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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].
- 2 -
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.
- 3 -
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:
- 4 -
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.
- 5 -
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].
- 6 -
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.
- 7 -
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
- 8 -
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.
- 9 -
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.
- 10 -
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.
- 11 -
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
- 12 -
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.
- 13 -
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
- 14 -
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.
- 15 -
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
- 16 -
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
(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.
- 18 -
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.
- 19 -
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
- 20 -
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
- 21 -
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.
- 22 -
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.
- 23 -
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.
- 24 -
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
- 25 -
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
- 26 -
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
- 27 -
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1 A patent has been issued on the maximum directivity (MD) beamforming algorithm