Exploring the UMTS WCDMA-Receiver Design

Space Using a Semianalytical Approach

Gunnar Fock, Jens Baltersee, Peter Schulz-Rittich, and Heinrich Meyr

Abstract— time-to-market and will be the receiver of choice for a gre-

A fast simulation technique for the analysis of the sy- at part of the first UMTS applications. In terms of detec-
stem performance of digital receivers is presented and ap- tion performance it is suboptimal, especially if compared
plied to the UMTS terrestrial radio access (UTRA). This se- to the MLSE, which is known to be optimal in the sen-
mianalytical method comprises the computation of receiver
se of minimal probability of error; its complexity, growing
output statistics, conditioned on a static channel model, a
given spreading sequence and a given transmitted symbol exponentially with the number of users and the channel
sequence. Averaging over the known channel tap probabi- influence length, is prohibitive for the implementation in
lity density function and over all symbol sequences yields most cases. In the scope of this paper the MLSE is used
the system performance, conditioned on the selected sprea- as a best-case reference. The channel models proposed in
ding sequence. This method permits the qualitative classifi- [5] are chip-tap models where each channel tap is assumed
cation and comparison of different detection algorithms for to be Rayleigh faded. Furthermore, the transmission chain
WCDMA in the performance-complexity design space. In
from the spreading to the channel convolution can be mo-
the UTRA environment, the performance is shown to va-
ry significantly with the choice of the OVSF spreading se-
deled in a simplified way to facilitate the computation of
quence. Simulation results for a Rake receiver in indoor and the aforementioned output statistics.
outdoor scenarios are compared to lower and upper bounds
of the probability of error of a maximum likelihood sequence II. S YSTEM MODEL
estimation (MLSE) algorithm. It is shown that a Rake re-
In a CDMA transmission system the user data sym-
bols fak g are oversampled by the spreading factor
ceiver provides sufficient detection performance in medium-
rate outdoor scenarios, whereas in high-rate indoor scena-
rios, especially in the uplink, alternative receiver structures N = T =Tc and then multiplied by a user spreading se-
must be considered. quence c = (c0 : : : cN ?1 ), T and Tc being the symbol and
chip duration, respectively. For the UTRA, Tc = 244:14 ns.
If a chip-tap model is available for a multipath fading chan-
nel of delay spread Lc
Tc , meaning that each path delay is
I. I NTRODUCTION
A great problem in the numerical simulation of digital an integer multiple of the chip duration, then the operati-
receiver performance is the large number of trials neces- ons spreading and channel convolution can be described
sary to gain bit error rates with sufficiently small varian- jointly in matrix notation and the received signal samples
ce. For receivers with relatively low complexity, such as are
the well-known Rake receiver [3], receiver output statistics
can be computed analytically for a simplified system mo- 0



10 a 1
i?L
B AB
C @ ... C
del. In order to make the results representative, averaging z0 0
; z0 Ls
; s

over several channel tap realizations and over the transmit- wi = @ ..

.
..
.
..
. A + ni
ted symbols is then performed. In this paper we employ zN ?1 0 ;


zN ?1 Ls
; ai
the technique to a transmission system according to the
UMTS terrestrial radio access standard draft [5]. It utilizes = Z ai + ni (1)
wideband code division multiple access (WCDMA). The
Rake receiver is well known to exploit the signal energy The vector wi contains exactly N chips belonging to
of several multipath components arriving at the receiver, the transmitted data symbol ai . The matrix Z has the di-
a scenario common in mobile transmission environments. mension N  (Ls + 1), Ls = b(Lc ? 1)=N c + 1 being the
It is suggested in [5] as a low-complexity solution for fast symbol equivalent influence length of the chip-tap chan-
nel model. The matrix Z is computed by multiplying the
(Ls + 1)N  (Ls + 1)N Toeplitz matrices C and H, descri-
The authors are with the Integrated Systems for Signal Processing
Laboratory, Aachen University of Technology (RWTH), Aachen, Ger-
many. Telephone: +49 (241) 80 7632. Fax: +49 (241) 8888 195. E-mail: bing the spreading and channel convolution, respectively,
ffock, balterse, rittich, meyrg@ert.rwth-aachen.de. and extracting every Nth column and the last N rows. A
 Rake receiver ^
c 1 h 1*
T

δ( k+ τT1c ) Σ
N

n 1
^
c 1 h *2
T
w
Σ
Σ
N
ak Z 2 g g* 2 δ( k+ τT2c ) 1
a^ k
^

...

...
c 1 h *q
T

δ( k+ τTqc ) Σ
N

Fig. 1. Transmission model with Rake reception

prerequisite for this model is the equivalence of analog III. P ROBABILITY OF ERROR FOR R AKE RECEPTION
and digital signal processing (i.e. [1]), which can easily be
The transmission model according to section II with a
shown if the transmit filter proposed in [5] - a root-raised
Rake receiver is depicted in Figure 1. The received data
cosine filter with α = 0:22 - is also used as a receive filter.
chips are distributed to a total of q Rake fingers. In each
An additional advantage when using this receive filter is
finger, the estimated path delay τ is compensated, desprea-
the whiteness of the additive white gaussian noise process
ding and symbol rate sampling are performed, followed by
after chip rate sampling.
maximum ratio combining. Throughout this paper we shall
The power delay profiles (PDP) of the chip-tap channel
assume perfect timing and channel estimation, i.e. the path
models used in this paper are shown in Figure 2.
delays τ and the channel tap weights h are assumed to be
perfectly known. Also, the multipath channel is assumed
indoor A
to be constant for the duration of one symbol interval.
0 The conditional symbol error probability at the output of
the Rake receiver can be expressed as
Tap Power [dB]

 E [ â j h a c ] sgn(a ) 
−10

−20 Ps ( âk 6= ak j h a c ) = Q
; ; pkVar[ â j h a c ] k ; ;

; ;
(2)
k

−30
E [ âk j h; a; c ] is the expected value of the data sym-
0 2 4 6 8 10 12 bol at the receiver output, conditioned on the know-
t / Tc
ledge of the instantaneous static channel tap vector
h = (h0


hLc ), the sequence of transmitted data symbols
a = (ak?Ls


ak+Lr ), and on the spreading sequence c. Lr
vehicular A

0 is the noncausal part of the data symbol sequence influ-

ence length, caused by the property of the Rake receiver to
Tap Power [dB]

assign the greatest delay to the multipath component arri-

ving first. Var[ âk j h; a; c ] is the corresponding conditional
−10

−20
variance. It was shown in [2] that the expected value can
be written as
−30

0 2 4
t / Tc
6 8 10 12
E [ âk j h; a; c ] (3)

Fig. 2. UTRA channel models q (k+1)N ?1 Ls

= ∑ ĥn ∑ ∑z j ( +τn =Tc ) mod N ;l a b j+τn =Tc c?L +l c j mod N
N s
n=1 j=kN l =0
The variance is given by Then,

Var[ âk j h; a; c ] (4) Pl ( âk 6= ak j h; c )  Ps( âk 6= ak j h c )

Pu ( âk 6= ak j h; c ):
; <

(8)
q q (k+1)L ?1 The computation of (6) requires - theoretically - the
= σn
2
∑∑ ĥn ĥm ∑ cimod N c(i+(τn ?τm ) Tc ) mod N knowledge of all terms in the infinite sum. Terms with
d  2dmin were shown to have no significant contribution
=

n=1 m=1 i=kL

and can thus be easily computed by multiplying the to the upper bound and were therefore omitted. Averaging
channel noise power σ2n with a factor dependent on h, c and of (6) and (7) is then performed according to (5) to yield
q. Monte-Carlo averaging over several channel tap realiza- error bounds conditioned on c.
tions and all QPSK modulated data sequences of length The presented bounds are tight in many scenarios, espe-
Ls + Lr + 1, which are assumed to be uniformly distribu- cially in the high SNR regions, as shown in the results
ted, leads to an error probability which is only dependent (section V). The lower bound, equivalent to single-symbol
on the chosen spreading sequence: errors, should be representative in most scenarios, an as-
sumption verified by Monte-Carlo simulation.

Ps (c) = ∑ ∑ p(a) p(h) Ps ( âk 6= ak j h; a; c )

V. S IMULATION R ESULTS
(5)
a h In order to reemphasize the fundamental difference of
the two presented detection algorithms in terms of imple-
With the assumed independence of the data, I- and Q-
mentation complexity, Figure 3 shows the number of mul-
components of the QPSK symbols can be treated separate-
tiplications necessary for the detection of one data sym-
ly by computing (5) for real and imaginary parts and sub-
bol. For the MLSE, a symbol equivalent channel influence
sequent averaging.
length of Ls = 1 is assumed. The complexity grows linearly
IV. E RROR BOUNDS FOR MLSE with the spreading factor and exponentially with the num-
ber of transmitting users. For the Rake receiver, the com-
Forney proposed upper and lower bounds for the proba- plexity grows linearly with the number of users.
bility of error of maximum likelihood sequence detection
in a PAM-system in [4]. These bounds can be employed for 20
10
a CDMA system by using the received data chips to com-
MLSE, N = 256
pute the euclidean distance metric. In a Viterbi implemen- 10
15

tation of the MLSE, these would constitute the path metric

increments. The conditional upper bound can be expressed 10
10
MLSE, N = 4

as
No. of mults

5
10

 d( â j h c )  Rake, 7 fingers

Pu ( âk 6= ak j h; c ) = ∑Q ∑
k ;
W (ε) Φ(ε);
d 2D 2σn ε2Ed
(6) 2
10 Rake, 2 fingers
where d denotes the euclidean distance of each error
event ε, W (ε) is the hamming weight of ε and Φ(ε) is
a weighting factor proportional to the a-priori probability
that ε will actually occur. Accordingly, D denotes the set
1
10

of all occuring euclidean distances d (ε) and Ed is the set of 5 10 15 20 25 30

all ε with d (ε) = d. The conditional lower bound is obtai- No. of users
ned by looking at the term in (6) with minimum euclidean
Fig. 3. Implementation complexity of Rake and MLSE
distance:

d jh c)
All simulated error probabilities are raw probabilities,
Pl ( âk 6= ak j h; c ) = Q
min ( âk
∑
;
W (ε) Φ(ε): i.e. no coding is included. For this reason, a target error
2σn ε2Edmin probability of Ptarget = 10?2 was assumed. The simulati-
(7) ons were performed with two users sending synchronous-
ly. In the downlink, both users ”see” the same channel VI. C ONCLUSION
realization, whereas in the uplink they differ from each A semianalytical simulation technique is presented and
other. Also, the modulation scheme in the uplink accor- applied to the simulation of the performance of two de-
ding to [5] is dual channel QPSK, where each channel has tection algorithms for WCDMA transmission according to
its own spreading sequence. The proposed scrambling is the UTRA standard draft. The method shows a simulation
not included in this model, underscoring the qualitative time reduction by factors of several hundred when compa-
nature of the results. Upon averaging over different chan- red to a classical Monte-Carlo approach. It is useful for the
nel tap realizations, is was shown that one ”bad” chan- qualitative classification of detection algorithms in the re-
nel can lead to a significant performance degradation. In ceiver design space with the dimensions performance and
this paper, averaging over 3000 realizations for the out- complexity. One major drawback of the presented method
door and 5000 for the indoor scenario led to sufficiently is the unability to include scrambling in the system mo-
stable results. Due to the destructive nature of unfavorable del. Cornerpoints of the design space have been quantified
channels, the Ps -region of interest is approximately reci- with the optimal but highly complex MLSE and the low-
procal to the number of channel realizations, in our case
for Ps  3:33
10?4 .
complexity but suboptimal Rake receiver. The Rake recei-
ver is shown to have sufficient detection performance in
When referring to best-case or worst-case scenarios, the downlink. In the uplink however, especially in high-
the classification is done with respect to the correlation rate indoor environments, alternative receiver structures li-
properties of the spreading sequences of both users. The ke decision-feedback equalizers must be further analyzed.
best-case sequence pairs have the lowest crosscorrelation These can be classified with the presented simulation me-
energy among all sequence pairs with the given spreading thod.
factor, with the worst-case pairs having the highest. The
scrambling proposed in [5] has an averaging effect on the R EFERENCES
detection performance, making it independent of the choi- [1] Heinrich Meyr, Marc Moeneclaey and Stefan Fechtel. Digital
Communication Receivers: Synchronization, Channel Estimation
ce of the spreading sequence. A system with scrambling
and Signal Processing, John Wiley and Sons, New York, 1998.
will thus have a detection performance between the two [2] Peter Schulz-Rittich. Untersuchung von WCDMA Detektionsalgo-
respective cases shown in this paper. rithmen bezüglich Leistungsfähigkeit und Realisierungsaufwand,
Diploma thesis, Integrated Systems for Signal Processing Labora-
tory, Aachen University of Technology (RWTH), Aachen, Novem-
Figures 4 and 5 show simulation results for a transmis- ber 1998.
sion scenario with the ”indoor A” PDP of Figure 2 and [3] R. Price and P.E. Green, Jr. A Communication Technique for Mul-
N = 4, corresponding to a raw bitrate of 2 MBit/s. In Figu- tipath Channels, Proceedings of the IRE, March 1958
[4] G.D. Forney, Jr. Maximum Likelihood Sequence Detection of Di-
re 4, both users transmit with equal power, i.e. the signal to gital Sequences in the Presence of Intersymbol Interference, IEEE
interference ratio (SIR) is 0 dB. Even with the worst-case Transactions on Information Theory, Vol. XX, May 1972
sequence pair selection, the 2 finger Rake receiver achieves [5] The ETSI UMTS Terrestrial Radio Access (UTRA) ITU-
Ptarget , though with a considerable SNR loss with respect R RTT Candidate Submission, http://www.itu.ch/imt/2-radio-
dev/proposals/etsi/utra.pdf, June 1998
to the MLSE. In Figure 5, an uplink transmission with
the best-case sequence pair is depicted. The target error
probability cannot be achieved by the Rake receiver. For
all indoor simulations, using more than 2 fingers does not
show a significant performance gain, in accordance with
the short channel influence length (Figure 2).
Figures 6 through 9 show results for the ”vehicular A”
PDP with N = 64, corresponding to a raw bitrate of 128
KBit/s. The downlink with SIR = 0 dB is depicted in Fi-
gures 6 and 7. A 7 finger Rake receiver is still able to
achieve Ptarget even with the worst-case sequence pair. In
the uplink with SIR = -10 dB, shown in Figures 8 and 9,
the dependence of the simulated performance on the choi-
ce of the sequence pair is even more obvious. A system
with scrambling will have a performance between these
two scenarios, making a Rake reception feasible.
 indoor A, N = 4 vehicular A, N = 64

10 −1 10 −1

worst-case

10 −2 10 −2

best-case
Ps Ps

10 −3 10 −3
MLSE lower bound
MLSE lower bound MLSE upper bound
MLSE upper bound 1 finger RAKE
1 finger RAKE 4 finger RAKE
2 finger RAKE 7 finger RAKE
10 −4 10 −4
0 5 10 15 20 25 30 0 5 10 15 20 25 30
SNR per Bit SNR per Bit

Fig. 4. Two users, downlink, SIR = 0 dB Fig. 7. Two users, downlink, SIR = 0 dB, worst case

indoor A, N = 4 vehicular A, N = 64

SIR = -10 dB
−1
10 10 −1

10 −2 10 −2
SIR = 0 dB
Ps Ps

10 −3 10 −3
MLSE lower bound
MLSE lower bound MLSE upper bound
MLSE upper bound 1 finger RAKE
1 finger RAKE 4 finger RAKE
2 finger RAKE 7 finger RAKE
10 −4 10 −4
0 5 10 15 20 25 30 0 5 10 15 20 25 30
SNR per Bit SNR per Bit

Fig. 5. Two users, uplink, best case Fig. 8. Two users, uplink, SIR = -10 dB, best case

vehicular A, N = 64 vehicular A, N = 64

10 −1 10 −1

10 −2 10 −2

Ps Ps

10 −3 10 −3
MLSE lower bound MLSE lower bound
MLSE upper bound MLSE upper bound
1 finger RAKE 1 finger RAKE
4 finger RAKE 4 finger RAKE
7 finger RAKE 7 finger RAKE
10 −4 10 −4
0 5 10 15 20 25 30 0 5 10 15 20 25 30
SNR per Bit SNR per Bit

Fig. 6. Two users, downlink, SIR = 0 dB, best case Fig. 9. Two users, uplink, SIR = -10 dB, worst case