Low complexity frequency domain equalization for cyclic prefix CDMA systems

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)  C08 

 1

March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

Low Complexity Frequency Domain Equalization For Cyclic Prefix CDMA Systems F. S. Al-kamali 1, M. I. Dessouky, B. M. Sallam, and F. E. Abd El-Samie 2 Department of Electronics and Electrical Communications, Faculty of Electronic Engineering

Menoufia University, Menouf, Egypt

Email: { 1 faisalalkamali, 2 fathi_sayed }@yahoo.com.

Abstract This paper presents four frequency domain interference cancellation receivers for the Single-Input Single-Output (SISO) as well as Single-Input Multiple-Output (SIMO) downlink CDMA systems. The proposed receivers employ an interference cancellation scheme to suppress the interference caused by the multipath fading channel. All filters in the proposed receivers are implemented in frequency domain. The performance of the suggested receivers is studied and compared to other traditional receiver schemes. The effects of channel estimation, and number of active users on the performance of the proposed schemes are also studied. The obtained results show a large performance improvement when using such an interference cancellation scheme in the receivers relative to the RAKE receiver, and frequency domain Equalization (FDE) only. 1. Introduction Future wireless systems must provide high data rate services to satisfy the increasing needs of the nextgeneration wireless networks [1-4]. As the bit rate increases, the problem of ISI becomes more serious. Conventional equalization in the time domain may become impractical because it requires one or more transversal filters with a tap number covering the maximum channel impulse response length [1]. The RAKE receiver becomes also impractical due to the constraint of hardware complexity [1]. Orthogonal frequency division multiplexing (OFDM) is an attractive technology to deal with the detrimental effects of multipath fading, but it has several inherent disadvantages such as the large peak-to-average power ratio and the sensitivity to carrier frequency offsets [1-4]. Recently, single carrier block transmission with frequency domain equalization has proved to be a promising candidate for broadband wireless communications, especially when implementation issues such as the power consumption and the system complexity are taken into consideration [1-4]. By inserting a cyclic prefix in front of each data block, the zero forcing (ZF) or the minimum mean square error (MMSE) linear equalization criteria can be easily implemented in frequency domain [2]. There are other block transmission schemes for CDMA similar to the cyclic prefix CDMA (CP-CDMA) such as CDMA with known symbol padding, or zero padding [2,3]. The main advantage of frequency domain equalization lies in its low complexity when compared to time domain equalization and the RAKE receiver. The price to be paid is a reduction of the data rate caused by the insertion of the cyclic prefix. To improve the performance of frequency domain linear equalization in CDMA systems, frequency domain interference cancellation can be used [5-7]. The SIMO architecture is one of the most efficient solutions for high data rate transmission due to its high capacity gains relative to the SISO architecture. A combination of FDE and the SIMO architecture can also be used to counteract the channel fading due to multipath propagation [5]. The objective of this paper is to enhance the performance of downlink CP-CDMA systems by mitigating the multiple access interference (MAI) and the intersymbol interference (ISI). Hybrid receiver schemes comprising linear FDE and frequency domain parallel interference cancellation (FD-PIC) are suggested and studied in the

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)    2

C08  March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ paper. Three efficient frequency domain interference cancellation architectures for downlink SISO CP-CDMA systems are proposed. In all of them, the MAI is regenerated in frequency domain and subtracted from the received signal before equalization. The performance of all schemes is studied. One of the proposed receivers for SISO system is also developed for SIMO systems. The remainder of this paper is organized as follows: in section 2, the system model for downlink CDMA is presented. In Sections 3 and 4, the proposed frequency domain interference cancellation schemes for SISO and SIMO downlink CP-CDMA systems are described. Section 5 deals with the different decision functions that can be used in the proposed schemes. Computer simulation results and conclusions are given in sections 6 and 7, respectively. Notations: The symbols (.)H, (.)T, and (.)-1 designate complex conjugate transposition, transposition of a matrix, and inverse of a matrix respectively. ψ-1 and ψ denote the fast Fourier transform and the inverse fast Fourier transform , respectively. Vectors and matrices are represented in boldface.

2. System Model We consider the downlink CP-CDMA block transmission in a single cell CDMA system with K active users over a frequency selective channel. A schematic diagram of the baseband equivalent block transmission system is depicted in Fig. (1). Each user transmits BPSK information symbols. Those symbols are spread with a specific spreading code for each user. After spreading, the resulting signal is scrambled using a complex scrambling sequence. A cyclic prefix of NCP chips is added at the beginning of each block to form the transmitted block. The length of the cyclic prefix must be greater than the maximum excess delay of the channel ( L ) to accommodate the inter block interference. The received block after removal of the cyclic prefix can be formulated as: r = H Cd + n (1) where r is the received block. d is the transmitted block. n is the noise vector. Hc is a circulant matrix and can be written as: ⎡ h[0] ⎢ . ⎢ . ⎢ HC = ⎢h[L − 1] ⎢ 0 ⎢ . ⎢ ⎣ 0

0 . 0 h[L − 1] . h[0] . . . . . . . . 0 h[L − 1]

. .

h[1] ⎤

. ⎥ . h[L − 1]⎥⎥ . 0 ⎥ . ⎥ . 0 ⎥ ⎥ . . h[0] ⎦ .

(2)

where L is the number of multipath components of the channel impulse response h. The vector d can be represented as follows [7,8]:

d = CSb

(3)

where C is an NM×NM scrambling code matrix, S is an NM×KM block diagonal matrix whose diagon consists of the spreading codes. N is the spreading factor (SF). M is the number of transmitted symbols. b is an MK×1 vector consisting of the users’ amplitudes and the transmitted bits. The structures of the individual components of Eq. (3 ) are found in [7,8]. In terms of MAI, the received signal can be written as follows:

r = H c CS

d es

b des + H c CUb

= H c d dse + H c d int + n

int.

+ n

(4)

where bdes is an M×1 vector consisting of the desired user’s bits, bint is a (K-1)M×1 vector consisting of the interfering users' bits, Sdes is an (NM)×L matrix consisting of the spreading code of the desired user, and U is an (NM)×(K-1)M matrix consisting of the spreading codes of the interfering users. From Eq. (4), it is found that only the first item contains the desired data, the second term is MAI, and the third term is due to noise.

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)  C08 

 3

March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ 3. The Proposed Schemes for SISO Downlink CP-CDMA Systems Frequency Domain RAKE with PIC In this section, the first suggested scheme is introduced. This scheme uses the frequency domain RAKE (FD-RAKE) receiver and FD-PIC to estimate, regenerate, and cancel all the interfering users. Then, the FDRAKE receiver is used to provide the enhanced desired user’s data. The suggested scheme is called FD-RAKEPIC. It is shown in Fig. (2). The steps of the FD-RAKE-PIC algorithm can be summarized as follows: 1- The Cyclic prefix is removed from the received signal . 2- After removing the cyclic prefix , the FFT is applied to the received signal. With the aid of Eq. (4), we get:

R T = ΛD des + ΛD int. + N

(5)

where D des , D int and N are the Fourier transforms of d des , d int and n, respectively. Λ is a diagonal matrix containing the FFT of the circulant sequence of HC. 3- The resulting signal after the FFT is first sent to the frequency domain channel estimator which estimates the channel coefficients. 4- The estimate of the channel coefficients is used at stage 1 to estimate the symbols of the interfering users with FD-RAKE receiver. The estimates of the symbols obtained here are the first decision made. This estimate is referred to a tentative decision. This step can be written as follows:

{

bˆ int = f dec U T C H ΨΛ

H

RT

}

(6)

where fdec(.) is a tentative decision function (tanh decision is considered). 5- The estimates of the interfering users’ symbols are used with the channel estimate to regenerate the interfering users' signal (MAI) as follows:

R MAI = ΛΨ

−1

( CU bˆ int

(7)

)

6- The MAI is then subtracted from RT to get the frequency domain interference free signal as follows:

Z = R T −R

(8)

MAI

7- A better estimate of the symbols of interest can be obtained by applying an FD-RAKE detection step on the interference free signal Z as follows:

{

bˆ des = f dec S Tdes C H ΨΛ H Z

}

(9)

where fdec(.) is a hard decision function. The main advantage of this receiver lies in its low complexity as compared to the other suggested schemes. However, the performance of this receiver deteriorates, as the number of users increases. This can be explained by the fact that, for heavily loads, the RAKE receiver sees too much interference which makes its decisions about interfering users unreliable.

3.2 Frequency Domain RZF Equalizer with PIC This section presents the second suggested scheme which is used to improve the performance of the previous scheme for downlink CP-CDMA systems. This scheme uses an FD-RAKE receiver to estimate the interfering bits. Then, an FD-PIC step is used to regenerate, and cancel all interfering users data. After that, a regularized zero forcing frequency domain equalizer (RZF-FDE) is used to provide a better estimate of the desired user’s

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)    4

C08  March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ data. The suggested scheme is called FDE-RZF-PIC (see Fig. (3)). The steps of the proposed FDE-RZF-PIC algorithm can be summarized as follows: 1. The steps from 1 to 6 of the FD-RAKE-PIC algorithm are performed. 2. The estimate of the symbols of interest can be obtained after RZF-FDE, IFFT, descrambling, and despreading steps as follows:

{

bˆ des = f dec S Tdes C H ΨW RZF Z

}

(10)

where

W RZF = ( Λ H Λ + α I ) − 1 Λ H = Q RZF Λ H

(11)

WRZF is the frequency domain regularized zero forcing equalization operator. The main advantage of this scheme is that, the statistics of the transmitted data and the additive noise are not required. Its performance is also better than that of the FD-RAKE-PIC. However, it is more complex than the FD-RAKE-PIC receiver.

3.3 Frequency Domain LMMSE Equalizer with PIC In this section, we suggest the combination of both LMMSE-FDE and FD-PIC to form a new equalization scheme which mitigates the interference in downlink CP-CDMA systems as shown in Fig. (4). The suggested scheme uses the LMMSE-FDE to estimate the interfering bits. Then, FD-PIC is used to regenerate, and cancel all the interfering users in frequency domain. Finally, the LMMSE-FDE equalizer is used to provide the desired user’s data. The suggested scheme is called FDE-LMMSE-PIC. The FDE-LMMSE-PIC algorithm is similar to that of FD-RAKE-PIC except that the FD-RAKE is replaced by an LMMSE-FDE. The LMMSE-FDE formula is given by [3]:

W LMMSE = ( Λ H Λ + (1 / SNR ) I ) − 1 Λ H

(12)

From Eq. (12), it is found that in the FDE-LMMSE-PIC scheme, the statistics of the additive noise and the transmitted data are required.

4. The Proposed Scheme for SIMO Downlink CP-CDMA Systems Figure (5) is the block diagram (two-antenna example, Nr=2) of the developed receiver for SIMO downlink CP-CDMA systems. It uses SIMO FDE to estimate the interfering symbols. Then, the FD-PIC is used to regenerate, and cancel the MAI in frequency domain. After that, the SIMO FDE is used to provide a better estimate of the desired user’s data. The proposed scheme is called the SIMO FDE-PIC scheme. The received signal can be represented as:

r = H CT d + n

(13)

where:

[

, and H CT = H C1

[

. . H CNr ] , r = r1 T

.

.

.

r Nr

]

T

n = [n 1

.

.

n Nr

]T

d is taken as in Eq. (3). After removal of the cyclic prefix from the received signals, they are transformed into frequency domain. Equation (13) can be represented in frequency domain as follows:

R = ΛD

+ N = useful

where:

ΛD des 12 3

diversity

+ ΛD int + 123 MAI

N {

Noise

(14)

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)  C08 

 5

March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ T T T R = [R 1 . . R Nr ] , and N = [N 1 . . N Nr ] Λ = [Λ1 . . Λ Nr ] , Λ j is a diagonal matrix containing the FFT of the circulant sequence HCj ( 1 ≤ j ≤ Nr ) . The first term of Eq. (14) represents the useful diversity. The second term is MAI. The third term is due to noise. Based on Eq.(14), the SIMO FDE can be employed as follows:

ˆ = WR D

(15)

where:

W = [W 1 , . .,

Wj,

. .

, W Nr ]

(16)

Wj can be chosen according to the channel parameters Λj and the MMSE criterion:

W j = Λ (Λ j Λ H j

H j

+(

σ 2j

σ d2

2

where σ j is the variance of the additive noise at the jth antenna, and

)I 0 ) − 1

σ d2

(17)

is the variance of the transmitted

signal. Then, the signal is converted to the time domain with an IFFT operation as follows:

dˆ = Ψ ( Dˆ )

(18)

The transmitted data symbols of the interfering users are obtained after descrambling and despreading. The estimates of the symbols obtained here are tentative decisions. This step can be written as:

bˆ int = f dec (U T C H dˆ )

(19)

where fdec is a tentative decision function. The tentative decision data is then spread and scrambled using the corresponding codes and a replica of the interfering signal is reconstructed using the channel parameters and an FFT operation. The interfering signal can be written as:

R

MAI

= Λ Dˆ int

(20)

where:

ˆ = Ψ −1 (CU bˆ ) D int int

(21)

The interfering signal is subtracted from the original received signal as follows.

Z = R − R

(22)

MAI

After interference cancellation, the SIMO FDE is performed as follows:

ˆ D Final = WZ

(23)

Finally, the desired user’s symbols can be obtained after an IFFT operation, descrambling and despreading as follows:

bˆ des = sgn(real(S

T d es

ˆ C H Ψ( D )) ) Final

(24)

This is the final decision. In order to improve the performance further, the suggested algorithm can be implemented in multistage. However, the multistage implementation leads to an increase in the complexity.

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)    6

C08  March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ 5. Decision Functions This section explains the most frequently used decision functions in CDMA systems. The performance of PIC step depends mainly on the tentative decision function used. So, due to error propagation, PIC with hard decisions may perform more worse than PIC with linear or soft decision functions [7,10]. •The hard decision function:

⎧1 x ≥ 0 ⎪ y = fdec(x) = ⎨ ⎪−1 x < 0 ⎩

(25)

It makes a hard decision for one of the two possible symbols.

•The null zone function: y = f des

⎧ 1, x > cn ⎪ ( x ) = ⎨ 0, x ∈ [− c n , c n ] ⎪ − 1, x < − c n ⎩

(26)

It makes a hard decision when the soft bit estimate lies outside the interval [-cn, cn ], and sets the decision results to zero when the soft bit estimate lies inside the interval [-cn , cn ]. cn is the null zone decision threshold and it lies in the interval [0,1]. • The linear decision function:

y = f dec ( x ) = x

(27)

It offers an analytical access to the PIC performance, but performs worse than other decision functions. •The unit clipper decision function:

⎧ 1, ⎪ y = f dec ( x ) = ⎨ x , ⎪ − 1, ⎩

x >1 x ∈ [ − 1,1]

(28)

x < −1

It makes a soft bit decision when the soft bit estimate lies inside the interval [-1 , 1] to avoid the propagation of errors, and makes a hard decision when the soft bit estimate lies outside the interval [-1,1] to avoid the noise magnification [10]. •The tanh decision function:

y = f dec ( x ) = tanh( x )

(29)

It was adopted as the optimum decision function for non-frequency selective channels for systems with a high number of users.

6. Simulation Results Several simulation experiments are carried out in this section to test the performance of the proposed algorithms and compare them to other traditional algorithms. The simulation environment is based on the downlink synchronous CP-CDMA system in which, each user transmits BPSK information symbols. More details of the simulation parameters are given in Table (1). All users are assigned the same power.

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)  C08 

 7

March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬

Transmitter

Channel

Receiver

Modulation

BPSK

Spreading Codes

OVSF codes with processing gain 16

Scrambling Code

Complex scrambling sequence

FFT points

P=256

Cyclic Prefix

NCP =16

Fading

Frequency selective with L=3

Noise Environment

AWGN

Equalization

RZF-FDE with α=1, MRC(FD-RAKE), and LMMSE-FDE

Channel Estimation

Ideal, and Pilot Channel Estimation

Table (1) Simulation Parameters.

Case 1: SISO System In this case, the performance of the suggested schemes for SISO downlink CPCDMA systems is studied. A comparison study between these schemes is performed. Figures 6, and 7 illustrate the BER versus the threshold of the null zone decision function (cn) at different SNR values and different number of users for an FD-RAKE-PIC receiver. It is clear that cnopt=0.4 is always the best choice of the threshold regardless of the value of SNR. Figures (6), and (7) show that cnopt is non-sensitive to the SNR-changes and to system-load changes. The effect of the regularization parameter on the performance of the FDE-RZF-PIC receiver is examined and shown in Figs. (8), and (9). The optimal value of the regularization parameter is found to be αopt=1. This value is non-sensitive to SNR-changes and to system-load changes. Thus, we will choose α=αopt=1 for the rest of the experiments. The effect of the tentative decision function on the performance of the FD-RAKE-PIC, the FDE-RZF-PIC, and the FDE-LMMSE-PIC receivers for K=16 (Full load ) is studied and shown in Figs. (10), (11), and (12), respectively. It is found that the best performance of FD-RAKE-PIC, and FDE-RZF-PIC receivers can be reached with the tanh decision function. On the other hand, the performance of the FDE-LMMSE-PIC receivers with a hard decision function outperforms the performance obtained with all other decision functions. Figures (13), and (14) introduce a comparison between the different proposed algorithms for K=8 and K=16. From the obtained results, its clear that for low SNR values all the proposed schemes have the same performance. At high SNR values, the FDE-LMMSE-PIC receiver gives the best performance. From Fig. (13), it can be observed that the performance obtained from the FDE-RZF–PIC receiver, and the FDE-LMMSE-PIC receiver is the same when the system load is low. This observation may be due to the propagation of errors. When the number of users is low, the FD-RAKE receiver provides reliable decisions and the resulting error is small. The effect of user loads on the performance of the suggested algorithms is studied and presented in Fig. (15). The BER of all receivers degrades with increasing the number users. In this case, the performance of the suggested algorithms degrades a little bit by increasing the number of users, but it is still better than the other traditional schemes. This observation may be due to the MAI. The higher the number of users, the larger the MAI. Even after interference cancellation, some residual MAI may still exist. Therefore, the performance loss may be attributed to the increased MAI. Figure (16) depicts the BER as a function of the number of cancelled users, at a fixed SNR per user of 12 dB. This graph shows that the performance of the suggested receivers improves when the number of cancelled users increases. The effect of the channel estimation on the performance of the proposed schemes for K=16 is tested and shown in Fig. (17). The performance of the FDE-RZF-PIC, and the FDE-LMMSE-PIC receivers with MMSE channel estimation shows a loss of about 3 dB at BER of 10-2 when compared to the case of perfect channel knowledge.

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)    8

C08  March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ Case 2: SIMO System In this case, the performance of the developed SIMO FDE-PIC receiver is compared to that of SIMO FDE, SISO FDE-PIC, and the RAKE receiver. Figures (18), and (19) show the BER versus the SNR for K=8 (half load), and K=16 ( full load), respectively. As shown in Figs. (18), and (19), the proposed SIMO FDE-PIC scheme is effective in reducing the ISI and the MAI. It improves the performance significantly, especially at high SNRs. With the proposed scheme, an SNR reduction of about 2 dB is achieved for a BER=10-4 from the SIMO FDE receiver as in Fig. (19). For the fully loaded case, with a typical BER level of 10-3, the SNR for the SISO FDE- PIC receiver is no less than 10 dB, whereas the SNR for SIMO FDE-PIC receiver is about 5 dB, which demonstrates a 5 dB improvement. Figure (20), shows the variation of the BER with the number of users. It is obvious from the figure that the BER of the SIMO FDE-PIC receiver is much lower than the BER of the RAKE receiver, the SISO FDE-PIC receiver, and the SIMO FDE receiver. From the results, it is clear that the SIMO FDE-PIC receiver increases the number of users of the system by about 4 times more than that of the SIMO FDE receiver. To show the impact of the channel estimation on the performance of the SIMO FDE-PIC receiver, and the SIMO FDE receiver, Fig. (21) illustrates the performance in terms of the BER versus SNR. We use the LMMSE frequency domain channel estimation, where a training sequence is used. The degradation in the SNR from ideal channel estimation case for a BER=10-3 is about 3 dB.

7. Conclusions In this paper, three interference cancellation architectures have been suggested and studied to suppress the interference for the SISO downlink CP-CDMA systems. The comparison studies show that the suggested schemes achieve a large performance improvement relative to the traditional receivers. The effects of the tentative decision function, the number of users, the channel estimation, and the number of cancelled users on the performance of these schemes are studied. It is found that, the FDE-LMMSE-PIC receiver with hard decision gives better performance than other receivers even with heavy loads. The proposed FDE-LMMSE-PIC receiver is also developed for SIMO downlink CP-CDMA systems. Simulation results show that the BER performance of developed SIMO FDE-PIC receiver is far better than the RAKE receiver , the SISO FDE-PIC receiver, and the SIMO FDE receiver. Furthermore, it provides more capacity when compared to the SIMO FDE receiver. The obtained results indicate that a reliable communication is possible with the proposed schemes.

References [1] D. Falconer et al., “Frequency Domain Equalization for Single-Carrier Broadband Wireless Systems,” IEEE Commun. Mag., Vol. 40, pp. 58–66, April 2002. [2] I. Martoyo, T. Wesis, F. Capar, and F.Jondral, “Low complexity cdma downlink receiver based on frequency domain equalization, ” in Proc. IEEE VTC., pp. 987-991, Oct. 2003. [3] F. Petre, G. Lues, L. Deneire, and M. Moonen, “Downlink frequency domain chip equalization for singlecarrier block transmission DS/CDMA with known symbol padding,” in Proc. GLOBCOM, pp. 453-457, Nov. 2002. [4] F. Adachi, D. Garge, S. Takaoka, and K. Takeda, “Broadband CDMA techniques," IEEE Wireless Communs., Vol. 12, No. 2, pp. 8-18, April 2005. [5] K. Takeda, K. Ishihara, and F. Adachi, “Downlink DS-CDMA Transmission with Joint MMSE Equalization and ICI Cancellation,” IEEE VTC., Vol. 4, pp. 1762-1766, Spring 2006. 4 [6] K. Takeda and F. Adachi, "Frequency-Domain Interchip Interference Cancellation for DS-CDMA Downlink Transmission,” IEEE Tr. VT, Vol. 56, No. 3, pp. 1286-1294, May 2007. [7] F. S. Al-kamali, M. I. Dessouky, B. M. Sallam, and F. E. El-Samie, “Efficient Implementation of Downlink CDMA Equalization Using Frequency Domain Approximation, ” UBICC Journal, Vol. 2, No. 4, 2007. [8] S. Werner, J. Lilleberg, “ Downlink channel decorrelation in CDMA systems with long codes" IEEE 49th Vehicular Technology Conference, vol. 2, pp. 1614 – 1617, 16-20 May 1999. [9] A. L. C. Hui and K. B. Letaief, “Multiuser asynchronous DS/CDMA detectors in multipath fading links,” IEEE Trans.commun, vol. 46, pp. 384–391, Mar. 1998. [10] 1. F. S. Al-kamali, M. I. Dessouky, B. M. Sallam, and F. E. El-Samie, “Regularized Zero forcing Equalizer with Soft Decision PIC for Multirate Downlink CDMA Systems,” International Conference on Engineering and Mathematics, ENMA 2007, Bilbao, Spain, pp. 133-140, 9-11 July 2007.

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)   9

C08  March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ User 1

Spreadin Ncp

User 2

Spreadin

Insert CP

Scrambling

Data block

CP

. .. .

. . . . . User K

P

Spreadin

Fig. (1) Downlink CP-CDMA transmitter and the transmitted block. Frequency Domain Channel Estimator

Stage 1

ΛH

Remove CP

FFT

FDRAKE

-

IFFT

Rx

Hard decision

Descrambling And , Despreading

desired user's data

K-1

Frequency Domain Interference Regeneration

Stage 2

Tentative decision

. . .

Fig. (2) Structure of the proposed FD–RAKE-PIC scheme.

-

IFFT

ΛH

Remove CP

QRZF

Frequency Domain Channel Estimator

FFT

RX

IFFT

RZF-FDE

desired user's

Descrambling and Despreading

Hard decision

Descrambling And , Despreading

Tentative

decision

FDRAKE K-1

Frequency Domain Interference Regeneration

. . .

Fig. (3) Structure of the proposed FDE –RZF-PIC scheme.

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)     10

C08  March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ Frequency Domain Channel Estimator

Rx

Hard Decision

-

IFFT

FFT

FDELMMSE

Descrambling Remove CP

desired user's data

And , Despreading K-1 . . .

Tentative decision

Frequency Domain Interference Regeneration

Fig. (4) Structure of the proposed FDE-LMMSE-PIC scheme.

Frequency Domain Channel Estimator

Rx1

Desired data

FFT

Remove CP

Hard Decision

Descrambling And despreading

-

IFFT

Rx2

SIMO FDE

FFT

Remove CP

K-1

Frequency Domain Interference Regeneration

Tentative decision

. . .

Fig. (5) The proposed SIMO FDE-PIC scheme with Nr=2. SF=16, Full Loaded

0

SF=16, Half Loaded

0

10

10

Null Zone Decision

Null Zone Decision -1

SNR=[ 6 9 12 15] db BER

BER

SNR=[ 6 9 12 15] db

10

-1

10

-2

10

-2

10

-3

-3

10

-4

10

10

-4

10

0

0.2

0.4

0.6

0.8

1

Threshold ( Cn )

Fig. (6) BER vs. null zone decision threshold at different SNR and K=8.

0

0.2

0.4

0.6

0.8

Threshold ( Cn )

Fig. (7) BER vs. null zone decision threshold at different SNR and K=16.

1

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)  C08    11 March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ SF=16, Half Loaded,Cyclic Prefix

0

SF=16, Full load, Cyclic Prefix

0

10

10

FDE-RZF-PIC

SNR=[ 6 , 9 , 12 ] dB

-1

SNR=[ 6 9 12 ] dB

-1

10

BER

10

BER

FDE-RZF-PIC

-2

10

-2

10

-3

-3

10

10

-4

-4

10

-3

10

-2

-1

0

10 10 10 Regularization Parameter ( α )

10

1

-3

10

10

Fig. (8) BER vs. regularization parameter at different SNR and K=8.

-1

0

1

10

Fig. (9) BER vs. regularization parameter at different SNR and K=16.

SF=16, Full lLoaded , Cn=0.4

0

-2

10 10 10 Regularization Parameter ( α )

SF=16, Full load,Cyclic Prefix

0

10

10

-1

10

-1

BER

BER

10

-2

10

RAKE -2

Null Zone

10

RAKE

Unit Clipper Hard

-3

Null zone Unit Clipper

10

Linear 10

Hard

Tanh

-3

Tanh

-4

0

5

10

10

15

0

SNR

10

15

SNR

Fig. (10) Performance of FD-RAKE-PIC with different decision functions(BER vs. SNR). K=16.

Fig. (11) Performance of FDE-RZF-PIC with different decision functions(BER vs. SNR). K=16.

SF=16, Half load, α=1, Cyclic prefix

0

SF=16,Full load, Cyclic Prefix

0

5

10

10

-1

10 -1

10

-2

BER

BER

10 -2

10

-3

10

RAKE

RAKE -3

LMMSE-FDE

Null Zone

10

10

Unit Clipper Hard

FDE-RZF-PIC

Tanh

-4

10

RZF-FDE FD-RAKE-PIC

-4

0

FDE-LMMSE-PIC

5

10

15

SNR

Fig. (12) Performance of FDE-LMMSE-PIC with different decision functions(BER vs. SNR). K=16.

0

5

10 SNR

Fig. (13) BER vs. SNR for different reception schemes for K=8.

15

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)     12

C08  March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ SF=16, Full load, α=1, Cyclic Prefix

0

SF=16, α=1, Cyclic Pref ix

-1

10

10

RAKE RZF-FDE LMMSE-FDE FD-RAKE-PIC

-1

10

-2

FDE-RZF-PIC

10

FDE-LMMSE-PIC

-2

BER

BER

10

-3

10

-3

10

RAKE LMMSE-FDE

-4

10

RZF-FDE FD-RAKE-PIC

-4

10

FDE-RZF-PIC -5

FDE-LMMSE-PIC 0

10

5

10

4

15

6

8

Fig. (14) BER vs. SNR for different reception schemes for K=16.

12

14

Fig. (15) BER vs. the number of active users for different reception schemes. SNR =12 dB.

SF=16, Full Load, α=1, Cyclic prefix

0

10

Number of users

SNR

SF=16,K=16

0

10

10

FD-RAKE-PIC FDE-RZF-PIC FDE-LMMSE-PIC

-1

-1

10

BER

BER

10

-2

10

-2

10

FDE-LMMSE-PIC chann. know n FDE-LMMSE-PIC chann. est. -3

FD-RAKE-PIC chann. know n

10

-3

10

FD-RAKE-PIC chann. est. FDE-RZF-PIC chann. know n FDE-RZF-PIC chann. est.

-4

10

-4

10

0

5 10 Number of Cancelled Users

15

2

4

6

8

10

SF=16,Half Load

16

18

SF=16,Full Load

0

10 1X1 RAKE

1X1 RAKE

1X1 SISO FDE-PIC 1X2 SIMO FDE 1X2 SIMO FDE-PIC

-1

10

1X1 SISO FDE-PIC 1X2 SIMO FDE

-1

10

-2

BER

BER

14

Fig. (17) BER vs. SNR for exact and LMMSE channel estimate for the different reception schemes.

10

10

-3

1X2 SIMO FDE-PIC

-2

10

-3

10

10

-4

10

12

SNR

Fig. (16) BER vs. the number of canceled users for different reception schemes. SNR =12 dB.

0

0

-4

0

2

4

6 SNR

8

10

12

Fig. (18) BER vs. SNR for different reception schemes for K=8 (half load).

10

0

2

4

6

8

10

12

SNR

Fig. (19) BER vs. the SNR for different reception schemes for K=16 (Full load).

25th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2008)  C08    13 March 18‐20, 2008, Faculty of Engineering, Tanta Univ., Egypt

‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ SF=16

0

-1

1x1 RAKE

1x2 SIMO FDE, chan. know n

1x1 SISO FDE-PIC 1x2 SIMO FDE

1x2 SIMO FDE , chan. estimation

-2

10

Capacity increase

1x2 SIMO FDE-PIC, chan. know n

-1

10

1x2 SIMO FDE-PIC

BER

BER

10

1x2 SIMO FDE-PIC,Chan. estimation

-2

10

-3

-3

10

-4

10

10

10

SF=16,Full Load

0

10

10

-4

4

6

8

10

12

14

Number of Users

Fig. (20) BER vs. the number of active users for different reception schemes. SNR =6 dB.

0

2

4

6

8

10

12

SNR

Fig. (21) BER vs. SNR for exact and LMMSE channel estimate for the different reception schemes. .