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THROUGHPUT ENHANCEMENT IN

WCDMA USING THE GENERALIZEDRAKE RECEIVER

Jay Kumar Sundararajan

Vaibhav Maheshwari

R. David Koilpillai

Department of Electrical Engineering

Indian Institute of Technology, MadrasChennai, India 600036

Abstract

In a multipath fading channel, when there are many interfering CDMA signals, the

multipath causes loss of orthogonality between different signals leading to intracell interfer-

ence. The Generalized RAKE receiver, proposed recently in the literature, is based on the

concept that this interference is not white but colored. Therefore, unlike the conventional

RAKE receiver, GRAKE tries to match to the channel as well as whiten the interference.

The GRAKE gives a typical improvement of 1-3 dB in SNR for a moderate increase in

complexity.

In this paper, we quantify the benefits of using the GRAKE in place of the RAKE

in a WCDMA downlink under realistic conditions as specified in the 3GPP standards. The

comparison is made both in the presence and absence of channel coding. After performing

channel coding, the block error rate and hence the system throughput is evaluated for both

receivers in a 144 kbps test case. It is demonstrated that the GRAKE provides significant

improvement in BER performance, which translates to higher data throughput, as well as

increased capacity.

Currently at MIT, USA; E-mail: [email protected] Currently at ETH, Zurich; E-mail: [email protected] Currently at IIT Madras; E-mail: [email protected]


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Index Terms

Wideband CDMA, DS-CDMA downlink receivers, Generalized RAKE Receiver, Col-

oration of interference

I. INTRODUCTION

The RAKE receiver is equivalent to a matched filter receiver that matches to the

multipath channel. Therefore it is the optimal solution in a situation where the only

impairments to the transmitted signal are the multipath fading channel and receiver

white noise.

However, in realistic situations, one has to account for time-dispersive propagation

environments. In general, channels are expected to appear more dispersive in third

generation cellular systems than in second generation cellular systems, as the signal

bandwidth in 3G systems is much higher. In particular, with the use of multi-code

transmission and low spreading factors, the multipath channel causes loss of orthogo-

nality between the signals of different CDMA signals. So this discussion becomes even

more important in third generation systems which use CDMA and their evolutions such

as HSDPA, cdma2000 and 1X-EV.

In CDMA systems, the signals of all users are added up and sent over the same

frequency band at the same time. So all of them pass through the same radio channel.

There will be inter-symbol and multiple access interference caused by delayed replicas

of the transmitted signal as well as the presence of many users in the system. Besides,

there are signals from neighboring base stations which also produce interference. The

interference gets distorted in the frequency domain due to the time dispersion and hence

cannot be treated as white noise. The problem with RAKE receiver is that it assumes

that such interference can be included under white noise. Actually, the interference

is colored because of multipath as well as pulse shaping. Thus, in the presence of

interfering signals, the RAKE receiver is not the best approach.


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The Generalized RAKE (GRAKE) receiver [1] is a new receiver that accounts for

these discrepancies in the RAKE. In the GRAKE, this idea is generalized in two ways:

The fingers can be placed in locations other than the channel taps

The weights associated with the fingers need not be conjugates of the channel taps

I I . INTERPRETATIONS OF THE GRAKE

An important property, specific to DS-CDMA systems, is that on the downlink, signals

within the same cell are transmitted using orthogonal waveforms so that they will not

interfere with one another. However, if the channel has multipath propagation, this

orthogonality property no longer holds. Thus intracell interference can be mitigated by

equalizing the dispersive channel.

Intercell interference does not have this orthogonality property. So, the approach of

equalizing the channel will not work here. Since the signal from the interfering base

station goes through a different multipath channel as compared to the signal from the

desired base station, the differences in spectral coloration must be exploited. Since the

multipath channel gives multiple images of the signal, one image of the interference is

used to cancel another image.

The GRAKE receiver utilizes these propeties of interference and uses a model for the

coloration of the interference to give a better downlink performance. It aims to achieve

a trade-off between two goals:

To equalize the multipath channel to restore orthogonality of the intracell interfering

signals

To use one image of the interference signal to cancel another image, thereby

suppressing intercell interference

Another interpretation of the GRAKE is that it is a whitening matched filter. This is

essentially an application of the matched filter theory for colored noise [7]. The structure

is similar to that of the conventional RAKE receiver. Assuming that the finger locations


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have been chosen, the weights are decided using a maximum likelihood formulation. For

this, the interference at the output of the fingers is modeled as colored noise. If J is the

number of fingers chosen, then a J x J noise correlation matrix R is formed where the

(i, j)th entry is the correlation between the noise terms on the ith and jth fingers. The

ML formulation results in the decision variable:z = cHR1x where c is the vector of

channel coefficients, x is the vector of finger outputs and R is the noise correlation matrix

described above. There is a trade-off between matching to the channel and whitening

with an aim to maximise the overall signal-to-interference-plus-noise ratio (SINR). It

can be shown that the R matrix can be factorized into one term corresponding to the

pre-whitening filter and another corresponding to the matching operation [2].

III. THE MATHEMATICAL FORMULATION

The notation followed here is the same as that used in [1]

A. The system model

The transmitted signal for user k is

xk(t) =Ek

i=

sk(i)ak,i(t iT) (1)

where Ek is the average symbol energy, T is the symbol duration, sk(i) is the ith symbol,

ak,i(t) is the user symbol-period-dependent spreading waveform which is expressed as:

ak,i(t) =

1N

N1

j=0

ck,i(j)p(tjTc) (2)

The data symbol is assumed to have unit energy.

The transmitted signal passes through an L-tap multipath channel whose baseband

equivalent impulse response is given by:

g() =L1l=0

gl( l) (3)


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Assuming there are K users totally, the received signal is expressed as

r(t) =K1j=0

L1l=0

glxk(t l) + n(t) (4)

The GRAKE receiver structure consists of a bank of J GRAKE fingers, each corre-

lating to a different delay of the received signal. Let the delay of the jth finger be dj .

For a given symbol, say symbol 0 of user 0, the correlator output (after despreading)

corresponding to this delay is:

y(dj) =

r(t)a0,0(t dj)dt (5)

These correlator outputs are combined through a weighted summation to produce a

decision statistic:

z=J

j=1

wjy(dj) = wHy (6)

where w = [w1, w2, , wJ]T is the vector of combining coefficients and

y = [y(d1), y(d2), , y(dJ)]T is the vector of correlator outputs.

B. Calculating the combining weights

If the correlator output vector can be expressed as :

y = hs0(0) + u (7)

then the combining weights are calculated using the following equation which is derived

using the ML formulation:

w = Ru

1h (8)

where Ru = E[uuH] is the noise correlation matrix of vector u (which is assumed to

be a complex-valued Gaussian noise vector with zero-mean).

The computation of the h vector and the noise correlation matrix is as described


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in [1]. The correlation in the noise terms is a result of several factors inter-symbol

interference, intracell interference and white noise. Each of these contribute to the noise

correlation matrix.

Once Ru has been found, it is inverted and multiplied with h vector, as in eqn. (8)

to get the GRAKE weights. These are then used as the combining coefficients during

maximal ratio combining.

IV. SIMULATION SETUP

A. Transmitter

1) Physical Channels incorporated: The following physical channels have been in-

corporated in the simulation as mentioned in [3]:

1) DPCH: Downlink Physical Channel

2) P-CPICH: Primary Common Pilot Channel

3) PICH: Paging Indicator Channel

4) P-CCPCH: Primary Common Control Physical Channel

5) SCH: Synchronization Channel

6) OCNS:Orthogonal Channel Noise Source

The spreading factors and format details of these channels have been specified in [4].

The OCNS is used to simulate the effect of the DPCHs of other users within the same

cell.

2) Power Allocation for the various channels: The relative powers of the various

physical channels has been fixed according to the Table C.3 in specification [3]. The

DPCH power is assumed to be -12 dB with respect to the total power. The total power

for all the OCNS signals put together is calculated by subtracting the power of all the

other channels from the total transmitted power. Note that the SCH and P-CCPCH are

time-multiplexed. Therefore, while subtracting the powers of the other channels, the

power of SCH and P-CCPCH are not subtracted separately, but only once commonly.


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Fig. 1. Operations performed in throughput simulation

3) Channel Coding: The throughput simulation is performed for the test case given

in Appendix A.3.3 in [3]. This is a 144 kbps. The slot format structure and all other

parameters are given in [4]. Each block of data bits is transmitted over 2 radio frames.

The raw data bits are subjected to several operations before being placed in the frame.

These operations have been shown in Figure 1. The full details of this sequence of steps

are available in the 3GPP specification [5].

4) Convolutional Coding: The block of 2904 bits, that results after 8 zeros have

been appended, is sent through a rate 1/3 convolutional encoder with a memory of 8


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bits. The initial state of the encoder is the all-zero state. The resulting bit sequence has

a length of 8712.

5) Modulation and Spreading: The bits of all the physical channels are modulated

using Quadrature Phase Shift Keying (QPSK).

The complex symbol is then spread using the channelization code that has been

assigned to the particular channel resulting in complex-valued chips whose number

depends on the spreading factor. The chips of all the channels are added and then

filtered through a pulse shaping SRRC filter with roll-off factor chosen to be 0.22 as

per the WCDMA specifications [6].

The chip sequence, after spreading, is multiplied with a scrambling code. The scram-

bling sequence varies from symbol to symbol.

B. Channel Profile used

The following is the channel profile that we have used in the simulations (Table 1).

It is based on an example in [1]. The multipath fading channel has been normalized in

such a manner that the sum of squares of the magnitude of the various taps is unity

on the average. This is achieved by dividing each tap by the square root of the sum

of squares of the nominal channel tap magnitudes. Note that the chip period in the

WCDMA system is 260.4 nanoseconds.

Delay Gain

(in nanoseconds) (in dB)

0 0260.4 -1.5

520.8 -3.0

780.3 -4.5

TABLE I

CHI P-SPACED CHANNEL


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V. RECEIVER

A. Channel Estimation

The received signal is correlated with a known version of the pilot channel (P-CPICH)

to get the estimates of the channel. A chunk of the pilot channel of length equal to

5120 chips is used to do the correlation. The chunk is chosen such that its center

point corresponds to the time instant at which the channel impulse response has to be

found. Exact knowledge of the channel tap delays is assumed. Now the pilot chunk

is positioned at these delays and the correlation with the received signal is computed

at these delays. Thus, the channel coefficients are found. The estimates of the channel

taps are divided by the norm of the pilot chunk used for the correlation in order to

normalize them.

It is assumed that the channel remains constant for half a slot (1280 chips). At the

Doppler frequency that has been used in our simulation, this is a reasonable assumption.

After half a slot, the channel estimates are updated. For this, a new pilot chunk is selected

from the known pilot signal, with its center point at the new time instant corresponding

to the next half-slot. The correlation is then performed as described in the previous

paragraph.

B. Finger Placement

The location of fingers need not coincide with the actual channel taps in the case of

GRAKE receiver. However, there is no closed form expression to find out exactly where

to place them. It has been observed that the performance of the GRAKE is very sensitive

to the finger locations. The methods suggested in [1] involve a brute force search among

all possible potential combinations of finger delays in order to find the one which gives

maximum SNR. However, this method has a very high complexity. The method used

in our simulation is described here. Symmetrical finger placement algorithm [2]: First

of all, GRAKE fingers are placed at the actual channel tap locations. The algorithm


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tries to cancel the interference on a channel tap by placing extra GRAKE fingers in

symmetrical places around that path. This is done on the channel taps in decreasing

order of their energy. It is ensured that none of the new fingers is too close to already

existing fingers, so that the diversity is utilized best. The total number of GRAKE

fingers is limited to twice the number of RAKE fingers as it is found that using more

fingers doesnt enhance the performance further significantly [1]. This is a sub-optimal

algorithm but is found to work well.

For each finger, the received signal is tapped at the correct position corresponding

to the finger delay. This segment of the signal is passed through a receive filter which

is matched to the SRRC filter used in the transmitter. The output of the filter is then

downsampled to one sample per chip. We assume that the ideal sampling point is known.

The estimated chip sequence is then subject to descrambling and despreading and then

maximal ratio combining is performed.

Subsequently, Viterbi decoding is performed for decoding the convolutional coding.

This is done blockwise. The block is tested using the CRC. If the block fails the CRC

test, a block error is recorded. In this manner the block error rate (BLER) can be found.

The throughput is then computed for the given BLER value using the following formula.

Throughput = (1 BLER) 100% (9)

VI. RESULTS

Channel profile : Chip-spaced channel

Test case : 144 kbps test case

Finger placement strategy : Symmetrical finger placement

For the throughput simulations, the same simulation model is used except that channel

coding blocks are included in the model. Rate 1/3 convolutional coding is performed

followed by puncturing as described in Section IV-A.3.


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Fig. 2. RAKE vs GRAKE: Raw Bit Error Rate

The first plot (Figure 2) shows the raw BER between the point after the channel

coding and before the decoding. The second plot (Figure 3) compares the information-

bit error rate. In this plot, the SNR values correspond to the SNR per information bit

with rate R = 2904/8464 coding. This is related to the actual SNR per channel bit in

the following manner.

SNR per information bit = SNR per channel bit k

n (10)

where k/n is the effective rate of the code after puncturing. In this simulation, this

corresponds to a 4.646 dB difference between the SNR per channel bit and the SNR

per information bit. The third plot (Figure 4), gives the comparison of the throughput

obtained by using the RAKE and the GRAKE. This figure shows that the RAKE reaches

an error floor due to which, the throughput cannot go higher than about 88% even for


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Fig. 3. RAKE vs GRAKE: Information Bit Error Rate

high SNR. However, the GRAKE enhances the throughput at low SNR values and is

able to reach close to full throughput at high SNR values.

VII. CONCLUSIONS

We have demonstrated that the generalized RAKE receiver gives a significant perfor-

mance gain over the RAKE receiver in terms of raw bit-error rate, information bit-error

rate as well as throughput of the system. For an information bit-error rate of 1%, the

RAKE requires 8 dB SNR per bit, whereas the GRAKE gives 1% error rate at 6 dB

itself. Thus there is a gain of 2 dB. This gain translates into a lower block error rate

for the GRAKE case. In turn, there is an enhancement of throughput.

For a throughput of 80 %, the GRAKE gives a gain of about 5.5 dB. Moreover, the

throughput of RAKE saturates at about 88% whereas the GRAKE gives a throughput


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Fig. 4. Throughput of the system

of almost 100 % for high SNR. This is because, even when the white noise is almost

absent, the RAKE is till affected by interference and therefore, the RAKE performance

reaches an error floor. This effect can be seen from the raw-bit-error rate plot of the

144 kbps test case plots.

At the same time, it is to be noted that the performance gains are sensitive to the

accuracy of channel estimation as well as the finger placement strategy used. Future

work can include a detailed study of these effects. Further investigation is necessary on

what kind of finger placement strategies work best and whether there is a simple way

to find the optimal location of the fingers. These aspects are critical in order to obtain

the promised enhancement in performance of the GRAKE over the coventional RAKE

receiver.


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VIII. ACKNOWLEDGEMENTS

We would like to thank Dr. Gregory Bottomley of Ericsson Research, USA, for useful

discussions related to this work.

REFERENCES

[1] Bottomley, G.E.; Ottosson, T., Wang, Y.-P.E. A generalized RAKE receiver for interference suppression, IEEE

J. Selected Areas Comm. 18, 8 (August 2000), 1536-1545.

[2] Kutz G and Amir Chass, On the Performance of a Practical Downlink CDMA Generalized RAKE Receiver,

IEEE 56th Vehicular Technology Conference, VTC Fall 2002.[3] UE radio transmission and reception (FDD). 3GPP TS 25.101, V5.5.0 (2002-12).

[4] Physical channels and mapping of transport channels onto physical channels (FDD). 3GPP TS 25.211, V 3.3.0

(2002-06).

[5] Multiplexing and channel coding (FDD). 3GPP TS 25.212, V3.3.0 (2002-06).

[6] Spreading and modulation (FDD). 3GPP TS 25.213, V3.3.0 (2002-06).

[7] S. M. Kay, Fundamentals of statistical signal processing. Volume 2: detection theory, Prentice Hall, 1998.

[8] Jay Kumar Sundararajan, Throughput Enhancement in WCDMA using The Generalized Rake Receiver, B.Tech.

project thesis, IIT Madras, 2003.

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