam pattern HMD yields the optimum directivity for a given set of constraints.

The proof of this is also given in[18]. Optimising the directivity by additional antenna

elements is quite costly. Thus, there must always be a trade off between steering nulls

and optimising the directivity.

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E Uplink ProcessingE Uplink ProcessingE Uplink ProcessingE Uplink Processing

For the uplink we will discuss single user detection, where multiple access interference

(MAI) due to imperfect synchronisation and non-orthogonality of codes is treated as

noise.

In general, single user processing is suboptimal compared to multi-user detection since

it ignores the information available from all users. However, multi-user detection is

computationally prohibitive in most cases. Furthermore, it is very sensitive to quickly

varying interference environments. Single-user detection offers a more robust solution to

the spatial filtering problem and also yields good performance results, so single-user

solutions seem to be promising for future wireless communication networks.

Path diversity can be exploited by a RAKE receiver at the base station in order to

increase the SNR. As long as the relative time delays of the individual transmission

paths of a certain user are more than one chip period, a space-time equaliser can be

designed to match the transmission channel [3, 19, 20, 21].

Two signal processing aspects must be considered: temporal equalisation and reduction

of cochannel interference. While equalisation is achieved by a conventional RAKE

receiver, impact of co-channel interference can be mitigated by implementing

beamforming processor at each finger of the RAKE receiver (see Fig. 10).

A beamformer for each finger is adjusted to take advantage of all signal components

arriving with a path delay similar to the dominant delay to which the finger is locked.

Multipaths arriving with another path delay cause an error due to non-orthogonality

between the codes. If those paths arrive with DoA other than the dominant paths, they

can be suppressed by the beamforming processor. Thus, the SNR is increased and a

better system performance can be achieved. This approach is often described in

literature as spatial filtering for interference reduction(SFIR).

Fig. 10: 2-D rake receiver with blind DoA-based MD beamformer in each fingerFig. 10: 2-D rake receiver with blind DoA-based MD beamformer in each fingerFig. 10: 2-D rake receiver with blind DoA-based MD beamformer in each fingerFig. 10: 2-D rake receiver with blind DoA-based MD beamformer in each finger

Provided that all DoA are known, constrained beamforming techniques can be used to

reject co-channel interferences while maximising the signal gain for the user of interest.

In[22]the phased array solution has been proposed for this purpose. However, no

undesired paths can be rejected by this solution (see Fig. 6).

Another approach is the MVDR beamformer

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where RRRRxx is the array covariance matrix, which also has been discussed in[22].

However, this approach has been shown to be hyper-sensitive to DoA mismatch. If the

estimated look direction differs from the true look direction μ* then the desired signal

will be nulled out. Also, the covariance RRRRxx differs from the true covariance due to

finite-snapshot error and time variance of the channel. Large time variance occurs, for

example, if voice activity control (VAC) is applied. Since VAC increases the overall

system capacity by a factor 8/3, it is an important component in CDMA-based systems

which must be taken into account for beamforming. DoA-based beamforming is

independent from the covariance, thus the results are more robust to the strongly time

varying nature of the channel.

A further blind method, also relying on second order statistics, has been presented in[21].

In the following we propose the MD solution (29) for STP beamforming. Assuming L

RAKE fingers locked on L dominant paths μ1,...,μL which are separable in time and

space. Each finger is equipped with an MD beamformer. The beam pattern of the l-th

finger is given by

where

holds. The receiver scheme is illustrated in Fig. 10. The directivity of this beam pattern

is given by

where al(l)is the l-th coefficient of the beam pattern of the l-th finger. The proof is

similar to the proof in appendix B.

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Figure 11 shows different beam pattern for the example of a 3-finger RAKE. In plot 11.

a the phased array is shown. This solution yields the optimum directivity, however no

interference cancellation by steering nulls is possible. The plots 11.b-d show the

maximum directivity (MD) beamformer, which is able to steer nulls towards

interferences with different time delays while maximising the overall directivity of the

beam pattern. This can be regarded as creating an AWGN channel for each finger.

Then with the results from paragraph 1. the SNR for the l-th finger is given by

where σ2s,l is the signal variance of the l-th path and σ2n,l the corresponding noise

variance.

Fig. 11: Uplink beamforming,Fig. 11: Uplink beamforming,Fig. 11: Uplink beamforming,Fig. 11: Uplink beamforming, MMMM = 8, three paths from 0°, 21° and 48° with= 8, three paths from 0°, 21° and 48° with= 8, three paths from 0°, 21° and 48° with= 8, three paths from 0°, 21° and 48° with

(a) phased array (b)-(d) MD beamformer(a) phased array (b)-(d) MD beamformer(a) phased array (b)-(d) MD beamformer(a) phased array (b)-(d) MD beamformer

In case that two paths from different directions arrive within one chip period, the above

approach can be extended to multiple beams. This will be described in the next section

where the downlink is discussed.

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F Downlink BeamformingF Downlink BeamformingF Downlink BeamformingF Downlink Beamforming

Although the use of antenna arrays in the mobile station seems not be feasible for the

time being, spatial processing in the downlink can be achieved by deploying

beamforming operation at the base station. The aim of directed transmission is

reduction of inter-cell interference: SFIR●

power efficiency●

exploitation of path diversity●

Downlink synchronisation is easier to achieve than uplink synchronisation. In the

following we assume that all users can be separated by orthogonal spreading sequences

(as it has been realised in IS-95[20]). Since blind beamforming is assumed, no feedback

signal is available. Thus, the downlink beamformer solely relies on the information

available from the uplink.

A possible approach is to use the same DoA for the downlink as for the uplink.

However, reciprocity for up- and downlink channel only holds for same time instants

and for same carrier frequencies. Most major cellular standards currently employ

frequency division duplex (FDD), i.e. separation between the uplink and downlink

frequencies are typically in the order of tens of MHz [23]. Consequently, frequency

dependent channel parameters will change. Especially the instantaneous fading on the

two links will be uncorrelated, so the signal strength of one propagation path can be

totally different in up- and downlink. Consequently, DoA can only be taken from the

uplink as long as the frequency offset between uplink and downlink is sufficiently small[3].

In time division duplex (TDD) based systems reciprocity for up- and downlink holds as

long as the duplexing time is small compared to the coherence time of the channel.

Thus, DoA-based techniques can be applied more easily.

In the following we will assume that the DoA of the transmission paths of the intended

user can be taken from the uplink and are a priori known. This is essential for the

applicability of DoA-based beamforming to the downlink. Additional signal parameters

like Doppler frequency, ToA (Time-of-Arrival) [2] or mobility models may be used to

improve the results.

1. Single Beam1. Single Beam1. Single Beam1. Single Beam

We start by considering the additive white Gaussian noise (AWGN) channel where only

the LoS path is present and therefore no temporal equalisation is needed. Then, the

optimum result is given by the phased array solution (7), which can be used to direct

one main beam towards the intended user, while minimising the amount of radiated

power (see Fig. 12).

Considering multipath propagation, path diversity can be used similarly to uplink

processing. This requires steering of beams and nulls towards dominant transmission

paths.

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The MD single beam solution (32) can also be applied to the downlink. Assuming a

look direction μK+1 the solution is found with the following constraints

and

A single beam towards μK+1 is steered while suppressing unwanted paths by nulls. In

case that no nulls are chosen, this is identical to the phased array solution.

Although this solution considers multipath propagation to a certain degree, the

exploitation of path diversity requires the generation of multiple beams.

2. Multiple Main Beams2. Multiple Main Beams2. Multiple Main Beams2. Multiple Main Beams

Multipath time delays and synchronisation errors deteriorate the orthogonality between

users at the mobile. Equalising at the base station seems not be feasible[3]. Instead,

path diversity can be exploited by a RAKE receiver at the mobile station being able to

resolve multiple transmission paths. This helps increasing the system performance in

situations where no LoS but dominant multipaths are available. It also leeds to a more

robust behaviour in situations where one path is obstructed or affected by fading. Then

one path can uphold the transmission while searching for new paths.

Consider two main beams with look directions μK+1 and μK+2 which are directed towards

the dominant paths upon which the RAKE fingers at the mobile are locked. Additionally,

K interfering transmission paths μ1,...,μK can be suppressed by steering of direct nulls

towards these known directions.

Fig. 12: Single beam Fig. 13: Multiple beamsFig. 12: Single beam Fig. 13: Multiple beamsFig. 12: Single beam Fig. 13: Multiple beamsFig. 12: Single beam Fig. 13: Multiple beams

Multiple beam steering with the MD-beamformer(32) can be realised in two different

ways. Each beam can be generated separately by the independent beam patterns H1 and

H2 being a solution of

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and

Two main beams can also be obtained by one single beam pattern H3. This means

reduced hardware complexity and computational burden. It is given by

Interestingly, the solution H3, although determined from an independent minimisation

problem, is given by the sum of the solutions H1 and H2 :

The array weights are given by

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This result could be achieved by reducing the nonlinear optimisation problem (42) to the

linear system of equations (43).

The directivity of the MD beam pattern is dependent on the number of antenna

elements, the number of constraints and the spacing between the look direction and the

nulls. In order to minimise the amount of radiated energy, all these parameters have to

be considered. Particularly the position of the null constraints play an important role. If

a null approaches the look direction it will cause distortion of the beam pattern and

decreasing directivity. The two paths are no longer resolvable and steering of one single

broad beam may be the better choice.

In order to control the beampattern distortion and to avoid of unwanted power radiation,

knowledge of the directivity D(H3) is required. It is given by

The proof is given in the appendix B. With this result we obtain a very simple and

computationally inexpensive criterion to decide whether two transmission paths we

resolvable or not. If the directivity becomes to small, spatial separation is not feasible.

Reduction of inter-cell CCI by steering nulls towards other users may also be

considered. However, in this paper only the single user case is investigated.

Furthermore, steering of a large number of nulls would also require a prohibitive large

number of antenna elements.

In the presence of insignificant angle spread, as it may occur in microcell environments,

no dominant paths may be available. In this case separation of different signal

components by constrained beamforming is not feasible. Instead, one broad null can be

steered towards the rough direction of the intended user. This can be realized by using

derivative constraints or closely spaced multiple main beams.

A relation between the directivity D(H3) and the directivities D(H1) and D(H2) has been

found. The inverse directivity of H3 can be written as

where the coefficients a ( k )K + 1 and a ( k )K + 2 of the k-th beam pattern can be

determined by (43). The proof is given in the appendix C.

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Fig. 14: Beam patternFig. 14: Beam patternFig. 14: Beam patternFig. 14: Beam pattern HHHH1111 ((((dotteddotteddotteddotted),),),), HHHH2222 ((((dasheddasheddasheddashed) and) and) and) and HHHH3333 ((((solidsolidsolidsolid) with) with) with) with MMMM = 8,= 8,= 8,= 8,

nullsnullsnullsnulls μμμμ1111 = -70° and= -70° and= -70° and= -70° and μμμμ1111 = 50° and look directions (a)= 50° and look directions (a)= 50° and look directions (a)= 50° and look directions (a) μμμμKKKK+1+1+1+1 = -20°,= -20°,= -20°,= -20°, μμμμKKKK+2+2+2+2 = 0°= 0°= 0°= 0°

(b)(b)(b)(b) μμμμKKKK+1+1+1+1 = -5°,= -5°,= -5°,= -5°, μμμμKKKK+2+2+2+2 = 0°= 0°= 0°= 0°

From (46) and Fig. 14 we see that the directivity of the overall beam pattern H3 is

always smaller than each directivity of H1 and H2.

G SDMAG SDMAG SDMAG SDMA

Another important aspect of space-time processing is the reuse of transmission

resources within the cell, often referred to as space division multiple access(SDMA).

With the above results the MD beamforming technique can also be used to realize

SDMA in CDMA-based systems where code reuse can be imagined. This is the most

demanding form of STP processing and it requires robust beam pattern control and

sophisticated spatial channel assignment.

The DoA-based MD beamformer proposed in this paper seems to suitable for spatial

user separation due to its robust nature of the beam pattern. Broad nulls may be used

to completely suppress dominant transmission paths in the presence of angular spread.

The directivity can then be used to control the beam pattern distortion and to decide

whether two sources should be separated by SDMA or by another multiplexing

technique.

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IV CONCLUSIONSIV CONCLUSIONSIV CONCLUSIONSIV CONCLUSIONS

The main focus of this paper has been the investigation and application of the new

blind DoA-based maximum directivity (MD) beamforming algorithm[17]to space-time

processing in CDMA wireless systems. Beamforming can be deployed within a

space-time processing framework to optimally exploit path diversity in up- and

downlink.

Blind beamforming generally is an attractive technique because it does not require any

training sequence or pilot signal in order to perform spatial channel equalisation.

Provided that all DoA of the transmission paths are a priori known, a closed form

solution of the antenna weights can be obtained which offers good convergence

properties.

However, classical DoA-based algorithms are known to be very sensitive to error

effects like DoA estimation errors, background noise and angle spread due to local

scatterers. Thus, new performance parameters are needed to assess the quality of the

beam pattern.

In this paper it has been shown that robust behaviour of the beam pattern can be

obtained by considering directivity and broad nulls. Analytical results have been

presented and different aspects of directivity controlled beamforming have been

discussed.

User separation (SDMA) under consideration of directivity and broad nulls seems to be

feasible provided that reliable DoA estimation is available. Although only a small

number of users can be separated due to the limited number of antenna elements,

SDMA would considerably increase the overall system performance.

Further extensive simulations and field tests will be necessary in order to prove the

effectiveness of the proposed MD beamforming scheme in CDMA space-time processing.

This will be the subject of future work.

ACKNOWLEDGEMENTACKNOWLEDGEMENTACKNOWLEDGEMENTACKNOWLEDGEMENT

The authors are grateful to Thomas Kuhwald from Technical University of Ilmenau for

fruitful discussions.

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APPENDIXAPPENDIXAPPENDIXAPPENDIX

A Proof of (16)A Proof of (16)A Proof of (16)A Proof of (16)

where σn is the variance of the AWG noise.

Next, with (12) the inverse of the directivity becomes

There are two different cases:

Thus, the directivity (12) can be rewritten as

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Substituting this in (47) yields

B Proof of (45)B Proof of (45)B Proof of (45)B Proof of (45)

With (12) and (29) the inverse directivity can be written as

With

equation (51) can be rewritten as

With (42) the directivity of the MD beamformer with two look directions is given by

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C Proof of (46)C Proof of (46)C Proof of (46)C Proof of (46)

The inverse directivity of H3 can be written as

With (28) we define

and consequently

Similarly, we have

Thus, the inverse directivity can be rewritten as

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1 A patent has been issued on the maximum directivity (MD) beamforming algorithm