Joint Transmitter-Receiver Adaptive Forward-Link DS-CDMA System
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1 # - Joint Transmitter-Receiver Adaptive orward-link D-CDMA ystem Li Gao and Tan. Wong Department of Electrical & Computer Engineering University of lorida Gainesville lorida 3-3 Abstract A joint transmitter-receiver adaptive D-CDMA system over a slow flat fading forward-link channel is considered in this paper. A set of spreading sequences is designed to support all users with a uniform target IR. This set of sequences reduces to the optimum solution of the transmitter optimization problem of choosing a set of sequences to meet the IR target with a minimum total transmission power when the channel reduces to an AWGN channel. The MME receiver is employed for signal reception and receiver weights of each user are adapted independently and simultaneously without information from other users. Estimates of the ME at each receiver are sent back to the base-station. An adaptive algorithm is designed to estimate channel parameters using the feedback information and update the spreading sequences at the basestation. The algorithm gives a set of sequences which satisfies the target IR and has total transmission power close to the theoretical total power after a moderate number of iterations. imulation results show that performance improvement can be achieved with the proposed joint adaptation scheme. Keywords D-CDMA forward link power control MME receiver I. INTRODUCTION Multiple access interference MAI is a factor which limits the capacity and performance of D-CDMA systems. General MAI suppression approaches except adaptive power control focus on the receiver design [] []. Recently more attention has been paid to the joint optimization of transmitter and receiver. One of the approaches [] is to precode all the transmitted signals by a linear transformation before transmitting to minimize MAI. The precoding transform and the linear receivers are chosen jointly to minimize the total ME at the receivers. The optimization problem of choosing a set of spreading sequences to use in the system with the minimum total power so that the signal-to-interference ratio IR targets of the users are met over an AWGN channel is solved in []. The optimal sequences are shown to be a set of generalized Welch-bound-equality WBE sequences. Variants of this transmitter optimization problem in a multicarrier setting and a multicode setting are also investigated independently in [8] and [] respectively. In this paper we extend the work in [8] and [] to a slow flat fading forward-link channel. We consider the issue of imperfect channel parameter estimation and the design of adaptive algorithms for practical wireless applications. We assume that all users are allowed to adapt their transmission. Each user is assumed to have no information about other users. Receiver weights of each user are adapted independently and simultaneously based on the MME criterion. Estimates of the mean squared error ME at each receiver are fed back to the basestation and are used for the estimation of the channel parameters. These imperfect estimates of the channel parameters are then employed to update the spreading sequences which are used in the transmission of the next block of data. Different from the approaches in [] and [] which update the spreading sequences at the receivers and send the new spreading sequences back to the base-station the approach we present here updates the spreading sequences at the base-station and reduces the bandwidth requirement in the feedback channel by feeding back a minimum amount of information. This approach makes the adaptive scheme more practical and feasible to use in reallife communication systems. The rest of the paper is organized as follows. In ection II we describe the system model and give a brief discussion on the optimal adaptive linear MME receiver weights. In ection III we introduce a set of spreading sequences which guarantees the IR requirements of all users over a slow flat fading channel. In ection IV we describe an adaptive implementation including both an adaptive structure and an adaptive algorithm for the proposed joint transmitter-receiver adaptive D-CDMA system. imulation results are presented in ection V to verify the performance of the proposed scheme. II. ORWARD-LINK D-CDMA YTEM MODEL A forward-link D-CDMA system is considered. We assume that there are users in the system and each user generates one stream of data symbols. The data stream of the th user for is given by. We assume that the data symbols are independent random variables with zero mean and unit variance. The data stream of the th user is spread with the periodic spreading sequence "$# & and then modulated to the carrier frequency + to give the transmitted signal.-/ 3 8: # ; 8:< ">= 8@? A-CBEDGH&/I&JAKMLGNPOQ where H is the chip interval and?.-/ is the chip waveform. We assume that? A-/ satisfies the Nyquist criterion for zero inter-chip interference and R? U A-/. T We consider the forward-link transmission and assume that different users undergo independent slow flat fading. Data streams of all users are detected simultaneously and independently. Without loss of generality we consider the detection of the first user s data. The complex baseband representation of -83--//$. IEEE
2 the received signal is given by.-/ I&J ; 8:< ">= 8? A- B DGH B A-/ 8: # where and denote the channel gain and the transmission delay from the base-station to the first user s receiver respectively accounts for the overall phase shift of the signals and A-/ represents the AWGN with power spectral density PD at the first user s receiver. We employ an adaptive equalizer based receiver proposed in [] and [3]. We assume that carrier synchronization has been achieved. Therefore the phase shift and the transmission delay can be taken into zero. The received signal is passed through a chip-matched filter and the filter output is sampled every chip interval. To detect the th symbol of the first user we arrange the samples observed in the interval / into an -dimensional column vector which can be expressed as 3 where is the component due to the first user s signal is the component due to the th user s signal for and denotes the contribution from the AWGN. The vector is fed into an IR filter and the filter weights are chosen to minimize the ME of the IR filter []: # where is the normalized total correlation matrix observed by the first user which is given by E " $##&# is an matrix formed by In above grouping all spreading sequences vectors and + is the effective noise density at the first user s receiver. The decision statistic is hard-limited to obtain the estimate of the th symbol of the first user. A simple analysis shows that the optimal MME receiver weights also maximize the receiver output IR [] which is given by IR # where is the effective noise-plus-interference correlation matrix defined by.- E - B The discussion above applies to any user by simply replacing the subscript index with the corresponding subscript index of that user. We can observe from that the IR achieved by the MME receiver depends on the choices of the spreading sequences. In the next section we are going to discuss the selection of the spreading sequences. III. PREADING EQUENCE ELECTION Transmitter optimization problem of choosing a set of spreading sequences so that IR targets are met for all data streams in the system with a minimum amount of transmission power over an AWGN channel is solved in []. Here we extend this transmitter optimization problem into a slow flat fading environment as modeled in. or simplicity we assume a uniform IR target for all users. Mathematically the optimization problem can be expressed as subject to /3 # for. The necessary and sufficient condition for the existence of a feasible solution of this optimization problem [8] is that the processing gain the number of users and the target IR satisfy the following constraint: 8 8 The fact that different users undergo different channel gains and noise level increases the complexity and difficulty of the optimization problem. The optimization problem in 8 has yet to be solved. Here we consider the problem of finding good spreading sequences which guarantee a uniform target IR for all data streams over the CDMA forward link as modeled in. or the case of : the constraint in is always satisfied. With signal synchronization in forward link transmission orthogonal sequences can be employed to eliminate MAI. The transmission power of the th user s signal is set to <; to satisfy the IR requirement. or the case of there exists a unique number >=? /@ HB such that E BADC 8 CB A C BE = BA with assumption of a descending order of the effective noise densities i.e. G. If the condition in is satisfied we can obtain a set of spreading ##&# 8
3 U D C " C " ig.. Adaptive CDMA system sequences that is characterized by where... A E "$# A ### A E " # A # A $# ### & = = #&## are transmission powers of users and is an unitary matrix to support all users. The total transmission power using this allocation is T A BE = E /8 CB B A C = 3 and When the channel gains and AWGN satisfy for the slow flat fading channel modeled in reduces to an AWGN channel. It is easy to show that the set of spreading sequences we introduced above reduces to the optimal spreading sequences for an AWGN channel [] []. IV. JOINT TRANMITTER-RECEIVER ADAPTATION Before constructing the set of spreading sequences stated above the base-station transmitter has to wait until it finishes estimating the channel parameters for each user in the system. In a practical communication system some users may leave the system and new users may enter the system at anytime. It is difficult for the base-station to estimate the channel parameters and construct a new set of spreading sequences every time the system state changes. It is also difficult for the MME receiver of a user to adjust its weights when a completely different spreading sequence is assigned to the corresponding user. In order to solve the problem practically we develop a joint adaptive structure to adapt the receiver weights and transmitter spreading sequences simultaneously. The joint adaptive structure is illustrated in ig.. Receiver weights of all the users are adapted independently and simultaneously based on the MME criterion. The base-station collects the feedback information from the receivers and adapts the spreading sequences of all users in a centralized manner. tep : The base-station transmits the & th block of training data symbols contain data bits of the th user with the current spreading sequence & for. The initial spreading sequence can be assigned arbitrarily. tep : The weight vector of the receiver of the th user is adapted using exponentially weighted RL algorithm [] for. At the end of reception of the & th block of data the ME for the & th block of transmission is estimated as + -. B and this estimates is sent back to the base-station. Here. is the is the / th chip-matched filter output vector and th last updated weight vector at the th receiver within the & th block of transmission. tep 3: The base-station knows the current spreading sequences & and applies eigenvalue decomposition to & & : & & & & & Define & 3 & & " #. Then estimates of the effective noise densities of users can be obtained by solving the following equations: B + " # #&## tep : Using s the base-station updates the spreading sequences of all users sequentially starting from the first user. or the th user its spreading sequence is updated according to where & & # & & & #&## is chosen so that &? # # & & & ##&# & &? & " and & &. The coefficient 8 8 At the end of the & th iteration the updated spreading sequences & are employed to transmit the next block of data. The adaptation process repeats from teps to until the training period finishes. If continuous updating of the spreading sequences and receiver weights are desired after the training period the system can be switched into a decision feedback mode. ymbol decisions made by the receivers are employed to replace the training symbols.
4 V. IMULATION ANALYI In this section we study the performance of the proposed adaptive implementation through computer simulations. We assume that the spreading gain is 3 and there are active users in the system. We set a uniform IR target for all db. The inverse of effective noise densities users as for are generated independently by exponential distribution with db. The performance of the system is measured via the receiver output IR which is defined as IR instantaneous power of signal average power of interference and noise With this definition the receiver output IR of the / th symbol in the & th block of the th user s data stream can be calculated by & & where & E & & " The total transmission power during the & th block of transmission & can be calculated as & & During the initial training period for each user are sent in blocks. According to the discussion in [] we employ a block length in the following simulation examples. irst we study the performance when there are a fixed number of users in the system. tarting from a set of independent random sequences all users adapt their transmissions. ig. shows the receiver output IRs and the total transmission power during the adaptation process. It is shown that the receiver output IRs of all users converge close to the target IR and the total transmission power approaches as calculated in 3. We also observe that due to imperfect channel parameter estimation there are oscillations in both the IR and the transmission power curves. In the second simulation example we examine the performance of the system when one new user is admitted into the system. Originally there are users in the system and after a number of iterations all users have achieved their target IR. Then one new user is admitted into the system and starts to adapt its spreading sequence and receiver weights. The admission of the new user increases the MAI level of the original users so all users in the system need to adapt their spreading sequences and receiver weights to meet the target IR. ig. 3 shows the adaptation process starting from the time when a new user is admitted into the system. We can see that the admission of the new user causes degradation of the IRs of the original users. However the adaptive structure and algorithm can adjust the spreading sequences and receiver weights to make each user achieve the target IR and total transmission power approaches the given in 3 receiver output NR in db transmission power normalized by P T ig.. ystem performance over slow flat fading channel The last simulation example examines the performance of the system when one user leaves the system. Originally there are users in the system and after a number of iterations all the users have achieved their target IR. Then one user leaves the system. The departure of one user decreases the MAI level of the other users and it is possible for the rest users to achieve the target IR with less transmission power. o the rest of the users in the system need to adapt their spreading sequences and receiver weights. ig. shows the adaptation process starting from the time when one user leaves the system. We can observe that right after a user leaves the system there is a performance degradation to the rest users due to changes in the set of spreading sequences. However after a number of iterations the receiver output IRs of the rest users recover to the target IR and total transmission power approaches the in 3. within a moderate number of iterations. VI. CONCLUION In this paper we have described and simulated a joint transmitter-receiver adaptation structure in a forward-link D- In igs. 3 and the total transmission power is normalized by the value of in 3 after a user is admitted into/leaves the system. 3
5 8 8 receiver output NR in db receiver output NR in db transmission power normalized by P T. transmission power normalized by P T ig. 3. ystem performance after admitting a new user. 8 8 ig.. ystem performance after a user leaves the system CDMA system. The MME receiver weights and the spreading sequence of each user are updated simultaneously to meet the target IR. The approach of updating the spreading sequences at the base-station reduces the bandwidth requirement in the feedback channel. Another contribution of this work is the introduction of a set of spreading sequences which guarantees a uniform target IR for all users when different users undergo independent flat slow fading. imulation results show improved system performance through this joint adaptation. REERENCE []. Verdú Minimum probability of error for asynchronous gaussian multiple-access channels IEEE Trans. Inform. Theory vol. 3 no. pp. 8 Jan. 8. [] R. Lupas and. Verdú Linear multiuser detectors for synchronous code-division multiple-access channels IEEE Trans. Inform. Theory vol. 3 no. pp. 3 3 Jan. 8. [3] U. Madhow and M. Honig MME interference suppression for directsequence spread-spectrum CDMA multiple-access channels IEEE Trans. Commun. vol. no. pp Dec.. [] M. Honig U. Madhow and. Verdú Blind adaptive multiuser detection IEEE Trans. Inform. Theory vol. no. pp. Jul.. []. Lin and L. B. Milstein uccessive interference cancellation in multicarrier D/CDMA IEEE Trans. Commun. vol. 8 no. pp. 3 ept.. [] W. M. Jang B. R. Vojcic and R. L. Pickholtz Joint transmitter-receiver optimization in synchronous multiuser communications over multipath channels Baltzer/ACM Wireless Networks vol. no. pp. 8 eb. 8. [] P. Viswanath V. Anantharam and D. N. C. Tse Optimal sequences power control and user capacity of synchronous CDMA systems with linear MME multiuser receivers IEEE Trans. Inform. Theory vol. no. pp ept.. [8] T. M. Lok and T.. Wong Transmitter and receiver optimization in multicarrier CDMA systems IEEE Trans. Commun. vol. 8 no. pp. Jul.. [] T.. Wong and T. M. Lok Transmitter adaptation in multicode D- CDMA systems IEEE J. elect. Area Commun. vol. no. pp. 8 Jan.. [] L. Gao and T.. Wong RL-based adaptive multicode CDMA system in Proc. IEEE Wireless Communications and Networking Conference ChicagoIL ept.. [] H. Y. Kwam and T. M. Lok Power control scheme with signature sequence adaptation for D-CDMA systems in Proc. WCNC ept.. []. L. Miller An adaptive direct-sequence-code-division multiple-access receiver for multiuser interference rejection IEEE Trans. Commun vol. 3 no. pp. eb./mar./apr.. [3] C. N. Pateros and G. J. aulnier An adaptive correlator receiver for direct-sequence spread-spectrum communication IEEE Trans. Commun. vol. no. pp. 3 Nov.. 3
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