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In recent times, there has been growing interests in integration of voice, data and video traffic in wireless communication networks. With these growing interests, WCDMA has immerged as an attractive access technique. The performance of WCDMA system is deteriorated in presence of multipath fading environment. The paper presents space-time coded minimum mean square error (MMSE) Decision Feedback Equalizer (DFE) for wideband code division multiple access (WCDMA) in a frequency selective channel. The filter coefficients in MMSE DFE are optimized to suppress noise, intersymbol interference (ISI), and multiple access interference (MAI) with reasonable system complexity. For the above structure, we have presented the estimation of BER for a MMSE DFE using computer simulation experiments. The simulation includes the effects of additive white Gaussian noise, multipath fading and multiple access interference (MAI). Furthermore, the performance is compared with standard linear equalizer (LE) and RAKE receiver. Numerical and simulation results show that the MMSE DFE exhibits significant performance improvement over the standard linear equalizer (LE) and RAKE receiver.

During the period of last one decade, the large demands for wireless services and high data speeds have driven the wireless cellular networks to a tremendous growth. These large demands require some advanced techniques like WCDMA that can support more users and higher data rates. WCDMA has been accepted as standard access method for the third and fourth generation wireless systems. The WCDMA system assigns each user a specific signature sequence from the signature set. One limiting factor in the capacity (i.e. the number of users) of the WCDMA systems is the multiple access interference (MAI). In fact, in WCDMA system, multiple access interference (MAI) and intersymbol interference (ISI) are caused by multipath dispersion and are major problems. These problems cannot be efficiently suppressed by conventional RAKE receivers. The MAI caused by one user is usually small, but as the number of interferers or their power increases, effect of MAI becomes noticeable. To alleviate the effect of MAI, a number of multiple user detection methods have been proposed in literature in recent years [

Another limiting factor in the cellular systems is fading. An usual technique for combating fading is spatial diversity. In WCDMA systems, two methods of spatial diversity and interference cancellation can be combined to increase the system performance and capacity. The combination of MUD and receive diversity techniques has been proposed in [2,3]. In third generation WCDMA systems, the processing transmit gain may be very small. This makes the use of diversity quite effective. Transmit diversity can be used to alleviate fading efficiently. There are several forms of transmit diversity. In openloop scenarios, where the transmitter does not have the channel state information, space-time transmit diversity (STTD) is generally used. When channel state information is available, closed-loop transmit diversity such as beam forming can be used. Over the period of last decade, various transmit diversity schemes have been proposed in modern wireless communications to combat fading. Among various proposed techniques, Alamouti’s space-time block code [

WCDMA downlink has two interesting features. One is that all transmissions are synchronized and the other is that the spreading codes can be orthogonal. By taking advantages of these features, the chip-level equalization has been proposed to mitigate MAI with a despreader [5, 6]. A despreader can mitigate the MAI after chip-level equalization to restore the orthogonality. In [

The zero forcing receivers can completely suppress the ISI and multi-user interference under certain conditions. However, explicit knowledge of all the signature waveforms is required and the noise may be enhanced. Hence, the receiver designed by using the MMSE criterion seems to be better than zero-forcing receivers in terms of their bit error rate (BER) performance. In this paper, we investigate and analyze a minimum mean-square error (MMSE) decision feedback equalizer (DFE) for spacetime coded WCDMA downlink channel to achieve better performance than the chip level LE and a RAKE receiver in a frequency selective channel.

The rest of the paper is organized as follows. The signals and system models have been introduced in section 2.In subsection 2.1 we have discussed the basic spacetime encoder in WCDMA. In subsection 2.2,we have presented the structure of a traditional decision feedback equalizer (DFE). The space-time coded decision feedback equalizer (DFE) has been formulated in subsection 2.3. Subsection 2.4 presents the mathematical analysis. In section 3, we have formulated the simulation environments. Computer simulation results are presented in section 4 to see the performance and we conclude the paper with some remarks in section 5.

_{0} is sent on transmit antenna A and c_{1}^{*} is sent on antenna B.

During symbol period 1, c_{1} is sent on transmit antenna A and c_{0}^{*} is sent on antenna B. It is assumed that the same channelization code is used to send these STTD encoded symbols. But, the pseudo-random scrambling codes are different for different symbol periods. Let h_{ji}(t) denote the continuous-time impulse response of the multipath channel from transmitter antenna i to the receive antenna j. A time-variant multipath signal propagation through the mobile cellular radio channel can be modeled as:

h_{ji}(t) = (1)

where Q is the number of channel multipath, d(×) is

the Dirac-delta function, and _{ji, q}(t), _{ji, q}(t) and _{ji, q}(t) are the time-variant attenuation, phase distortion and propagation delay of the qth path from transmit antenna i to receive antenna j, respectively.

We first describe a traditional decision feedback equalizer (DFE) receiver, upon which a two dimensional DFE for WCDMA system builds.

Also, r(n) → received signal, d(n) → transmitted symbols information, → output of DFE.

We concentrate on WCDMA downlink channel with transmit diversity. The system employs two transmit antennas at the transmitter side and one receive antenna at the receiver side. We assume that there are K active users in the cell under consideration and that the intercell interference is negligibly small in cellular scenario. Also, there are M transmit antennas and V receive antennas in the system.

Now, the transmitted signal of user k from antenna m, represented by, is given by

= (2)

where, , n = 0, …., N-1, is the kth user’s spacetime coded data sequence to be transmitted from antenna m within a specific time-frame A_{k} is the average amplitude of the kth user T_{s} is the symbol duration w_{k},_{n}(t) is the signature waveform of user k at the nth symbol period

The signature waveform w_{k}_{,n}(t) is represented as

= (3)

where G is the processing gainT_{c} is the chip durationp(t) is the chip pulse shape signal s_{k},_{n}(i) is the kth user’s signature sequence The spread signal is transmitted over the frequency and time selective channels. The channels from the two base station antennas to the receiver are modeled as Rayleigh multipath fading channels. Then, according to basic equation (1), the impulse response of the channels between the base station transmitter and the mobile station receiver is

h^{(m)}(t) = (4)

where Q is the number of pathsh_{q}(m) is a complex coefficient which is used to model the qth path t_{q} is the delay related to the q^{th} path.

We assume that the number of paths and their delay times are equal for the two channels. Finally, the received signal from all K users at a mobile base station after demodulation is given by r(t) =

(5)

where u(t) is the additive white Gaussian noise (AWGN) with noise variance of s^{2}.

It may be more convenient to consider a discrete-time signal model. Accordingly, the received signal sequence is written as r(n) =

(6)

where r(n) is the received signal sequence, and u_{k} is the white noise sequence.

To achieve transmit diversity; we use Alamouti’s spacetime block code for two transmit and one receive antennas [_{k}(n), n = 0, …., 2N-1, is split into two blocks of odd and even symbols, each having length N. Further, these two blocks are space-time encoded and transmitted during two subsequent periods, each having a duration of NT_{s}. This means that for the first and second period, we have

where n = 0, ……, N–1.

If we place a guard-time t_{g} between two transmission periods, the received signal r(t) consist of two noninterfering signals. Now, let d_{o}(2n) and d_{o}(2n + 1) be the desired symbols to be detected at the receiver. According to _{v}, v = 0, …, i – 1. Then, we have r_{1} =

(8)

r_{2} =

For ideal correlation properties of signature waveforms, there shall be no_{ }ISI and MAI in above samples. Thus, in ideal scenario, a RAKE receiver and a linear equalizer (LE) can work as optimum receiver [_{0}(2n), is written as d_{e}= +

The expression in equation (10) may be written in matrix form as under:

d_{e} = F^{H} Y (11)

Here

F^{H} = [f_{11}(L_{f }– 1), … , f_{11}(0), f_{21}(L_{f }– 1), …..f_{21}(0), b_{11}(L_{b}_{ }– 1), … , b_{11}(0), b_{21}(L_{b }– 1), ….., b_{21}(0)]

And

Y= [r_{1, 0}, ….., r_{1}, L_{f }– 1, r_{2, 0}, ….., r_{2}, L_{f }– 1, d_{o}(2n–2)

….., d_{o}(2n – 2L_{b}), d_{0}(2n – 1), ….., d_{o}(2n_{ }– 2L_{b} + 1)]^{J}

The mean square error (MSE) is given by e = E {|d – d_{o} (2n)|^{2}}

Now, to achieve the performance improvement, we have to minimize the mean square error (MSE). For that purpose, we must decide appropriate value of weight vector. The solution to the MMSE problem is given by F^{H} = A^{–1 G} (14)

where

A= E.{ Y Y^{ H}} (15)

and

G = E{ Y Y d_{o}^{*}(2n)} (16)

To determine matrix A and vector G, we must know the channel model and also we assume that the interfering user’s signature codes and all the information symbols are independent random sequences. Now, the minimum mean-square error for the system can be written as

e_{min} = 1 – G^{ H} S^{–1 G} (17)

We can estimate the overall signal-to-noise ratio per symbol, using the Gaussian approximation, from the MMSE as [

SNR = (1 – e_{min}) /e_{min} (18)

Hence, the bit error rate (BER) can be approximated as under:

P_{e} =

P_{e} =

From above expression, it is obvious that P_{e} depends upon the coefficients of the channel and signature waveform of the desired user.

We study the performance of a chip-rate DFE in a WCDMA downlink channel using QPSK modulation scheme and a spreading factor of 32. We have assumed Rayleigh fading channels and channel coefficients as complex Gaussian random variables. The system transmits the data at 480 kbps, and the frame structure of 10ms duration includes 15 slots. Each slot consists of 160 QPSK symbols that are spread by the Walsh-Hadmard code with period 32. As a whole, a chip rate of 3.84 Mc/s is used. The channel taps are each subject to the Rayleigh fading around their mean value. Throughout the simulation work, the estimation is performed at S/N = 10 dB. We assume 16 active users within the same cell/frequency. However, the actual number of users may be more depending upon the service.

For two transmit antenna structure shown in figure 3, the feed forward filters are represented by f_{mv}(n), m, v Î {1, 2}, each having L_{f }taps and sampling is performed at i times the chip rate. Also, the feedback filters are represented by b_{mv}(n) , m, v Î{1, 2}, each having L_{b} taps and operating at the symbol rate. Throughout the simulation work, the Rayleigh fading channel uses Q = 3 paths and the number of DFE feed-forward taps, L_{f} is equal to four. Because of shorter length of channel memory than the period of symbols, it is evident that ISI is produced only by the adjacent symbols. Thus, the DFE feedback filters each requires only single tap. This means that we take L_{b} = 1. Further, simulation has been performed on over 4000 blocks each consisting of 800 space-time coded symbols and also channel is assumed constant during each frame.