Spatiotemporalinterference rejectioncombiningdownloads.hindawi.com/books/9789775945099/art02.pdf8 Spatiotemporal interference rejection combining h 1[l] models the channel between

2Spatiotemporal interferencerejection combining

David Astely and Bjorn Ottersten

2.1. Introduction

During the last decade, the use of second-generation cellular systems such as GSMhas undergone a rapid growth, and we currently see deployments of third-genera-tion systems based on CDMA. The success of GSM and the introduction of newservices, such as packet data and video telephony, motivate continuous efforts toevolve the systems and to improve performance in terms of capacity, quality, andthroughput.

Receive diversity is commonly used at the base stations in cellular networksto improve the uplink performance. Relatively simple combining methods havebeen used to date. However, as the users eventually compete with each other forthe available spectrum, interference in terms of cochannel interference (CCI), ad-jacent channel interference (ACI), and possibly also interference between differentsystems will be the limiting factor. With this in mind, more sophisticated meth-ods, that offer interference suppression, appear attractive and to be a natural stepin the evolution. Further, to improve the downlink, the use of multiple antennasat the terminal is also of relevance. The recent interest in so-called multiple-inputmultiple-output (MIMO) links and their potential gains in many environmentsmay lead to the development of multiple antenna terminals. The multiple ter-minal receive antennas can then be used to increase the link performance withboth spatial multiplexing and interference suppression depending on the operat-ing conditions.

Herein, the problem of spatiotemporal interference rejection combining (IRC)is addressed. For burst oriented systems such as GSM, we consider the use of a vec-tor autoregressive (VAR) model to capture both the spatial and temporal correla-tion of interference such as CCI and ACI. Some technical background and previ-ous work in the area are first presented below and the underlying data model is in-troduced in Section 2.2. The VAR model is described and examined in Section 2.3.Two basic metrics for sequence estimation are presented in Section 2.4 in additionto reduced complexity sequence estimators. Several numerical examples are then

6 Spatiotemporal interference rejection combining

presented in Section 2.5 and the application to GSM is discussed in Section 2.6.Spatiotemporal IRC utilizing both spatial and temporal correlation of interferenceis of interest also for WCDMA. As outlined in Section 2.7, a different approach notusing a VAR model may then be taken. Some concluding remarks are finally givenin Section 2.8.

2.1.1. Background and some related work in the literature

In burst oriented TDMA systems such as GSM/EDGE, the modulation and thetime dispersion in the radio channel introduce intersymbol interference (ISI).Even though ISI can be viewed as a form of interference, it is herein considered as apart of the signal to be detected. To handle the ISI, a maximum likelihood sequenceestimator (MLSE) [1], or a suboptimum version with lower complexity, such as thedelayed decision feedback sequence estimator (DDFSE) [2], is therefore assumedto be used. To cope with other forms of disturbance, such as CCI and ACI, in ad-dition to ISI, there has been renewed interest in the approach taken in [3]. In [3],interference is modeled as a spatially and temporally colored Gaussian process, andan MLSE that takes the second-order properties of the CCI into account is derived.Some related contributions include [4, 5, 6, 7, 8, 9, 10], which utilize a Gaussianassumption for the CCI to derive an MLSE which may detect the signal in the pres-ence of ISI and simultaneously suppress CCI. In [3, 5, 10], the sequence estimatorproposed by Ungerboeck in [11] is generalized to the multiple-antenna case. Theresulting structure consists of a multiple-input single-output (MISO) filter frontend followed by a sequence estimator. The filter may be viewed as the concatena-tion of a MIMO whitening filter and a filter matched to the whitened channel. TheMLSE proposed by Forney in [1], and generalized to multiple channels and mul-tiple signals in [12], has been derived for temporally white but spatially colorednoise and studied for CCI rejection, see [4, 7, 13, 8]. Forney’s and Ungerboeck’sformulations for sequence estimation are equivalent and a unification is presentedin [14].

A suboptimum approach to handle CCI with a MISO filter and a Forney formof MLSE is proposed in [15]. Other front-end filters are considered in [16, 17].The unified analysis of front-end filters in [18] includes a Forney form of MLSE,derivations of optimal filters of infinite length, and, based on numerical studies,guidelines on how to truncate the filters. In [19], a front-end filter for a decisionfeedback equalizer is used with a DDFSE for joint equalization and interferencesuppression.

An MLSE with spatiotemporal IRC accounts also for the temporal correla-tion of the interference, and in general truncation is needed, both in the front-end filter and also in the memory of the sequence estimator. A straightforwardapproach is to use a finite-order linear predictor and to assume that the predic-tion errors are temporally white and complex Gaussian. This is equivalent to us-ing a complex Gaussian VAR model. Autoregressive modeling of interference insingle-antenna spread spectrum receivers has been proposed in [20] and a VARmodel is used in [21] to handle spatiotemporally correlated clutter in radar signal

D. Astely and B. Ottersten 7

processing. In the field of blind channel identification from second-order statistics,linear-prediction-based methods which exploit the simultaneous moving average,and autoregressive nature of the received signals in the multichannel setting havebeen proposed [22, 23, 24]. The use of a VAR model for interference rejection hasalso been mentioned in, for example, [16] and investigated in [25, 26]. As will beseen, with a VAR model, metrics both for Forney and Ungerboeck forms of MLSEcan be derived, which is interesting since a Forney form of sequence estimator mayoffer alternative strategies as compared to the Ungerboeck form when the param-eters are to be estimated and tracked, see [8, 14].

The prediction error filter corresponding to the VAR model introduces a fi-nite amount of additional ISI, so that the complexity of the sequence estimator in-creases exponentially with the amount of temporal correlation accounted for. Thismotivates the use of reduced complexity sequence estimators as in [19, 27, 28]. Al-ternatively, a general sequence estimator such as the generalized Viterbi algorithm(GVA) [29], which includes the DDFSE as a special case, may be applied.

In direct-sequence code division multiple access (DS-CDMA) systems, suchas WCDMA, RAKE receivers are typically used in time-dispersive radio channels.To incorporate spatiotemporal IRC in such a receiver structure, an alternative tothe VAR model may be used. Some previous work on this can be found in, forexample, [30, 31, 32]. Similar to the use of a VAR model for burst oriented TDMAsystems such as GSM, we show how both spatial and temporal correlation of theinterference are exploited.

Finally, we note that to handle digitally modulated interference, such as CCI,the finite alphabet property may be exploited by means of joint multiuser detec-tion [12, 33, 34]. The approach considered herein, and referred to as interferencerejection, utilizes only second-order statistics of the interference. This is in gen-eral inferior to joint detection. On the other hand, joint detection requires theknowledge of the channels of the interference and not only second-order statis-tics. An interference rejecting approach is also expected to be more robust if thefinite alphabet assumption is invalid, for example, due to frequency offsets, or ifthe modulation format of the interference is unknown. Interference rejection maythus be applicable to a larger class of interfering signals, such as ACI and intersys-tem interference in addition to CCI, if the second-order moments of the signal ofinterest and the interference span sufficiently different spaces.

2.2. Data model

A discrete time model with symbol rate sampling is considered for a quasistation-ary scenario with time dispersive propagation. A signal of interest is transmittedwith a single antenna, NT = 1. The signals received by NR antennas are modeled as

r[n] =L1−1∑l=0

h1[l]b1[n− l] + j[n], (2.1)

where r[n] is an NR × 1 vector modeling the received samples, the NR × 1 vector


h1[l] models the channel between the transmitter and the receive antennas fora time delay of l samples, b1[n] is the nth transmitted symbol, and j[n] modelsnoise and interference on the channel. Oversampling with respect to the symbolrate can be included by treating the different sampling phases as virtual anten-nas. Properties of one-dimensional signal constellations such as binary phase-shiftkeying (BPSK), or minimum shift keying (MSK) de-rotated, can be exploited in asimilar way, see [35], but this is not pursued herein.

Noise and interference are modeled as the sum of signals received from K − 1interfering users with single transmit antennas and additive noise,

j[n] =K∑k=2

Lk−1∑l=0

hk[l]bk[n− l] + v[n], (2.2)

where v[n] represents additive white Gaussian noise. The kth interferer transmitsa sequence of symbols, bk[n], and the channel is modeled with Lk symbol spacedtaps denoted hk[l].

A spatiotemporal model for a number of consecutive vector samples is used.We stack P + 1 consecutive vector samples and define the NR(P + 1) × 1 column

vectors�rP[n],�jP[n], and�vP[n] as

�rP[n] =[

rT[n] rT[n− 1] · · · rT[n− P]]T

,

�jP[n] =[

jT[n] jT[n− 1] · · · jT[n− P]]T

,

�vP[n] =[

vT[n] vT[n− 1] · · · vT[n− P]]T

,

(2.3)

the NR(P + 1)× (L1 + P) matrix HP as

HP =

h1[0] h1[1] · · · h1[L1 − 1]

. . .. . .

h1[0] h1[1] · · · h1[L1 − 1

] , (2.4)

and form the (p + 1)× 1 column vector �b1[n; p] as

�b1[n; p] =[b1[n] b1[n− 1] · · · b1[n− p]

]T. (2.5)

Further, let L be the maximum channel length among the interferers,

L = max2≤k≤K

Lk, (2.6)

and define the NR × (K − 1) matrix G[n] as

G[n] =[

h2[n] · · · hK [n]]

, (2.7)


where hk[l] = 0 for l ≥ Lk. The NR(P + 1) × (K − 1)(L + P) matrix GP is thenformed as

GP =

G[0] G[1] · · · G[L− 1]

. . .. . .

G[0] G[1] · · · G[L− 1]

, (2.8)

and the (p + 1)(K − 1)× 1 column vector�i[n; p] is defined as

�i[n; p] =[b2[n] · · · bK [n] b2[n− 1] · · · bK [n− p]

]T. (2.9)

For model order P, we get from (2.1)

�rP[n] =HP�b1[n;L1 + P − 1

]+�jP[n], (2.10)

where�jP[n] can be written using (2.2) as

�jP[n] = GP�i[n; L + P − 1

]+�vP[n]. (2.11)

For P = 0, the spatiotemporal model coincides with a space-only model.

2.2.1. Why spatiotemporal interference rejection?

With an antenna array withNR antennas, it is well known that up toNR−1 narrow-band interferers may be rejected. If the interfering signals have propagated throughchannels with time and angle dispersion, several resolvable paths are incident onthe array from each interferer. Each path requires roughly one spatial degree offreedom, and if the antenna array is large, spatial interference rejection may be suf-ficient. However, for a small antenna array, this may not be the case. From (2.10)and (2.11), the observations may be written as

�rP[n] =HP�b1[n;L1 + P − 1

]+ GP

�i[n; L + P − 1] +�vP[n]. (2.12)

If the rank of GP is less than NR(P+1), it is possible to form linear combinations ofthe spatiotemporal observations which contain no interference. Then, if the chan-nel HP is not completely in the space spanned by the columns of GP , these linearcombinations will contain a signal part for estimating the desired data. Consid-ering the random nature of the radio channel, the latter condition appears to berelatively mild, at least for deployments with low fading correlation. Further, a suf-ficient condition for GP to have rank less than NR(P + 1) is that GP is a tall matrix,that is, the number of rows is greater than the number of columns,

NR(P + 1) > (K − 1)(L + P

). (2.13)


As long as L is finite and K − 1 < NR, this inequality may be satisfied with P suffi-ciently large. Thus, we expect large gains for spatiotemporal interference rejection(P > 0) as compared to space-only interference rejection (P = 0) in interferencelimited scenarios when the rank of G0 is NR due to time dispersion and angularspread of the CCI. Joint space-time processing then requires fewer antennas, orchannels, compared to space-only processing to achieve comparable interferencerejection. Important applications include two-branch spatial or polarization di-versity, for example, in mobile terminals [13].

Finally, note that the subspace for interference rejection can be determinedfrom the second-order statistics of the interference only, and that this is done im-plicitly when the parameters of the VAR model introduced below in Section 2.3 arecalculated. Thus, interference rejection only requires knowledge of second-orderstatistics, which in practice requires few assumptions on the interference and iseasier to estimate than the channels and modulation formats of the interferingtransmitters.

2.3. Autoregressive modeling of interference

To reject time dispersive interference with a sequence estimator which handlesboth ISI and temporally correlated interference, one may, as mentioned in theintroduction, use Ungerboeck’s formulation in [3, 10, 14]. By considering the un-derlying structure of the interference in (2.2), it can be seen that in the generalcase, the front-end filters to generate statistics for a sequence estimator as wellas the memory of the sequence estimator need to be truncated, see also [18].Herein, a different truncation approach is taken in the sense that a measurementmodel with a suitable structure is assumed. This formulation also reveals howtemporally correlated CCI may be included in Forney’s form of the sequence esti-mator.

A straightforward way to handle the temporal correlation of the interferenceis to use the prediction error filter associated with a Pth-order linear predictor.The order of the predictor, P, is a design parameter which also controls the ad-ditional amount of ISI introduced. By choosing the model order high enough,we also expect the prediction error filter to be able to temporally whiten any sta-tionary process [36]. Furthermore, for an autoregressive process, the best linearpredictor is of finite order. Thus, the finite-order prediction error filter is the truewhitening filter of some autoregressive process. We also note that methods basedon linear prediction have been developed for blind channel identification fromsecond-order statistics. Such methods may exploit the simultaneous moving aver-age and autoregressive nature of the signals in the multichannel case [22, 23, 24].In fact, with zero thermal noise and finite channel lengths, the CCI in (2.2) may bemodeled with a finite-order autoregressive model. Conditions for this to hold maybe found in, for example, [22, 23]. One condition is that the number of interferersis strictly less than the number of antennas, K − 1 < NR. Thus, in interference-limited scenarios, with negligible thermal noise, the use of an autoregressive modelappears to be very suitable indeed.


It should be stressed that a VAR model for the interference and noise is anapproximation which in general does not agree with the underlying signal modelintroduced in (2.2). However, by adjusting the model order, it may perform suf-ficient whitening and it integrates in a straightforward way with a sequence es-timator. We therefore formulate the measurement model. The Pth-order linearpredictor of j[n] is modeled as

j[n | n− 1, . . . ,n− P] = −P∑

p=1

APpj[n− p], (2.14)

and the corresponding prediction error is

eP[n] = j[n]− j[n | n− 1, . . . ,n− P] =W(AP)�jP[n], (2.15)

where the prediction error filter W (AP) is defined as

W(AP) = [INR AP

1 AP2 · · · AP

P

]. (2.16)

The covariance of the prediction error, denoted QP , may then be written as

QP = E{

eP[n]e∗P [n]} =W

(AP)RPW

∗(AP), (2.17)

where

RP = E{�jP[n]�j∗P [n]

}, (2.18)

and the expectation is evaluated with respect to the interfering data symbols mod-eled as independent sequences. If the coefficients of the Pth-order linear predictorare chosen so that the prediction error is orthogonal to j[n− 1], . . . , j[n− P], thenthe expected squared value of any component of eP[n] is minimized according tothe orthogonality principle [36]. The orthogonality principle is used for the pre-dictor of each of the NR components of eP[n], and in this way, a set of equations isobtained which may be written as

R j j[l] +P∑

p=1

APpR j j[l − p] =

QP l = 0,

0 1 ≤ l ≤ P,(2.19)

where

R j j[l] = E{

j[n]j∗[n− l]}. (2.20)

The equations are known as the Yule-Walker equations, and for P > 0, they mayalso be written in matrix form as[

INR AP1 AP

2 · · · APP

]RP =

[QP 0NR×PNR

]. (2.21)


Indeed, the solution minimizes the trace of QP , the sum of the mean squared pre-diction errors. Furthermore, the modeling assumption made is that the predictionerror of the Pth-order linear predictor is a temporally white, complex Gaussian pro-cess,

E{

eP[n]e∗P [n− k]} =

QP k = 0,

0 k �= 0.(2.22)

Thus, it is assumed that the interference may be temporally whitened with a Pth-order linear predictor, and it is further assumed that the prediction errors arecomplex Gaussian. The Gaussian assumption is not motivated by the law of largenumbers, but primarily because the solution to the sequence estimation problemis easily obtained. The choice P = 0 will be referred to as space-only IRC, andsuch a modeling assumption has been previously made to derive detectors in, forexample, [4, 7, 8]. We next consider the linear predictor for some special cases.

(i) With spatially and temporally white noise, RP is a diagonal matrix, andthe solution to the Yule-Walker equations is

W(AP) = [INR 0NR×PNR

]. (2.23)

The solution corresponds in this case to space-only processing with maximumratio combining.

(ii) We consider the case with negligible thermal noise, with �vP = 0 in (2.11).For independent temporally white symbol sequences, the linear predictor is thendetermined as the minimum norm solution to

W(AP)GPG

∗P =

[QP 0NR×PNR

]. (2.24)

Suppose that the received signal is first filtered with the prediction error filter. Ifthe covariance matrix of the filtered interference, QP , is singular, then the filteredinterference is confined to a subspace and may be rejected by spatial filtering in asecond step. Using the structure of GP in (2.8), it can be shown that the rank of QP

cannot increase with P, see [25] for details. If G0 has rank less than NR, then QP issingular for all P. Otherwise, we increase P until GPG

∗P is singular but GP−1G

∗P−1

is not. Then, as shown in [25],

det(GPG

∗P

) = det(

QP)

det(GP−1G

∗P−1

), (2.25)

from which we see that QP is low rank. Thus, for complete interference rejectionin the noiseless case, P should be chosen so that GPG

∗P is singular. Note that as P

is increased, GP will eventually be a tall matrix if L is finite and K − 1 < NR so thatGPG

∗P is singular. This agrees with the discussion in Section 2.2.1.(iii) We finally consider the case with high signal to noise ratio (SNR) and

assume that

RP = GPG∗P + σ2INR(P+1), (2.26)


where σ2 is the noise power, and that GPG∗P has low rank. In [25], it is argued that

the signal to interference and noise ratio (SINR), after filtering the received signalwith the prediction error filter and whitening it with Q−1/2

P , is proportional to 1/σ2

as σ2 → 0 under mild conditions. Thus, the SINR grows as the noise vanishes.For the case K − 1 < NR it is possible to reject all CCI given that the VAR

model order P is chosen so that GPG∗P is low rank.

2.4. Sequence estimation

Consider the received signal filtered with the prediction error filter for a VARmodel of order P. By combining (2.10) and (2.15) we obtain

z[n] =W(AP)�rP[n] = FP

�b1[n;L1 + P − 1

]+ eP[n], (2.27)

where the NR × (L1 + P) matrix FP is defined as

FP =W(AP)HP =

[f[0] f[1] · · · f

[L1 + P − 1

]], (2.28)

and represents the concatenated response of the prediction error filter and thechannel for the signal of interest. Recall that the prediction errors, eP[n], are mod-eled as temporally white, spatially colored complex Gaussian samples, (2.22). Theunderlying process is in general not a Gaussian VAR process, and the predictionerror filter is therefore an approximate whitening filter. Using the assumed tem-poral whiteness and neglecting terms that do not depend on the transmitted data,the maximum likelihood estimate of the data sequence is

{b1[n]

} = arg min{b1[n]}

∑n

∥∥Q−1/2P

(W(AP)�rP(n)− FP

�b1[n;L1 + P − 1

])∥∥22. (2.29)

This form of sequence estimator is referred to as the Forney form after [1], see also[14]. To find the estimate, the minimization is to be carried out over all possibletransmitted sequences with symbols from a finite alphabet. As is well known, theViterbi algorithm with a memory of L1 +P− 1 symbols can be used. With a binarysymbol alphabet, the number of states in the trellis is 2L1+P−1. Thus, the complex-ity grows exponentially with the model order P corresponding to the amount oftemporal correlation accounted for.

As shown in [10, 11, 14], the sequence estimator may also be implementedwith a matched MISO space-time filter followed by an MLSE operating on a scalarsignal. This form of the sequence estimator is referred to as the Ungerboeck form.It can be shown, following [14], that the sequence estimate of (2.29) may also bewritten as

{b1[n]

} = arg max{b1[n]}

∑n

Re{b∗1 [n]

(z[n]− sP�b1

[n;L1 + P − 1

])}, (2.30)


where z[n] is obtained by filtering z[n] with a MISO filter as

z[n] =L1+P−1∑l=0

f∗[l]Q−1P z[n + l]. (2.31)

In turn, z[n] is obtained by filtering the received signal with the prediction errorfilter, see (2.27). The statistic for the sequence estimator, z[n], is thus obtained byfiltering the received signal r[n] with a MISO filter. The 1 × (L1 + P) vector sP isdefined as

sP =[

12s0 s1 · · · sL1+P−1

], (2.32)

with

sk =L1+P−1−k∑

l=0

f∗[l]Q−1P f[l + k]. (2.33)

The Forney form presented in (2.29) and the Ungerboeck form in (2.30) are equiv-alent if the full trellis is used. However, when reduced complexity sequence esti-mators are used, the two forms show different performance, see also [37] and thetwo last examples in Section 2.5.

2.4.1. Reduced complexity sequence estimation

Performance may be significantly improved by accounting also for the temporalcorrelation of the interference. The cost for this is an exponential increase in com-plexity of the sequence estimator. Therefore, it is of interest to consider reducedcomplexity detectors such as the GVA of [29]. The GVA uses as state, or label, thelast µ ≤ L1 + P − 1 symbols of each survivor sequence. For simplicity, only binaryalphabets are considered. There are then 2µ states in the trellis, and in each state,S ≥ 1 survivors are retained. The GVA can be described as follows.

(1) At time n− 1 there are S survivors for each of the 2µ labels.(2) At time n all survivors with the two possible symbols extend to form can-

didates. Calculate in a recursive way the metric for each candidate. These S2µ+1

candidates are classified according to their labels, the last µ symbols, into 2µ lists.(3) If several candidates in each list have the same last L1 +P−1 symbols, keep

only the candidate with the best metric. This is known as path merge elimination.(4) From each of the 2µ lists, select the S candidates with the best metric. They

will form the survivors at time n.For µ = 0, the GVA coincides with the M-algorithm [38], and for µ < L1+P−1,

S = 1, it coincides with the DDFSE in [2]. The full MLSE implemented with theconventional Viterbi algorithm is obtained with µ = L1 +P− 1, S = 1. If S > 1, theGVA selects the S candidates with the best metric from a list with 2S candidates.Thus, since the M-algorithm requires ordering of the survivors, it has a higher


complexity than the DDFSE. The DDFSE only needs to find the survivor with thebest metric.

We also discuss the choice of metric. For the Forney form in (2.29), the analy-sis of the single antenna case, NR = 1, of the DDFSE in, for example, [2] shows thatmost of the energy must be concentrated in the first taps for best performance. Itis thus desirable that the channel is minimum phase. In a fading environment, thephase of the channel varies and an alternative is to use the Ungerboeck form in(2.30) together with the DDFSE as proposed in [28, 37]. The Ungerboeck form isnot dependent on the phase of the channel. On the other hand, it may be limitedby ISI, which can introduce an error floor [37].

2.5. Numerical examples

Simulations were done to illustrate the performance in terms of bit error rate(BER) of space-only and spatiotemporal IRC. The first examples illustrate howperformance is improved with increasing model order P at the cost of higher com-plexity when a full MLSE is used. Then, some further examples show that similargains can be obtained using reduced complexity sequence estimators. Thus, noisesensitivity can be traded for interference rejecting capability by increasing P whilekeeping the complexity roughly the same. Herein, the cost for calculating the met-ric is neglected and the number of retained survivors in the trellis is used as ameasure of complexity.

Data was transmitted in bursts of 200 bits. The channel was stationary duringeach burst but generated independently from burst to burst. The fading of the an-tennas was uncorrelated and the channels between a transmitter and each receiveantenna had the same power delay profile with a number of symbol spaced rayswith the same average strength. Temporally and spatially white Gaussian noise wasadded.

First, two receive antennas were used and a single cochannel interferer waspresent. The SNR per antenna was 10 dB and the channels were modeled with tworays, L1 = L2 = 2. The BER as a function of signal to interference ratio (SIR) perantenna is shown in Figure 2.1 using a full MLSE. There are not enough degrees offreedom to reject the time-dispersive interferer with space-only processing, P = 0.By increasing P, the interference may be effectively suppressed.

Recall that as the noise vanishes, the SINR after the prediction error filtergrows linearly with the inverse noise power given that K − 1 < NR and that P issufficiently large. To illustrate this, a case with two antennas and one interfererwith the same SNR as the signal of interest is considered. The average BER as afunction of SNR is displayed in Figure 2.2. For P = 0, the interference spans theentire space, and as the noise vanishes, performance is limited by CCI. For P > 0,the BER decreases as the noise vanishes. Performance without CCI is also included.

The two previous examples demonstrated the advantage of spatiotemporalprocessing over space-only processing since G0 spans the whole space whereas thecolumns of G1 only span a subspace. Performance also depends on the structureof the disturbance, and in the next example the number of interferers was varied.


P = 0P = 1

P = 2P = 3

−40 −30 −20 −10 0 10 20 30

SIR (dB)

10−4

10−3

10−2

10−1

100

BE

R

Figure 2.1. Two antennas and one interferer. Two uncorrelated taps of equal average power. The SNRis 10 dB. Full MLSE.

P = 0, SIR 0 dBP = 1, SIR 0 dBP = 2, SIR 0 dB

P = 3, SIR 0 dBP = 0, no CCI

−5 0 5 10 15 20

SNR (dB)

10−6

10−5

10−4

10−3

10−2

10−1

100

BE

R

Figure 2.2. Two antennas, one interferer, and channels with two taps of equal power. The SIR is 0 dB.The performance with no interferer is also included. Full MLSE.

All channels were modeled with two taps, and the results are plotted in Figure 2.3for P = 0, 3 and K = 1, 2, 3. The SNR was 20 dB for the cases with CCI. With noCCI, the SINR is equal to the SNR, and, as can be seen, spatiotemporal processingis equivalent with space-only processing. For one interferer, the interference con-tribution is confined to a subspace for P large enough. For two interferers of equalpower, there is still gain with spatiotemporal processing, but since the interference


P = 0, no interfererP = 3, no interfererP = 0, one interferer

P = 3, one interfererP = 0, two interferersP = 3, two interferers

−6 −4 −2 0 2 4 6 8

SINR (dB)

10−6

10−5

10−4

10−3

10−2

10−1

100

BE

R

Figure 2.3. Two antennas, different number of interferers, and two tap channels. For the cases withinterferers, the SNR is 20 dB and the SIR is varied. For the case with no interference, the SINR equalsthe SNR, which is varied. Full MLSE.

is not confined to a subspace no matter how large P is made, the gain is smallerthan for the case with one interferer.

We now consider an example with reduced complexity sequence estimators.The signal of interest had three taps, L1 = 3, and the two interferers had L2 = 2and L3 = 3 taps. Four antennas were used and in Figure 2.4, the performancefor different P is shown. The SIR was −10 dB and the SNR was 9 dB at each an-tenna. The complexity was constrained so that the sequence estimators retainedfour survivors except for the full MLSE with complexity increasing with P. FromFigure 2.4, we see that by retaining fewer paths in the sequence estimator, spa-tiotemporal processing may be used to reject interference without an exponentialincrease in complexity. For the Forney form, it can be seen that the M-algorithm,µ = 0, is preferable.

Another example with two antennas and one interferer was considered. Thechannels for both the signal of interest and the interferer were modeled with L1 =L2 = 2 taps. The SIR was 0 dB and the results are plotted as a function of SNR inFigure 2.5. As can be seen, the performance of the M-algorithm with the Unger-boeck metric degrades at high SNR. An explanation for this may be found in [37];the accumulated metric will not account for anticausal ISI if the trellis is reduced.This means that ISI may limit the performance, see [37], for a remedy.

2.6. Interference rejection combining for GSM

The increasing speech and data traffic in today’s GSM networks motivates thestudy of techniques such as IRC. The study in [39] demonstrates that the systemcapacity can be increased by about 50% in a tightly planned GSM network by using


Forney, DDFSE (µ = 2, S = 1)Ungerboeck, DDFSE (µ = 2, S = 1)Forney, M-algorithm (µ = 0, S = 4)

Ungerboeck, M-algorithm (µ = 0, S = 4)MLSE (µ = 2 + P, S = 1)

0 0.5 1 1.5 2 2.5 3 3.5 4

P

10−5

10−4

10−3

10−2

10−1

BE

R

Figure 2.4. Four antennas, two interferers, and all algorithms retain four survivors except for theMLSE, which uses 22+P survivors. The SNR is 9 dB, the SIR is −10 dB.

P = 0, MLSE (µ = 1, S = 1)P = 4, forney, DDFSE (µ = 1, S = 1)P = 4, ungerboeck, DDFSE (µ = 1, S = 1)

P = 4, forney, M-algorithm (µ = 0, S = 2)P = 4, ungerboeck, M-algorithm (µ = 0, S = 2)P = 4, MLSE (µ = 5, S = 1)

0 2 4 6 8 10 12 14 16 18

SNR (dB)

10−5

10−4

10−3

10−2

10−1

BE

R

Figure 2.5. Two antennas and one interferer. All algorithms retain two survivors except for the P = 4MLSE, which retains 32 survivors. The SIR is 0 dB.

a simple form of space-only IRC at the base stations. The gain depends to a largeextent on the uplink-downlink balance of the system. If the balance is neglectedand only the uplink is considered, the results indicate that the uplink capacity maybe increased by up to 150%. Downlink improvements by means of IRC have alsoreceived much interest lately [40]. In fact, as outlined in [17, 40], IRC can be em-ployed even with a single receive antenna.


For the actual implementation of spatiotemporal IRC, several aspects have tobe considered. Functionality is of course required to cope with imperfections en-countered in the down conversion to digital baseband such as DC and frequencyoffsets. Algorithms developed for white interference and noise may need to berevisited, as is done for burst synchronization in [41]. When it comes to estimat-ing the parameters required by the sequence detector, we note that there are severalchallenges. Although the channel may perhaps be regarded as time-invariant dur-ing the burst, significant changes in the interference may occur during the trans-mission of a burst if the network is not burst synchronized. On the other hand, ifthe network is synchronized, the correlation between training sequences used indifferent cells may require some care, for example, planning as well as joint detec-tion and estimation of the channels of the interferers.

The number of parameters to estimate grows with the chosen model orderP, see also [25, 26], and estimation errors may degrade performance significantly.Iterating between parameter estimation and data detection may be an alternative.The simulation study in [42] shows that performance may be significantly im-proved in this way, and that performance of a linear receiver may be better thanan MLSE structure, especially in the presence of estimation errors and time vari-ations. Another possibility is to adapt the model order to the instantaneous inter-ference scenario. Ungerboeck’s formulation could be considered as a starting pointsince it can be trained in a different way, see also [3, 8, 14]. Another approach isto utilize the structure of the interference. This is done in [43] to improve the esti-mates of the parameters of the VAR model and in [44] to construct a zero-forcingfront-end filter.

2.6.1. Experimental results

Data collected with a testbed for the air interface of a DCS 1800 base station wasprocessed. A dual polarized sector antenna was mounted on the roof of a building40 meters above ground, and the environment was suburban with 2–6 floor build-ings. One mobile transmitter and one interferer were present on the air simulta-neously. The angular separation between the two transmitters was small and neverexceeded ten degrees. The average distance to the mobile transmitter of interestwas about one kilometer, and the distance to the interferer was about 500 meters.The SNR was high, both transmitters traveled at speeds 0–50 km/h and there wastypically no line-of-sight between the transmitters and the receiving dual polarizedantenna.

Results from processing 20000 data bursts are shown in Figure 2.6. Both trans-mitters were synchronized so that the bursts overlapped completely. The 26 bitlong training sequence was used to estimate the parameters required for the se-quence detector. An unstructured approach was taken in the sense that FP andW (AP) were estimated from a least squares fit and the covariance matrix of theresiduals was used as an estimate of QP , see also [26]. Burst synchronization wasdone as described in [41].


P = 0P = 1

−25 −20 −15 −10 −5 0 5

SIR (dB)

10−3

10−2

10−1

100

BE

R

Figure 2.6. Experimental data, dual polarized sector antenna, NR = 2, and one interferer.

As can be seen from Figure 2.6, a gain of 3–5 dB was observed at BER between1% and 10% for spatiotemporal IRC as compared to space-only IRC. The time dis-persion was probably small, and this may explain the modest gains, as comparedto the very large gains demonstrated in the simulations when spatiotemporal in-terference rejection was compared to space-only interference rejection.

2.7. Interference rejection combining for WCDMA

Third-generation systems based on wideband code division multiple access(WCDMA) are currently being deployed around the world [45]. System perfor-mance in terms of coverage and capacity is affected by interference, and it is there-fore of interest to consider advanced receiver algorithms that offer interferencerejection. In addition to multiple access interference from other users operatingon the same frequency band, there can be other terms of interference, referredto herein as external interference (EI). Examples of EI include ACI from adjacentcarriers including the TDD mode and other communication systems as well asinterference from narrowband communication systems operating in the same fre-quency band or causing intermodulation products. EI may in principle affect thecoverage and capacity already at low loads, and it can therefore be of interest toconsider interference rejection already at an early stage of system deployment.

Sequence estimators are typically used in GSM/EDGE to handle ISI, and theuse of a VAR model as described in the previous sections represents a possibleway to evolve such a receiver structure to include spatiotemporal IRC. The FDDmode of WCDMA is based on DS-CDMA with long aperiodic spreading codesand commonly RAKE receivers are used to handle time dispersive radio channels.The basic receiver structure thus differs from GSM/EDGE, and the approach takenherein to spatiotemporal IRC for WCDMA is therefore different as well. Common


for the two cases is that both spatial and temporal correlations of the interferenceare exploited in a conventional receiver structure. The present section is thus acomplement to the previous sections outlining a possible approach for WCDMA.

Commonly, a RAKE receiver with a limited number of fingers is used inWCDMA. A delay is associated with each finger, and the receiver will for eachfinger despread the received signal by correlating it with the spreading waveformappropriately delayed [30, 31, 32, 45]. We assume that F delay estimates are usedand that the signals received by all antennas are despread for each finger. The NR

despread samples associated with finger f for symbol n may then be modeled as

z f [n] = h f b[n] + j f [n], (2.34)

where h f represents the channels of finger f , b[n] models the transmitted symbol,and j f [n] is despread interference and noise. We define the NRF × 1 vectors�z[n],�h, and�j[n], as

�z[n] =[

zT1 [n] zT2 [n] · · · zTF [n]]T

,

�h =[

hT1 hT

2 · · · hTF

]T,

�j[n] =[

jT1 [n] jT2 [n] · · · jTF [n]]T

,

(2.35)

and define the covariance matrix of the despread noise and interference Q as

Q = E{�z[n]�z∗[n]

}. (2.36)

The expectation is evaluated with respect to the interfering data symbols andscrambling codes which are modeled as sequences of independent QPSK symbols.Further details on this data model, including expressions for the covariance ma-trix and the resulting channel, may be found in [31] for the downlink with a singleantenna and for the uplink with multiple antennas in [30, 32]. The RAKE receiverforms a decision variable as

b[n] = �w∗�z[n], (2.37)

from which the transmitted symbol and bits may be detected. The conventionalRAKE receiver assumes that the despread noise and interference of different fingersis uncorrelated. Combining weights can then be expressed as

�w = (Q� INRF)−1�h, (2.38)


where � denotes the element-by-element matrix product. Further, a space-onlyIRC RAKE, as described in, for example, [30, 45], assumes that the covariancematrix is block diagonal. Only the spatial correlation of noise and interference isthen handled. However, narrowband interference and interfering wideband sig-nals that have propagated through multipath channels cause temporal correlationin the sense that the despread interference and noise of fingers with different de-lays is correlated. A RAKE receiver with spatiotemporal IRC will determine thecombining weights as

�wIRC = Q−1�h. (2.39)

As demonstrated in [30], large gains as compared to space-only interference re-jection and conventional RAKE combining may be obtained for rejection of EI inthe uplink, especially for cases with wideband EI when there are not enough spa-tial degrees of freedom. In this case, a similar behavior to that in Figure 2.1 canbe observed. In the downlink, the orthogonality between the spreading codes ofdifferent channels is destroyed and the despread interference of different channelsfingers is correlated in time dispersive multipath channels. Significant gains maythen be obtained with a single-antenna generalized RAKE receiver as shown in[31]. Another interesting observation is that in the case of temporally correlatedinterference, it is advantageous to use more fingers than there are resolvable raysin the channel.

2.8. Concluding remarks

Spatiotemporal interference rejection combining for burst oriented systems suchas GSM was considered, and an autoregressive model was introduced to captureboth the spatial and temporal correlation of the interference. We saw that completeinterference rejection is possible if the number of interferers is less than the num-ber of antennas and the model order is chosen so that the interference is confinedto a subspace in the spatiotemporal model formulated. The interference model wasthen incorporated into a maximum likelihood sequence estimator and two metricswere presented. Numerical examples demonstrated significant performance gainscompared to space-only processing in interference-limited scenarios at the cost ofan exponential increase in complexity of the sequence estimator. Therefore, re-duced complexity sequence estimators were introduced, and numerical examplesillustrated that noise sensitivity can be traded for improved interference rejectioncapabilities. Thus, spatiotemporal interference rejection can be performed withroughly the same order of complexity as space-only interference rejection. ForGSM, we also showed some experimental results and discussed implementationaspects, such as estimation of the parameters for the detector, see also [42, 44].

Finally, we also outlined interference rejection combining for WCDMA. Inthis case, the conventional RAKE receiver may be generalized to account for spa-tially and temporally correlated interference.


Abbreviations

BER Bit error rate

BPSK Binary phase-shift keying

CDMA Code division multiple access

DCS Digital cellular system

DDFSE Delayed decision-feedback sequence estimator

DS-CDMA Direct-sequence code division multiple access

EDGE Enhanced data for global evolution

FDD Frequency division duplex

GSM Global system for mobile communications

GVA Generalized Viterbi algorithm

IRC Interference rejection combining

ISI Intersymbol interference

MIMO Multi-input multi-output

MISO Multiple-input single-output

MSK Minimum shift keying

QPSK Quadrature phase-shift keying

SIR Signal-to-interference ratio

SNR Signal-to-interference and noise ratio

TDMA Time division multiple access

VAR Vector autoregressive

WCDMA Wideband code-division multiple access

Bibliography

[1] G. Forney Jr., “Maximum-likelihood sequence estimation of digital sequences in the presence ofintersymbol interference,” IEEE Trans. Inform. Theory, vol. 18, no. 3, pp. 363–378, 1972.

[2] A. Duel-Hallen and C. Heegard, “Delayed decision-feedback sequence estimation,” IEEE Trans.Commun., vol. 37, no. 5, pp. 428–436, 1989.

[3] J. Modestino and M. Eyuboglu, “Integrated multielement receiver structures for spatially dis-tributed interference channels,” IEEE Trans. Inform. Theory, vol. 32, no. 2, pp. 195–219, 1986.

[4] G. E. Bottomley and K. Jamal, “Adaptive arrays and MLSE equalization,” in IEEE 45th VehicularTechnology Conference, vol. 1, pp. 50–54, Chicago, Ill, USA, July 1995.

[5] G. E. Bottomley, K. J. Molnar, and S. Chennakeshu, “Interference cancellation with an array pro-cessing MLSE receiver,” IEEE Trans. Veh. Technol., vol. 48, no. 5, pp. 1321–1331, 1999.

[6] P. Chevalier, F. Pipon, J.-J. Monot, and C. Demeure, “Smart antennas for the GSM system: exper-imental results for a mobile reception,” in IEEE 47th Vehicular Technology Conference, vol. 3, pp.1572–1576, Phoenix, Ariz, USA, May 1997.

[7] S. N. Diggavi and A. Paulraj, “Performance of multisensor adaptive MLSE in fading channels,” inIEEE 47th Vehicular Technology Conference, vol. 3, pp. 2148–2152, Phoenix, Ariz, USA, May 1997.

[8] K. J. Molnar and G. E. Bottomley, “Adaptive array processing MLSE receivers for TDMA digitalcellular/PCS communications,” IEEE J. Select. Areas Commun., vol. 16, no. 8, pp. 1340–1351, 1998.

[9] F. Pipon, P. Chevalier, P. Vila, and D. Pirez, “Practical implementation of a multichannel equalizerfor a propagation with ISI and CCI—application to a GSM link,” in IEEE 47th Vehicular Technol-ogy Conference, vol. 2, pp. 889–893, Phoenix, Ariz, USA, May 1997.

[10] P. Vila, F. Pipon, D. Pirez, and L. Fety, “MLSE antenna diversity equalization of a jammedfrequency-selective fading channel,” in Seventh European Signal Processing Conference (EU-SIPCO ’94), pp. 1516–1519, Edinburgh, UK, September 1994.

[11] G. Ungerboeck, “Adaptive maximum-likelihood receiver for carrier-modulated data-transmis-sion systems,” IEEE Trans. Commun., vol. 22, no. 5, pp. 624–636, 1974.


[12] W. van Etten, “Maximum likelihood receiver for multiple channel transmission systems,” IEEETrans. Commun., vol. 24, no. 2, pp. 276–283, 1976.

[13] M. Escartin and P. A. Ranta, “Interference rejection with a small antenna array at the mobilescattering environment,” in First IEEE Signal Processing Workshop on Signal Processing Advancesin Wireless Communications, pp. 165–168, Paris, France, April 1997.

[14] G. E. Bottomley and S. Chennakeshu, “Unification of MLSE receivers and extension to time-varying channels,” IEEE Trans. Commun., vol. 46, no. 4, pp. 464–472, 1998.

[15] J.-W. Liang, J.-T. Chen, and A. J. Paulraj, “A two-stage hybrid approach for CCI/ISI reductionwith space-time processing,” IEEE Commun. Lett., vol. 1, no. 6, pp. 163–165, 1997.

[16] D. T. M. Slock, “Spatio-temporal training-sequence based channel equalization and adaptive in-terference cancellation,” in IEEE International Conference on Acoustics, Speech, and Signal Process-ing (ICASSP ’96), vol. 5, pp. 2714–2717, Atlanta, Ga, USA, May 1996.

[17] H. Trigui and D. T. M. Slock, “Cochannel interference cancellation within the current GSMstandard,” in IEEE International Conference on Universal Personal Communications (ICUPC ’98),vol. 1, pp. 511–515, Florence, Italy, October 1998.

[18] S. L. Ariyavisitakul, J. H. Winters, and I. Lee, “Optimum space-time processors with dispersiveinterference: unified analysis and required filter span,” IEEE Trans. Commun., vol. 47, no. 7, pp.1073–1083, 1999.

[19] S. L. Ariyavisitakul, J. H. Winters, and N. R. Sollenberger, “Joint equalization and interferencesuppression for high data rate wireless systems,” IEEE J. Select. Areas Commun., vol. 18, no. 7, pp.1214–1220, 2000.

[20] R. A. Iltis, “A GLRT-based spread-spectrum receiver for joint channel estimation and interferencesuppression,” IEEE Trans. Commun., vol. 37, no. 3, pp. 277–288, 1989.

[21] A. L. Swindlehurst and P. Stoica, “Maximum likelihood methods in radar array signal processing,”Proc. IEEE, vol. 86, no. 2, pp. 421–441, 1998.

[22] K. Abed-Meraim, P. Loubaton, and E. Moulines, “A subspace algorithm for certain blind identi-fication problems,” IEEE Trans. Inform. Theory, vol. 43, no. 2, pp. 499–511, 1997.

[23] A. Gorokhov, P. Loubaton, and E. Moulines, “Second order blind equalization in multiple inputmultiple output FIR systems: a weighted least squares approach,” in IEEE International Conferenceon Acoustics, Speech, and Signal Processing (ICASSP ’96), vol. 5, pp. 2415–2418, Atlanta, Ga, USA,May 1996.

[24] D. T. M. Slock, “Blind fractionally-spaced equalization, perfect-reconstruction filter banks andmultichannel linear prediction,” in IEEE International Conference on Acoustics, Speech, and SignalProcessing (ICASSP ’94), vol. 4, pp. 585–588, Adelaide, SA, Australia, April 1994.

[25] D. Astely, Spatial and spatio-temporal processing with antenna arrays in wireless systems, Ph.D.thesis, Royal Institute of Technology, Stockholm, Sweden, 1999.

[26] D. Asztely and B. Ottersten, “MLSE and spatio-temporal interference rejection combining withantenna arrays,” in Ninth European Signal Processing Conference (EUSIPCO ’98), pp. 1341–1344,Rhodes, Greece, September 1998.

[27] P. Jung, “Performance evaluation of a novel M-detector for coherent receiver antenna diversity ina GSM-type mobile radio system,” IEEE J. Select. Areas Commun., vol. 13, no. 1, pp. 80–88, 1995.

[28] R. Krenz and K. Wesolowski, “Comparative study of space-diversity techniques for MLSE re-ceivers in mobile radio,” IEEE Trans. Veh. Technol., vol. 46, no. 3, pp. 653–663, 1997.

[29] T. Hashimoto, “A list-type reduced-constraint generalization of the Viterbi algorithm,” IEEETrans. Inform. Theory, vol. 33, no. 6, pp. 866–876, 1987.

[30] D. Astely and A. Artamo, “Uplink spatio-temporal interference rejection combining forWCDMA,” in Third IEEE Workshop on Signal Processing Advances in Wireless Communications(SPAWC ’01), pp. 326–329, Taiwan, China, March 2001.

[31] G. E. Bottomley, T. Ottosson, and Y.-P. E. Wang, “A generalized RAKE receiver for interferencesuppression,” IEEE J. Select. Areas Commun., vol. 18, no. 8, pp. 1536–1545, 2000.

[32] T. F. Wong, T. M. Lok, J. S. Lehnert, and M. D. Zoltowski, “A linear receiver for direct-sequencespread-spectrum multiple-access systems with antenna arrays and blind adaptation,” IEEE Trans.Inform. Theory, vol. 44, no. 2, pp. 659–676, 1998.


[33] S. Y. Miller and S. C. Schwartz, “Integrated spatial-temporal detectors for asynchronous Gaussianmultiple-access channels,” IEEE Trans. Commun., vol. 43, no. 234, pp. 396–411, 1995.

[34] S. W. Wales, “Technique for cochannel interference suppression in TDMA mobile radio systems,”IEE Proceedings Communications, vol. 142, no. 2, pp. 106–114, 1995.

[35] M. Kristensson, B. Ottersten, and D. Slock, “Blind subspace identification of a BPSK communi-cation channel,” in Conference Record of the Thirtieth Asilomar Conference on Signals, Systems andComputers, vol. 2, pp. 828–832, Pacific Grove, Calif, USA, November 1996.

[36] S. Haykin, Adaptive Filter Theory, Prentice Hall International, Englewood Cliffs, NJ, USA, 3rdedition, 1996.

[37] A. Hafeez and W. E. Stark, “Decision feedback sequence estimation for unwhitened ISI channelswith applications to multiuser detection,” IEEE J. Select. Areas Commun., vol. 16, no. 9, pp. 1785–1795, 1998.

[38] J. Anderson and S. Mohan, “Sequential coding algorithms: A survey and cost analysis,” IEEETrans. Commun., vol. 32, no. 2, pp. 169–176, 1984.

[39] S. Craig and J. Axnas, “A system performance evaluation of 2-branch interference rejection com-bining,” in IEEE 56th Vehicular Technology Conference (VTC 2002-Fall), vol. 3, pp. 1887–1891,Vancouver, BC, Canada, September 2002.

[40] M. Austin, Ed., “SAIC and synchronized networks for increased GSM capacity,” Tech. Rep., 3GAmericas, Bellevue, Wash, USA, September 2003, white paper.

[41] D. Astely, A. Jakobsson, and A. L. Swindlehurst, “Burst synchronization on unknown frequencyselective channels with co-channel interference using an antenna array,” in IEEE 49th VehicularTechnology Conference, vol. 3, pp. 2363–2367, Houston, Tex, USA, May 1999.

[42] A. M. Kuzminskiy, C. Luschi, and P. Strauch, “Comparison of linear and MLSE spatio-temporalinterference rejection combining with an antenna array in a GSM system,” in IEEE 51st VehicularTechnology Conference (VTC 2000-Spring), vol. 1, pp. 172–176, Tokyo, Japan, May 2000.

[43] G. Klang, D. Astely, and B. Ottersten, “Structured spatio-temporal interference rejection withantenna arrays,” in IEEE 49th Vehicular Technology Conference, vol. 1, pp. 841–845, Houston, Tex,USA, May 1999.

[44] G. Klang and B. Ottersten, “Structured semi-blind interference rejection in dispersive multichan-nel systems,” IEEE Trans. Signal Processing, vol. 50, no. 8, pp. 2027–2036, 2002.

[45] H. Holma and A. Toskala, Eds., WCDMA for UMTS: Radio Access for Third Generation MobileCommunications, John Wiley & Sons, New York, NY, USA, 2000.

David Astely: Ericsson Research, 164 80 Stockholm, Sweden

Email: [email protected]

Bjorn Ottersten: Department of Signals, Sensors and Systems, Royal Institute of Technology, 100 44Stockholm, Sweden

Email: [email protected]

mailto:[email protected]

mailto:[email protected]

Documents

Spatiotemporalinterference rejectioncombiningdownloads.hindawi.com/books/9789775945099/art02.pdf8 Spatiotemporal interference rejection combining h 1[l] models the channel between