IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 4, APRIL 2002
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Hopfield Multiuser Detection of Asynchronous MC-CDMA Signals in Multipath Fading Channels Ebrahim Soujeri, Student Member, IEEE, and Huseyin Bilgekul, Member, IEEE
Abstract—Multiuser reception using Hopfield neural network (HNN) for asynchronous multicarrier code-division multiple access (MC-CDMA) in a multipath fading channel is investigated. We have shown that by the appropriate choice of HNN parameters from the channel state information, the HNN can collectively resolve the MPF effects and the multiple-access interference in the system. Index Terms—Hopfield neural network, MC-CDMA, multipath fading channel.
I. INTRODUCTION
M
ULTIUSER reception using Hopfield neural network (HNN) detector in AWGN channel has earlier been studied and shown to have excellent sub-optimum performance by Miyajima and Kechriotis [1], [2]. In this study, we are showing that the HNN proposed by [1] and [2] fails to exhibit multiple-access interference (MAI) resilient performance in a multipath fading (MPF) channel. The reason behind this failure is that HNN parameters were set without considering the MPF channel characteristics. Multicarrier code-division multiple access (MC-CDMA) schemes are receiving a lot of attention in multiuser communications [3], [4]. We are considering the HNN detection in conjunction with asynchronous MC-CDMA. The main contribution of this letter is to design a HNN detector capable of jointly canceling MPF effects and MAI from the received signal in the system. This is achieved by deriving the Hopfield receiver parameters using the channel state information (CSI) provided by a channel estimator. Simulation results show that when CSI is incorporated into the HNN parameters, the required MAI resilience in MPF channel is obtained.
Fig. 1. Structure of MC-CDMA transmitter.
to a subcarrier spaced apart from its neighboring subcarrier by Hz, where with and representing the symbol, bit and chip durations, respectively. All the chips of parallel transmitted bits are modulated on orthogonal of the subcarriers is given subcarriers. The th frequency , where [4]. The by generalized MC-CDMA transmitter structure employed here is shown in Fig. 1. Several multipath models have been used in the literature, varying from the very comprehensive one to the simple tapped delay line model. In this letter, the multipath fading channel is modeled as consisting of a fixed number of resolvable Rayleigh faded paths. The low-pass impulse response of the channel for user is given by (1)
II. SYSTEM MODEL We are considering an uplink scenario where the base station active users with different energies receives the signals of over different paths, at the absence of power control. It is assumed that all users transmit data in equal symbols of length . A single data bit within the symbol is replicated into parallel , from a known set of length , multiplies the copies. A chip th branch of the parallel stream which is then BPSK modulated
is a where is the total number of resolvable paths, and complex Gaussian r.v. with zero mean and variance represents the channel delay of the th path. The path gains are independent for different and . Here, is a Rayleigh is a uniform random variable random variable and the angle . This channel model is illustrated in Fig. 2. in the interval The composite asynchronous MC-CDMA received signal in MPF channel is given by [4]
Manuscript received October 4, 2001. The associate editor coordinating the review of this letter and approving it for publication was Prof. Z. Zvonar. The authors are with the Department of Electrical and Electronics Engineering, Eastern Mediterranean University, Magosa-KIBRIS, Mersin-10, Turkey (e-mail:
[email protected]). Publisher Item Identifier S 1089-7798(02)04491-5. 1089-7798/02$17.00 © 2002 IEEE
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IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 4, APRIL 2002
In the previous study of HNN that was proposed for an AWGN channel [1], [2], the signature waveform of user , was taken as (6)
Fig. 2.
Multipath fading channel model with
9 taps.
The terms involved in describing the received signal are given as received signal energy of user ; AWGN with power spectral density ; subcarrier index, given by ; propagation delay of user ; th user, th path channel delay; random phase for each subcarrier; th data bit in the transmitted stream of user ; th chip in the spreading sequence of user . are randomly chosen integers such that Propagation delays and channel tap delays are assumed seconds away from each other as shown in Fig. 2. to be III. INTERFERENCE ANALYSIS The application of power control is not assumed such that without fading, signals from different users would not necessarily arrive at the base station receiver with equal power. In order to derive HNN parameters from the CSI, we must proceed in the following manner. We express the signature waveform of in terms of the th spreading sequence the th user and the th path gain and phase rotation as follows
It can be easily verified that the signature waveform of the previous design given by (6) is a special case of the signature waveform of the multipath case given by (3). By choosing and , then (3) is converted to (6). The multipath performance analysis of HNN multiuser detection of MC-CDMA signals is the main contribution of this work. We choose the HNN parameters by using the multipath signature waveform expressed in (3). We must emphasize that the presence of accurate and perfect CSI to the receiver is very crucial, because imperfections in CSI degrade the HNN receiver performance. One can achieve channel estimation by sending training sequences or using pilot channel. Periodic transmission of training sequences, make the identification of CSI feasible since both input and output signals are known during the transmission of these sequences. In this work, the CSI estimation procedures are outside our scope; we assume either perfect CSI or CSI with error. The percentage error in CSI estimation used in the simulations presented in this work is defined as the same percentage error introduced to both the magnitude and phases of all the paths. IV. HOPFIELD NETWORK DESCRIPTION Once the cross-correlation matrices , and the MF outputs are determined in the fashion described in (4) and (5), we could build the Toeplitz cross-correlation matrix as described in [2]. The optimum multiuser by detection (OMD) algorithm calculates the estimate minimizing the likelihood function as [1], [2] (7) with
(3) cross-correlation Having done this, we can express the [1], [2] by deriving their th matrices , that stands for MAI between user and user element as follows:
standing for candidates of the estimate and standing for the multiuser MF receiver output given by (5). Now, we may transform the minimization of the likelihood function given in (7) into the minimization of HNN energy described by the expression [1], [2] function (8)
(4) stands for complex conjugate operation. Moreover, where we can express the th matched filter (MF) output of user , as
(5) The expressions given by (4) and (5) are needed in deriving the HNN parameters as shown in next section.
and . Note that in (8), is the output by setting of HNN neurons and is the interconnection matrix between HNN neurons. The reader could refer to [1] or [2] for more informative details about the dynamics of HNN receiver. Once the above transformation is done, the sub-optimum escould be simply driven from the HNN receiver timate . output by using V. SIMULATION RESULTS In this section we examine the performance of the HNN multiuser detector for asynchronous MC-CDMA transmissions
SOUJERI AND BILGEKUL: MULTIUSER DETECTION OF ASYNCHRONOUS MC-CDMA SIGNALS
(
)
Fig. 3. Performance of the HNN detector vs. MAI E =E in MPF channel without using CSI. HNN performance in AWGN is included for comparison.
149
(
Fig. 5. Performance of the proposed HNN detector vs. MAI E =E MPF channel ( paths) with various errors in CSI estimation.
9=3
) in a
Assuming perfect CSI estimation, the multipath parameters are incorporated into the HNN detector and the performance is indicated in Fig. 4. Under this condition, the HNN performance is similar to the AWGN performance with respect to irrespective of the number of paths. The performance of the proposed system depends on the accuracy of the CSI delivered to the receiver. We have also examined our system performance for the case in which the CSI delivered to the receiver contains errors in the range of 2%–10%. The performance under such conditions is given in Fig. 5. It is clearly observed that the less the error in the CSI, the better the HNN performance. The case of 0% error in Fig. 5 corresponds to the delivery of perfect CSI to the HNN receiver. VI. CONCLUSION
(
Fig. 4. Performance of the proposed HNN detector vs. MAI E =E MPF channel for various number of paths and perfect CSI estimation.
) in a
in a multipath channel. Computer simulations were performed users, using the following system parameters chips/bit (drawn from Gold sequences), bits/symbol and the energy of the desired user to AWGN density ratio dB. Propagation delays are randomly introduced . Performance of the HNN detector deas signed for AWGN channel but used in a multipath channel is illustrated in Fig. 3. The BER is plotted with respect to MAI, (average energy of the undesired which is expressed as users to the energy of the desired user). The performance in AWGN channel that was studied by [1], [2] is included for comparison. The HNN detector shows rapid performance or the number of paths increase. In fact, degradation as the HNN performance is very similar to the MF performance in multipath situations.
The HNN detector performance has been studied in asynchronous multipath channel. When CSI is not utilized, HNN performance degrades similar to matched filter. However, when CSI is incorporated into HNN parameters, the HNN detector shows excellent MAI resilience property. Under erroneous CSI conditions, the proposed HNN continues to keep its MAI resilience property with some degradation. REFERENCES [1] T. Miyajima and T. Hasegawa, “Multiuser detection using a Hopfield network for asynchronous code-division multiple-access systems,” IEICE Trans. Fund. Elect., Commun. Comp. Sci., vol. E79-A, no. 12, pp. 1963–1971, Dec. 1996. [2] G. I. Kechriotis and E. S. Manolakos, “Hopfield neural network implementation of the optimal CDMA multiuser detector,” IEEE Trans. Neural Networks, vol. 7, pp. 131–141, Jan. 1996. [3] S. Hara and R. Prasad, “Overview of multicarrier CDMA,” IEEE Commun. Mag., vol. 35, no. 12, pp. 126–133, Dec. 1997. [4] E. A. Sourour and M. Nakagawa, “Performance of orthogonal multicarrier CDMA in a multipath fading channel,” IEEE Trans. Commun., vol. 44, pp. 356–366, Mar. 1996.
