WCDMA

1. DRAFT
On the Site Selection Diversity Transmission
Jyri H¨am¨al¨ainen, Risto Wichman
Helsinki University of Technology, P.O. Box 3000, FIN–02015 HUT, Finland
Abstract— We examine site selection diversity trans-
mission (SSDT) for 3GPP WCDMA forward link by
means of analytical tools. Hard handover (HHO), soft
handover (SHO) and SSDT are compared by using the
receiver bit error probability as a performance measure
taking into account the effect of feedback bit errors as
well as the shadow fading. Results show that without fast
transmission power control the performance gain from
SSDT can be seriously degraded by feedback bit errors.
I. INTRODUCTION
A handover in wireless cellular systems is per-
formed when a mobile station moves from one cell
to another. In hard handover (HHO), transmission is
disconnected and switched to a new base station when
mobile station leaves the cell area, whereas in soft
handover (SHO), mobile station may be connected
simultaneously to several base stations so that addition
and removing a base station from the active set is
performed softly. Soft handover implements macro
diversity, which improves the quality of the received
signal and can be further exploited by reducing the
transmit power, which reduces interference and in-
creases system capacity.
In multipath channels, the performance of soft han-
dover is limited by the number of RAKE fingers that
can be implemented in mobile station. This may lead
to the situation, where the mobile station is not able to
exploit the signals of all base stations transmitting to
it. In this case, SHO does not improve signal quality
but increases interference to the system. Furthermore,

2. DRAFT
updating the active set is slow and requires a lot of
higher layer signaling.
Site selection diversity transmission (SSDT) [1]
in WCDMA was designed to alleviate the problems
described above. In SSDT, mobile periodically chooses
one of the base stations from the active set based
on the instantaneous received powers. Subsequently,
the mobile station sends the identification (ID) of the
selected base station to all base stations in the active
set. According to the identification sent by the mobile,
other base stations in the active set suspend their trans-
mission to the mobile station. The selected base station
is referred to as primary base station while other
base stations are called non-primary base stations.
Primary base station is selected by using physical layer
signaling, which makes it possible to track fast changes
in the connection. High speed downlink packet access
(HSDPA) extension of WCDMA [2] contains fast cell
selection concept, which is very similar to SSDT.
In this paper, we compare SSDT, SHO and HHO
using bit error probability as a performance measure.
For simplicity, we ignore the latency in SSDT pro-
cessing so that the results apply to slowly moving
users. Recently, SSDT has been studied in [3], [4]
using link-level simulations, and it was observed that
SSDT gives substantial capacity gains in low mobility
environments.
The paper is structured as follows: The system
model is introduced in Section II while the analysis of
the macro diversity methods is carried out in Section
III. Paper is concluded in Section IV.
II. SYSTEM MODEL
A. Hard Handover
In hard handover, the transmitting base station
among K alternatives is selected directly based on the
average signal to interference and noise ratio (SNIR)
defined for user k by
SNIRk =
Ck
Ik + I + N
, Ik =
K
l=1,l=k
Il,
where Ck is the power of the own cell carrier, N is the
noise term, Ik is the interference power from an other
base station in the active set, and I is the interference
from base stations, which do not belong to the active
set.
We assume that the mean received power in decibels
follows Gaussian distribution with expectation µ and
standard deviation σ [5]. The deviation σ is based on
measurements and values 3−9 dB have been reported
in the literature depending on the environment. Fur-
thermore, we assume that HHO is too slow to mitigate
fast fading. This assumption is reasonable since time
delay between consecutive handovers in WCDMA is at
least tens of milliseconds, more likely some hundreds
of milliseconds. The selection of the base station is
assumed to be error free since long term signalling
with good reliability can be employed.
Received signals from different base stations in flat
fading environment are modeled as follows: Let sk
be the transmitted symbol from kth base station, 1 ≤
k ≤ K. Then the received signals are of the form rk =
hksk + nk, where hk and nk refer to channel impulse
response and noise, respectively. We assume that hk
and nk are complex zero-mean Gaussian variables
and denote by γk = |hk|2
the instantaneous SNR
corresponding to the kth base station. The selection
between base stations in HHO is based on the mean
signal levels, denoted by ¯γk = E{γk}.
B. Soft Handover
In soft handover, two or more base stations transmit
the same data to the mobile station and the received
signals are combined at the mobile station by maximal
ratio combining (MRC), and the instantaneous SNR is
given by γ =
K
k=1 γk.

3. DRAFT
C. Site Selection Diversity Transmission
In SSDT, mobile selects the base station with the
largest received instantaneous SNR using fast phys-
ical layer signaling. Hence, γ = max{γk : 1 ≤
k ≤ K}. We assume that the feedback bit error
probability is constant and bit errors are uniformly
distributed in time. The model can be considered to be
approximately valid in FDD WCDMA since the fast
uplink power control is applied to the dedicated control
channel carrying the feedback information. Naturally,
the assumption does not hold any more with high
mobile speeds when the delay of the feedback loop
exceeds the coherence time of the channel. However,
the assumption is well justified within low mobility
environments.
III. ANALYSIS
Here we will study the performance of HHO, SHO
and SSDT in terms of bit error probabilities (BEP)
assuming BPSK modulation and flat Rayleigh fading
environment. Under the assumptions, BEP of single
antenna transmission (SA) as well as the BEP corre-
sponding to MRC and selection combining (SC) are
well known. The mathematical formulas are the same
for both uplink and downlink direction provided that
powers are properly scaled.
When base station antennas are not placed within
the shadow fading coherence distance, mean received
powers ¯γk(µk) of fast fading process are different,
and BEP can be written in the form P(¯γ) :=
P(¯γ1(µ1), ¯γ2(µ2), . . . , ¯γK(µK)), where µk refers to
average power level of shadow fading from kth base
station. After finding the suitable BEP formulas, the
remaining problem concerns with the selection of µk.
We assume that µk are identically distributed, because
the assumption favours SHO and SSDT. Although
being identically distributed, the values of µk are not
equal but follow Gaussian distribution.
It is well known that bit-error probabilities of com-
posite fading channels cannot be solved in closed
form. Instead, we approximate the BEP by replacing
{µk}K
k=1 by mean values of the corresponding order
statistics
¯µ(k) = E{µ(k)}, µ(1) ≥ µ(2) ≥ · · · ≥ µ(K),
where the subscript in the brackets refers to
the ranking of the variables. The final BEP re-
sults are then given in the form P(¯γ) :=
P(¯γ1(¯µ(1)), ¯γ2(¯µ(2)), · · · , ¯γK(¯µ(K))), where ¯γ is the
total system power and the scaling of the powers is
defined as
¯γk = ¯γνk/ν, νk = 10¯µ(k)/10
, ν =
K
k=1
νk. (1)
Hence, ¯γ1 + ¯γ2 + · · · + ¯γK = ¯γ. We note that first
moments of order statistics for Gaussian distribution
are needed to make comparisons between the three
methods. It will be seen that approximative analytical
results align well with simulation results of composite
log-normal and Rayleigh fading channels.
A. Hard Handover
Hard handover is based on long term channel mea-
surements, and the average received power correspond-
ing to the dedicated base station is given by
µ(1) = max{µ1, µ2, . . . , µK}, (2)
where µk is the mean SNR (in decibels) corresponding
to the base station k. We assume that HHO is too
slow to mitigate the fast fading and therefore the BEP
corresponding to HHO depends only on µ(1). This
results in the problem of finding the maximum among
Gaussian variables. In general, the distribution of the
maximum of K n.i.i.d random variables is given by
f(µ) =
K
k=1
fk(µ)
K
l=1,l=k
Fl(µ), (3)
where fk(·) is the pdf and Fk(·) is the cdf of the av-
erage SNR related to kth base station. In the proposed

4. DRAFT
model we have
fk(µ) =
1
√
2πσk
e−(µ−¯µk)2
/2σ2
k ,
Fk(µ) =
1
2
1 + erf
µ − ¯µk
√
2σk
.
(4)
In the following analysis we consider the case where
path loss and shadow fading characteristics of all base
stations are the same ¯µ0 := ¯µ1 = ¯µ2 = · · · = ¯µK,
σ0 := σ1 = σ2 = · · · = σK , and the distribution of
the maximum is now given by
f(1)(µ) = K · f0(µ)F0(µ)K−1
.
The performance of HHO is evaluated as follows: First
we compute the expectation for the average received
power,
¯µ(1) = E{µ(1)} =
∞
−∞
Kµf0(µ)F0(µ)K−1
dµ. (5)
Then the result is substituted into the BEP formula
of single antenna transmission, which in case of flat
Rayleigh fading is given by
PHHO(¯γ) =
1
2
1 −
¯γ
1 + ¯γ
, (6)
where ¯γ = 10¯µ(1)/10
refers to the mean SNR. Let us
consider the special case of two base stations, which
allows a closed-form solution for ¯µ(1) given by
¯µ(1) = ¯µ0 +
σ0
√
π
. (7)
A detailed computation of the result can be found in
the Appendix. More closed-form and numerical results
for the moments of order statistics of Gaussian random
variables up to K = 7 can be found in [6], [7].
B. Soft Handover
The distribution of the instantaneous SNR, received
from kth base station is given by
fk(γ) =
1
¯γk
e−γ/¯γk
, γ > 0 (8)
and in the following we have ¯γk = ¯γl if k = l. This is
due to the assumption that base stations are not placed
within the shadow fading coherence distance, see [8].
With MRC the distribution of the received SNR from
K base stations is known to be
f(γ) =
K
k=1
akfk(γ), ak =
K
l=1,l=k
¯γk
¯γk − ¯γl
.
and after proper integration the bit error probability
becomes
PSHO(¯γ) =
1
2
K
k=1
ak 1 −
¯γk
1 + ¯γk
. (9)
C. Site Selection Diversity Transmission
Now the distribution f(·) of SNR is obtained by
combining (3), (8), and the cumulative distribution cor-
responding to (8). Bit error rate of BPSK modulation
for a fixed mean SNR is given in terms of comple-
mentary error function, and the bit error probability as
a function of SNR is given by
PSSDT(¯γ) =
∞
0
f(γ)g(γ)dγ, g(γ) =
1
2
erfc(
√
γ).
Let us briefly recall the computation of BEP for SSDT
when mean received powers are not equal. Assume
that F(·) is the cumulative distribution function cor-
responding to f(·). Using integration by parts we find
that
PSSDT(¯γ) = −
∞
0
F(γ)g′
(γ)dγ.
Here the expression for g′
(·) is obtained from 7.1.19
of [9] and we find that the bit error probability attains
the form
PSSDT(¯γ) =
1
√
4π
∞
0
e−γ
√
γ
K
k=1
(1 − e−γ/¯γk
)dγ.
The product term can be expressed as a sum
K
k=1
(1 − e−γ/¯γk
) =
L
l=1
ale−blγ
,
where L = 2K
and coefficients al and bl are easily
found when K is small. By employing the sum ex-
pression and analytical integration we find that
PSSDT(¯γ) =
1
√
4π
L
l=1
al
∞
0
e−γ(1+bl)
√
γ
dγ =
1
2
L
l=1
al
√
1 + bl
.
(10)

5. DRAFT
The same power normalization is applied as explained
before. In the special case of two base stations the BEP
attains the form
PSSDT(¯γ) =
1
2
1−
¯γ1
1 + ¯γ1
−
¯γ2
1 + ¯γ2
+
¯γ1¯γ2
¯γ1 + ¯γ2 + ¯γ1¯γ2
,
where ¯γ1 and ¯γ2 are defined according to (1).
Feedback Errors: In FDD WCDMA, the number
of base stations in SSDT is limited to eight due to the
length of the temporary ID field. Based on the received
ID, base stations independently decide whether to
transmit or not, and in case of feedback errors it
is possible that none of the base stations, or more
than one base station are transmitting. In the latter
case we assume that the receiver is able to combine
all the transmitted signals using MRC, and transmit
power is evenly divided among the transmitting base
stations. For simplicity, we assume that feedback error
probability p is the same in all base stations, although
in practice, error probabilities vary due to different
shadow fading and path loss characteristics.
Consider first a general model concerning a system
of K base stations and feedback word length of κ bits,
and assume that a feedback word w0 is transmitted
from mobile station. Then, after being corrupted by the
physical channel, feedback words wk, k = 1, 2, . . ., K
are received in the K base stations. There are K · L,
L = 2κ
different combinations of received feedback
words in total, and we introduce an additional subscript
λ and denote by wλ = (wk,λ)K
k=1 the joint received
feedback word, where λ refers to the set Λ of indices
corresponding to all possible combinations. The BEP
of SSDT in the presence of feedback errors can now
be expressed in the form
Pp
SSDT(¯γ) =
λ∈Λ
p(wλ|w0)P(¯γ|wλ), (11)
where p(wλ|w0) is the probability that base stations
receive the feedback words wk,λ on the condition
that word w0 is transmitted from mobile station and
P(¯γ|wλ) is the receiver BEP in the mobile station
on the condition that downlink transmission obeys the
joint feedback word wλ.
Since received feedback words in different base
stations are independent we find that
p(wλ|w0) =
K
k=1
p(wk,λ|w0). (12)
Let us denote by p0 = 1 − (1 − p)κ
the probability
of a feedback word error in the presence of feedback
bit error probability p. Without losing the generality
we can assume that the first base station (k = 1) is
selected according to uncorrupted feedback word w0.
Then we have
p(wk,λ|w0) ∈



{p0, 1 − p0}, k = 1,
{ p0
L−1 , 1 − p0
L−1 }, k > 1,
where p0/(L −1) is the probability that a base station
which is not selected according to w0 will receive an
erroneous feedback word asking for the transmission.
Consider next a lower bound for BEP of SSDT. If
all base stations suspend their transmission, then the
BEP in the receiver is 1/2 and there holds
Pp
SSDT(¯γ) ≥
1
2
· p0 1 −
p0
L − 1
K−1
=
1
2
· pout, (13)
where the last term in the right indicates the probability
of no transmission denoted by pout. It is found that the
receiver BEP strongly depends on pout which further
depends on the feedback bit error probability p. If
channel coding is not applied, then estimate (13) shows
that SSDT will work properly only if p is very small.
For example, WCDMA simulations typically assume
a nominal 4 % feedback bit error probability. Then,
according to the bound (13) the receiver BEP is 5 − 6
% depending on the number of base stations when
κ = 3. Furthermore, it is straightforward to calculate
the corresponding feedback word error probabilities
for different ID codes given in [1].
The situation is not that bad when channel cod-
ing is employed, because the decoder in the mobile

6. DRAFT
station may take into account the reliability of the
received soft bits and the lack of the received signal
is practically seen as a code puncturing. If the SSDT
selection is done several times during the interleaving
period, the rate of the code puncturing remains small.
In WCDMA, the maximum number of updates is five
per 10 ms radio frame [1]. In this case we may ignore
the probability of no transmission, and the probabilities
of different joint feedback words need to be scaled by
pout in (11). Furthermore, WCDMA specification [1]
states that base station is selected as a non-primary one
if the received ID does not match the base station’s ID
and the received signal quality is less than a predefined
threshold. The additional threshold condition has the
effect of decreasing the value of pout when compared
to that in (13).
Let us study in more detail the case K = 2. Assume
that w0 refers to the first base station and further,
assume that w1 refers to the joint event ’Only the first
base station is transmitting’, w2 refers to the event
’Only the second base station is transmitting’ and w3
refers to the event ’Both base stations are transmitting’.
Then we obtain
p(w1) = (1 − p0) 1 −
p0
L − 1
, p(w2) =
p2
0
L − 1
,
p(w3) = (1 − p0)
p0
L − 1
, pout = p0 1 −
p0
L − 1
.
The corresponding receiver bit error probabilities for
w1, w2 and w3 are given by
P(¯γ|w1) = PSSDT(¯γ), P(¯γ|w2) = PMin(¯γ),
P(¯γ|w3) = PSHO(¯γ),
where PMin(·) refers to the BEP corresponding to
the transmission from the second base station for
which γ = min{γ1, γ2}. By employing the derivations
presented in this section it is not difficult to see that
PMin(¯γ) =
1
2
¯γ1¯γ2
¯γ1 + ¯γ2 + ¯γ1¯γ2
.
Now we have means to compute Pp
SSDT(·) from (11).
−10 −5 0 5 10 15 20
10
−3
10
−2
10
−1
SNR [dB]
BitErrorProbability
Fig. 1. Bit error probabilities for SSDT with p = 0 (solid line),
p = 0.01 (△), p = 0.04 (∇) and p = 0.1 (£) when K = 2 and
σ = 6.
D. Performance Comparisons
In the following we assume that κ = 3 correspond-
ing to the WCDMA specification. Let us begin by
studying the effect of feedback errors to the perfor-
mance of SSDT. Figure 1 depicts BEP curves when
K = 2 and σ = 6 dB for different feedback bit
error rates. First set of curves corresponds to the case
where BEP of event ’No transmission’ is 1/2, and the
presence of error floor is clearly seen. The BEP curves
in the second set are computed by neglecting the effect
of suspended transmission. The curves in the second
set do not seriously suffer from erroneous feedback.
It is found that the BEP of SSDT is heavily corrupted
by feedback bit errors if event ’No transmission’ is not
taken into account in the channel decoding scheme.
Figures 2 and 3 depict performance results for HHO,
SHO and SSDT in terms of BEP for K = 4 and
σ = 6 dB and σ = 12 dB, respectively, assuming
error-free feedback in SSDT. Solid lines refer to an-
alytical approximations and dashed lines denote BEP
obtained by simulating composite fading channels. It
is found that SSDT provides the best performance
when feedback is error free. Moreover, for high BEP

7. DRAFT
levels (BEP>0.1) HHO outperforms SHO. Analytical
and simulation results agree well except with small
BEP, which is partly due to limited number of trials
(1000) to simulate different shadow fading powers µk.
Comparing the two figures shows that the performance
of SSDT and SHO is deteriorated when deviation of
the shadow fading increases.
Finally, we note that the ranking of the studied
three methods from performance point of view may be
different when an additional fast transmission power
control is applied in the forward link — as can be
the case in real systems designed for voice transmis-
sion. However, then the transmit powers with different
handover methods become different, fair comparison
between the methods is difficult, and the additional
performance gain might be obtained with the cost of
additional interference in the network.
IV. CONCLUSIONS
We compared site selection diversity transmission
(SSDT) with hard handover and soft handover using
the receiver bit error probability as a performance
measure. Results show that feedback bit errors reduce
the link level performance of SSDT caused by the error
event when all base stations suspend their transmis-
sions. Analytical results approximating the effect of
composite fading by first moments of order statistics of
log-normal distribution align well with the simulations
of composite fading channels.
V. APPENDIX
Here we consider the computation of the expectation
of the maximum of K equally distributed Gaussian
variables. By combining (4) and (5) we obtain
¯µ(1) =
∞
−∞
Kµe
−
(µ−¯µ0)2
2σ2
0
√
2πσ0
µ
−∞
e
−
(ξ−¯µ0)2
2σ2
0
√
2πσ0
dξ
K−1
dµ.
−10 −5 0 5 10 15 20
10
−3
10
−2
10
−1
SNR (dB)
BitErrorProbability
Fig. 2. Bit error probabilities for HHO (x), SHO (*) and SSDT
with p = 0 (o) when K = 4 and σ = 6 dB. Solid and dashed
curves refer to analytical and simulation results, respectively.
−10 −5 0 5 10 15 20
10
−3
10
−2
10
−1
SNR (dB)
BitErrorProbability
Fig. 3. Bit error probabilities for HHO (x), SHO (*) SSDT with
p = 0 (o) when K = 4 and σ = 12 dB. Solid and dashed curves
refer to analytical and simulation results, respectively.
Let us substitute t = (ξ − ¯µ0)/
√
2σ0 and s = (µ −
¯µ0)/
√
2σ0. Then the expectation ¯µ(1) attains the from
¯µ(1) =
K
√
2σ0
√
π
∞
−∞
se−s2 1
√
π
s
−∞
e−t2
dt
K−1
ds
+
K ¯µ0
√
π
∞
−∞
e−s2 1
√
π
s
−∞
e−t2
dt
K−1
ds.
(14)
Here the integral in brackets can be written in terms

8. DRAFT
of error function,
1
√
π
s
−∞
e−t2
dt =



1
2 (1 + erf(s)), s ≥ 0,
1
2 (1 − erf(s)), s < 0.
After dividing the integration in (14) with respect to
point s = 0 we find that
¯µ(1) =
K
√
2σ0
√
π
I+
1 − I−
1 +
K ¯µ0
√
π
I+
2 + I−
2 (15)
where each of I±
k refer to an integral, defined by
I±
1 =
∞
0
se−s2 1
2
(1 ± erf(s))
K−1
ds,
I±
2 =
∞
0
e−s2 1
2
(1 ± erf(s))
K−1
ds.
If K = 2 then we have
I+
1 −I−
1 =
∞
0
se−s2
erf(s)ds, I+
2 +I−
2 =
∞
0
e−s2
ds.
(16)
The latter integral is equal to
√
π/2 and a closed-form
expression for the former integral can be obtained by
7.4.19 of [9] after substituting s =
√
u. The result is
then given by (7).
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