Generalized Receiver with Decision-Feedback Equalizer for

Multicode Wideband DS-CDMA

VYACHESLAV TUZLUKOV

Department of Technical Maintenance of Aviation and Radio Electronic Equipment

Belarusian State Aviation Academy

77, Uborevicha Str., 220096 Minsk

BELARUS

or at most equal to that of linear equalizers. When all the active codes belong to the desired user, the ideal deci-

sion-feedback equalizer is able to eliminate multicode interference and approach the performance of the single-

code case at high signal-to-noise ratio (SNR) range. Secondly, we apply the hypothesis-feedback equalizer or

tentative-chip decision-feedback equalizer in the multicode scenario. The tentative-chip decision-feedback equ-

alizer outperforms the chip-level linear equalizer and the decision-feedback equalizer that only feeds back the

symbols already decided. The performance gain increases with SNR, but decreases with the number of active

codes owned by the other users. When all the active codes are assigned to the desired user, the tentative-chip

decision-feedback equalizer eliminates the multicode interference and achieves single-user performance at the

high SNR, similarly, to the ideal decision-feedback equalizer. The asymptotic performance of the decision-feed-

back equalizer is confirmed through the bit error rate (BER) simulation over various channels.

access (DS-CDMA) technology [1], [2] is the high-

speed and multirate wireless communication scheme

Multicode DS-CDMA technology separates the data

symbols of a user into several parallel streams and

spreads them using different channelization codes.

Thus, users with heterogeneous data rates can be su-

pported. Multicode transmission has been incorpora-

ted into the five-generation wideband DS-CDMA

(WDS-CDMA) physical layer standards [3].

In WDS-CDMA wireless communication syst-

multiuser chip signals received by a mobile station

are synchronous and suffering the same frequency-

selective fading. The channelization codes associa-

ted with a given user are known at the receiver. The-

followed by the code correlator, is proposed to sup-

press both intersymbol interference and multiuser

access interference. Training-based or blind adapti-

ve linear equalizers have appeared in, for instance,

[10] and [11].

It has been shown [12], [13] that decision-feed-

back equalizer can further reduce the effect of the

intersymbol interference in the short code case,

where the periodic short codes and the physical cha-

back equalizer has to operate at the chip level. How-

ever, feedback chips cannot be reliably determined

until the whole symbol has been received. One way

to solve this dilemma is to only feedback the chips

of the past symbols of the desired user, which we

call the past symbol decision-feedback equalizer.

The past symbol decision-feedback equalizer can-

cels the intersymbol interference caused by the alre-

ady decided symbols, leaving the interchip interfere-

nce caused by the chips in the current symbol intact.

than actual decisions of multicode symbols of the

desired user.

In this paper, we first analyze the symbol-level

minimum mean-square-error (MMSE) of an ideal

chip-level decision-feedback equalizer assuming

that the interchip interference associated with the

multicodes of the reference user can be completely

removed by feeding back all the past chips of the in-

tra user signals. It is found that the ideal decision-fe-

edback equalizer always outperforms the linear equ-

tative-chip decision-feedback equalizer in multicode

scenario. The simulation of the bit-error rate (BER)

demonstrates that the tentative-chip decision-feed-

back equalizer does achieve the single-code perfor-

mance at the high SNR range when all the active co-

des are assigned to the reference user.

The rest of this paper is organized as follows.The

system model is described in Section 2. The genera-

and some users may be assigned multiple codes.

, for

,where

is the nu-

base station transmitter and the mobile station rece-

iver takes the form:

of the k-th path, respectively;

is the transmitter

slot and Rayleigh fading independently from frame

to frame.

The signal received by the mobile station takes

the form

is the chip period and

nal processing theories can deliver only the suffici-

ent statistics of the mean or variance of the likeliho-

od function. Thus, the generalized approach to sig-

nal processing in noise implementation allows us to

obtain more information about the parameters of the

desired transmitted signal incoming at the generaliz-

The generalized receiver (GR) consists of three

channels (see Fig. 2): the GR correlation detector

channel (GR CD) – the preliminary filter (PF), the

multipliers 1 and 2, the model signal generator

(MSG); the GR energy detector channel (GR ED) –

the PF, the additional filter (AF), the multipliers 3

and 4, the summator 1; and the GR compensation

these two filters or linear systems have the same am-

plitude-frequency characteristics or impulse respon-

ses. The AF central frequency is detuned relative to

the PF central frequency.

There is a need to note the PF bandwidth is mat-

ched with the transmitted signal bandwidth. If the

detuning value between the PF and AF central freq-

uencies is more than 4 or 5 times the transmitted si-

gnal bandwidth to be detected, i.e.,

, where

eve that the processes at the PF and AF outputs are

uncorrelated because the coefficient of correlation

between them is negligible (not more than 0.05).

This fact was confirmed experimentally in [19] and

[20] independently. Thus, the transmitted signal plus

noise can be appeared at the GR PF output and the

noise only is appeared at the GR AF output. The sto-

are the impulse responses

AF bandwidth and central frequency can be

assigned, too (this bandwidth can-not be used by the

transmitted signal because it is out of its spectrum).

The case when there are interfering signals within

the GR AF bandwidth, the action of this interference

on the GR detection performance, and the case of no

ideal condition when the noise at the GR PF and GR

AF outputs is not the same by statistical parameters

are discussed in [21] and [22].

Under the hypothesis

(“a yes” transmitted sig-

nal), the GR CD generates the signal component

caused by interaction between the model

signal

, forming at the MSG output, and the in-

ED generates the transmitted signal energy

the random component

tion between the transmitted signal

at the PF output. The main purpose of the

same nature of the noise

the transmitted signal to be detected

and the

model signal

is defined as:

(8)

where

mponent

of the GR ED. Satisfying the GR

Practical realization of the condition (8) at

output, see Fig. 2, can be defined as

where

hypothesis

and for all i and k, the process

the same statistical parameters as the noise

practice, there is a difference between the statistical

parameters of the noise

fference impacts on the GR detection performance is

discussed in detail in [17, Chapter 7, pp. 631-695]

and in [23]-[29].

The decision statistics at the GR output present-

tennas and antenna arrays is effective to mitigate the

where

is the vector of the random process at the GR PF

output and

cision statistics

the statistical sense, respectively:

is the background

and subtracted from the received samples. The

(17)

.

that mini-

The above expression indicates that in the general

case, under the assumption of perfect past decisions,

the mean-square error is contributed by both precur-

We now find a precise solution to the problem in

(22). As shown in Appendix I, using a calculus-of-

variation, we can obtain an integral equation for

then integrating from minus to plus infinity over va-

riable t, we can obtain a set of linear equations invo-

lving

for

where

. (27)

. (29)

is

. (31)

is the Dirac delta-function. From (32),

with the number of active codes

,