-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
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
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
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
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.
- 17 -
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