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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 10, OCTOBER 2001
Partial Successive Interference Cancellation in Hybrid DS/FH Spread-Spectrum
Multiple-Access Systems
Jin Hoon Kim and Sang Wu Kim
Abstract—Partial successive interference cancellation is considered in hybrid DS/FH spread-spectrum multiple-access (SSMA)
systems. We first show that the lowest BER attained by employing
full interference cancellation in DS/SSMA systems can almost be
achieved by employing a partial interference cancellation in hybrid DS/FH systems. The reduction in the number of cancellations
translates into an alleviation of correlator speed requirements and
a reduction in delays incurred in interference cancellations. The
optimal number of frequency slots that minimizes the BER is investigated as a function of the number of interference cancellations.
The effect of imperfect power control on the BER is investigated.
I. INTRODUCTION
I
N THIS letter, we consider a partial successive interference
cancellation in hybrid direct-sequence/frequency-hopped
spread-spectrum multiple-access (DS/FH SSMA) systems. The
drawback of successive interference cancellation (SIC) is the
requirement for a high processing speed of the correlator. For
users, the data from the weakest
DS/SSMA systems with
correlation times. Therefore,
user is decoded only after
bps, the correlator must
in order to ensure a data rate of
bps.
perform the correlation at a much higher rate of
Thus, the processing speed of the correlator may limit the
number of possible cancellations, particularly for a large . In
this letter, we show that the lowest BER attained by employing
full interference cancellation in DS/SSMA systems, can almost
be attained by employing a partial interference cancellation in
hybrid DS/FH systems. The reduction in the number of cancellations translates into a reduction of both the correlation speed
requirement and the delay incurred in cancelling interference.
We consider a hybrid DS/FH SSMA system [1] in which there
are frequency slots, and a DS signal having a spreading gain,
defined as the number of chips per information bit, of , is sent
(bandover a frequency slot. We assume that the product
width expansion factor) is fixed to maintain the overall band) and the FH system
width fixed. Note that the DS system (
) are two extreme cases of the hybrid DS/FH systems.
(
users, in which each user
For hybrid DS/FH systems with
selects a frequency slot randomly, the average number of in. Therefore, the average
terfering users in a slot is
number of interference cancellations can be reduced by a factor
of , while the spreading gain is also reduced by a factor of
because of the fixed total bandwidth. When the number of interference cancellations is limited (partial cancellation), BER can
Paper approved by C.-L. Wang, the Editor for Equalization of the IEEE Communications Society. Manuscript received January 14, 2000; revised September
15, 2000, and January 31, 2001. This paper was presented in part at the 2000
IEEE 51st Vehicular Technology Conference, Tokyo, Japan, May 15–18, 2000.
The authors are with the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305–701, Korea.
Publisher Item Identifier S 0090-6778(01)09105-X.
be reduced by increasing beyond 1, because the amount of interference left after a partial cancellation can be decreased by
increasing . However, a further increase of does not essentially decrease the BER, because the interference can almost be
cancelled even with a limited number of cancellations, when is
large. Increasing results in only decreasing the spreading gain.
Therefore, we expect that there exists an optimum (and )
that minimizes BER for a given number of interference cancellations. In particular, if the multiple-access interference (MAI)
can be fully cancelled (full cancellation), we would expect that
(DS) yields the lowest BER, because increasing beyond 1 does not essentially decrease the amount of interference left after full cancellation and results in only decreasing
the spreading gain. We investigate the optimum as a function
of the number of interference cancellations. We will also investigate the effect of imperfect power control on the BER by simulation.
The rest of this letter is organized as follows. Section II describes the system model. In Section III, we derive the average
BER of a hybrid DS/FH SSMA system with SIC as a function
of the number of interference cancellations. In Section IV, we
present our numerical results and then discuss advantages that
the hybrid system provides over the conventional DS system
with full interference cancellation. We also present simulation
results for the situation where the power control is not perfect.
Finally, conclusions are made in Section V.
II. SYSTEM MODEL
We consider an asynchronous hybrid DS/FH SSMA system,
wherein there are users. The th user generates a binary data
at a rate of
bps which is multiplied by a
sequence
and then sent over one of
random spreading sequence
possible frequency slots using a random frequency hopping pat. We assume a slow frequency-nonselective Rayleigh
tern
fading channel. This assumption is valid for channels with a
small delay spread, such as indoor systems. Then, the received
is given by
signal
(1)
is a random variable
where is the transmitted power, and
representing the power control error for the th user. We assume
is log-normally distributed with standard deviation
that
[dB] [4], [5]. It is shown in [4] that
is between 1 and 2 [dB]
is the channel gain of the th user which
in practical systems.
for all . and
are
is Rayleigh distributed with
the channel induced delay and the phase of the th user, which
0090–6778/01$10.00 © 2001 IEEE
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 10, OCTOBER 2001
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Fig. 1. Overall receiver block diagram.
are uniformly distributed over
and
, respectively.
is the Gaussian noise with mean zero and two-sided power
. It was shown in [7] and [8] that interspectral density of
ference cancellation is fairly robust to phase and timing errors.
Therefore, we assume that the estimations on the time delay and
phase are perfect as in [2], [3], and [6]. We also assume that the
receiver knows the spreading sequences and hopping patterns of
all users.
The overall receiver block diagram for the hybrid DS/FH
system is illustrated in Fig. 1. The received signal is first
dehopped, and users occupying the same frequency slot go
through (partial) successive interference cancellations. If we let
be the number of occupied frequency slots, then successive
groups
interference cancellations are performed in all
be the signal after dehopping and
simultaneously. We let
lowpass filtering and the number of hit users in the frequency
. Then the correlator outputs
slot of the desired user be
are compared, and the strongest correlator
output goes through a hard decision to get the data estimation,
after regeneration [2]. The remaining
and is cancelled from
signals are cancelled in order of decreasing magnitudes of
cancellations are completed. The
correlator outputs until
data estimations for uncancelled users are made based on
the correlator outputs after the th cancellation. We assume
no knowledge of the users’ powers. We use the outputs of
correlation receiver to rank the users instead of separate channel
estimates.
III. PERFORMANCE ANALYSIS
In this section, we derive the BER of partial SIC
,
system assuming that power control is perfect (
) and users are cancelled in order of
,
. The
received signal strengths
actual algorithm, using correlator outputs to rank users, may
have this order changed. However, we will see that comparisons
with simulation show good accuracy. The effect of imperfect
power control ( being random variable) will be analyzed by
computer simulation.
be the ordered set of
, so that
We let
.
for the th strongest user
The decision variable
) is given by [2]
(
(2)
where
and
is the data bit,
or
, of the th strongest user,
(3)
where
, and
In (3), the first term is the MAI caused by the uncancelled users,
the second term is due to the Gaussian noise, and the third term
is the cumulative noise due to imperfect cancellations.
is a Gaussian random variable with
We assume that
mean zero [1], [2]. For the case of perfect power control, since
and
,
of , normalized by
, is given by
the variance
(4)
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 10, OCTOBER 2001
where
is the information bit energy. The probability
of
, given
, is given by
density function (pdf)
[2]
(5)
and
,
, are the
where
pdf and cumulative distribution function (cdf) of the unordered
, respectively. It folRayleigh distributed random variable
lows from (5) that
(6)
Therefore, the error probability
, is given by
user, given
for the th strongest
Fig. 2.
[dB].
P versus E =N [dB], K = 20, N = 10, qN = 100, = 0
(7)
The detailed derivations of (6) and (7) are given in [9]. Then,
, is
the conditional average BER, given
(8)
It follows from (4) and (6)–(8) that the average BER
is given by [1]
averaging over
after
(9)
where
asynchronous frequency hopping
synchronous frequency hopping
is the number of bits per
is the probability of a full hit, and
obtained
hop. Fig. 2 is a plot of average BER’s versus
by simulation and analysis. We can see that comparisons with
simulation show good accuracy. Similar observations have been
made in [2].
IV. NUMERICAL RESULTS AND DISCUSSIONS
Fig. 3 is a plot of the average BER , versus the number
deof cancellations for several values of . As expected,
creases as increases, but then gets saturated beyond a certain
value of . The saturation is attained faster with a larger because of the reduced average number of interfering users in each
frequency slot. Once all interfering users are cancelled, a further
increase of does not essentially decrease BER. The lowest
is attained with
(corresponding to the largest ) and
P versus J , E =N = 25 [dB], K = 20, N = 10, qN = 100,
= 0 [dB].
Fig. 3.
(full interference cancellation). But, it can almost be
when we use
, thereby alleviating
achieved with
the high correlation speed requirement and reducing the delay
incurred in cancelling interferences.
versus for several values of . We
Fig. 4 is a plot of the
find that there exists an optimal number of frequency slots that
,
minimizes the BER for a given . For example, where
, is 10. When no
the optimal number of frequency slots,
, FH
interference cancellation is performed
provides a slightly lower BER than does DS
.
, that minimizes the
Fig. 5 is a plot of the optimum ,
versus . We find that as decreases,
inaverage BER
creases. This indicates that avoiding interference by increasing
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 10, OCTOBER 2001
P versus q , E =N = 25 [dB], K = 20, N = 10, qN = 100,
= 0 [dB].
Fig. 4.
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Fig. 6.
100.
P versus [dB], E =N = 25 [dB], K = 20, N = 10, qN =
V. CONCLUSION
Fig. 5.
q
versus J , K = 20, N = 10, qN = 100, = 0 [dB].
is better than increasing the spreading gain when the number
of interference cancellations is limited.
The effect of imperfect power control is illustrated in Fig. 6,
.
where BER is plotted against [dB] for several pairs of
We find that when the interference cancellation is not employed
, the FH
is more robust to power control er. We also find that the lowest BER
rors than the DS
attained by DS with full interference cancellation,
case, can almost be achieved by a hybrid DS/FH system
case, for all . Parwith partial cancellation,
dB (practical range of interests), the
ticularly, for
average BER is almost insensitive to power control errors for
both systems.
We considered a partial successive interference cancellation
in hybrid DS/FH SSMA systems. We derived the average BER
as a function of the number of interference cancellations in
a frequency-nonselective Rayleigh fading channel. We found
that the lowest BER attained by employing full interference
cancellation in DS/SSMA systems can almost be achieved
by employing a partial interference cancellation in hybrid
DS/FH systems. The reduction in the number of cancellations
translates into an alleviation of correlation speed requirements
along with a further reduction of delays incurred in interference
cancellations. We also found that the optimum number of
frequency slots that minimizes the average BER increases
as the number of interference cancellations decreases. This
indicates that avoiding interference by increasing the number
of frequency slots is better than increasing the spreading gain
when the number of interference cancellations is limited. When
no interference cancellations are performed, we found that a
) than DS
slightly lower BER can be provided with FH (
). We also found that, even when the power control is
(
not perfect, the hybrid DS/FH system with partial cancellation
can almost achieve the lowest BER of DS/SSMA system with
full cancellation.
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