|Year : 2010 | Volume
| Issue : 2 | Page : 94-101
Chip Equalized Adaptive Rake Receiver for DS-CDMA UWB Systems
GS Biradar, SN Merchant, UB Desai
SPANN Laboratory, Department of Electrical Engineering, Indian Institute of Technology, Mumbai-400 076, India
|Date of Web Publication||8-May-2010|
G S Biradar
SPANN Laboratory, Department of Electrical Engineering, Indian Institute of Technology, Mumbai-400 076
| Abstract|| |
Conventional Rake receiver is a popular and effective method of utilizing the diversity offered by a DS-CDMA and multipath communication channel. The proposed Rake receiver is useful for suppression of multiple access interference in a multipath channel. The receiver works on chip level equalization on each Rake finger to cancel multi-access interference. Simulation results show that the convergence, diversity gain and bit error probability performance of the proposed receiver is much better than conventional adaptive Rake receiver in multipath channels.
Keywords: Adaptive techniques, DS-CDMA, Multiaccess, Multiuser detection, Rake receiver, Ultra wideband
|How to cite this article:|
Biradar G S, Merchant S N, Desai U B. Chip Equalized Adaptive Rake Receiver for DS-CDMA UWB Systems. IETE J Res 2010;56:94-101
| 1. Introduction|| |
The robustness of Ultra Wideband (UWB) signals to multipath fading is due to their fine delay resolution, which in combination with Rake receiver leads to high diversity order , . Multipath components having differential delays of the order of nanoseconds are resolved. However, in order to have the advantage of high delay resolution, the Rake receiver must be able to capture most of the energy carried by a very large number of different multipath signals. Indeed, the number of detectable multipaths, defined as those exceeding a threshold of 6 dB above the noise floor can be up to one hundred  .
The ideal Rake receiver that combines all of the resolvable multipath components is called All-Rake (ARake). Providing a receiver with a large number of correlators increases the receiver complexity and defeats the purpose of making new devices low-power and low-cost. In practice, the number of multipath components that can be utilized in a typical Rake combiner is limited by power consumption issues, design complexity, and the channel estimation  . The impact of the number of Rake fingers is then a critical design issue  . This has motivated studies on suboptimum Rake combining receivers that process only a subset of the available resolvable multipath components.
Under a multiple access scenario, the presence of multiple signals transmitted at the same time is a typical source of interference for wireless signals, which affects the bit error rate (BER) performance considerably; the range and the capacity of UWB receivers. Several multiple access schemes are proposed for UWB, namely, Time Hopping (TH)  , Frequency Hopping (FH)  and Time-Frequency hopping (FTH)  . In TH, multi-access interference can be reduced by increasing the number of time hops, but this is at the cost of reduced data rate. Similarly, in FH, MAI can be reduced by increasing the number of frequency hops. However, the maximum number of frequency hops that can be achieved in FCCs UWB spectrum is fifteen  .
Direct Spread Code Division Multiple Access (DS-CDMA) is a well known multi-access technique in the presence of narrowband interference and additive white Gaus-sian noise (AWGN). Several multi-user detection techniques have already been reported in literature ,,, . The detailed analysis of multi-user capacity, throughput bit error performance has also been reported  . However, the analysis is limited to AWGN channel. These techniques cannot be directly extended to multipath channels, as these systems are very sensitive to signal mismatch and interchip interference.
The Rake architecture is a suboptimal but efficient implementation of a CDMA re-ceiver , . Each single Rake finger is an independent receiver for the signal from a specific path and correlates with spreading code. Multipath propagation channels are handled by employing multiple fingers one for each propagation path in question. The output symbols of all fingers are then combined coherently and synchronously by the Rake receiver combiner block to yield the received data symbols. In order to combat multi-user and multipath interference, channel has to be estimated at regular intervals. Most of the available literature on Rake receiver discuss either Rayleigh or Log-Normal multipath channel with single user and symbol level equalization ,,,,, .
In this paper, we propose adaptive chip level equalization in each Rake finger, which combines the power of Rake, UWB and DS-CDMA technique. An expression has been derived for optimum tap vectors and implemented using LMS algorithm. The rest of the paper is organized as follows: Signal and system model is developed in Section 2. The proposed Rake receiver and its implementation using LMS algorithm is presented in Section 3. Simulation results are discussed in Section 4. Finally, concluding remarks are made in Section 5.
| 2. Signal and System Model|| |
We consider a K user DS-CDMA UWB system transmitting over multipath channel. Each user employs orthogonal spreading codes modulated by the second derivative of the Gaussian pulse. The transmitted signal generated by kth user is given by
where, T S , is symbol duration, b k (n) is the kth user information bearing sequence (±1) with zero mean and unit energy. The sequence of each user is independent and identically distributed (i.i.d) and S K is the spreading waveform of kth user with unit energy and given by
where, N S, is the spreading gain, T C is the chip duration and p(t) is the second derivative of the Gaussian pulse and given by
where, τm is the pulse shaping parameter.
As shown in [Figure 1], the received signal for asynchronous multipath channel for each user is
where, τK is the relative delay offset of the received asynchronous channel for kth user, g K is unknown multipath channel for user k, x is convolution, z(t) is a zero mean additive white Gaussian noise with variance σ2z
Assuming g k(t) has finite impulse response of maximum order q, the chip rate sampled received signal after UWB pulse matched filtering with length N S is given by
where, h k is effective spreading code of kth user and given by
S k ∈R (Ns+L-1)Χ(L) , code filtering matrix composed of delayed versions of the spreading code of user k, and g k is the unknown multipath parameter vector of user k . These are given respectively by:
Let us assume k = 1is the user of interest at receiver. We can rewrite (5)
where, i MAI is the multi-access interference contributed by other users and given by
| 3. Proposed Rake Receiver|| |
MMSE criterion has been considered to estimate desired signal of user 1. From [Figure 2], the estimate of the desired signal is given by
where, L ≤ q is number of Rake fingers, y l = y(n-lTc )w l is the receivers lth path tap weight vector of same length (N S) as the data vector y l , and H is Hermitian transpose.
The output cost function J to be minimized is given by
The generalized cost function equation is given by
Where, . Optimum receiver lth path tap weight vector Wlopt is found using gradient descent method  . Taking the gradient of (12) with respect to w and equating it to zero results in
The least square estimate of output is given by
3.1 Adaptive Implementation of Proposed Rake Receiver Using LMS
In time varying multipath channels, the optimum filter weights must be computed periodically. Implementation of (13) requires inversion of input correlation matrix which increases computational complexity. The proposed receiver uses LMS algorithm, which has lower computational complexity and simple to implement.
In gradient descent optimization the tap weight vector is moved in negative direction to minimize the cost function J with step size μ. After the nth iteration the weight vector wl is given by
using the standard techniques  equation for weight vector is given by
Similarly, for conventional Rake receiver [Figure 3] next tap weight vector is given by
where, μ is in the range is the order of filter.
| 4. Simulations and Results|| |
This section deals with investigation of performance of a DS-CDMA UWB Rake receiver system based on the achievable multipath diversity gain and bit error probability improvement. Simulations were carried out to evaluate and compare the diversity gain and bit error probability performance of the proposed adaptive MMSE Rake receiver in multipath channels with AWGN. The system for simulations considered is, synchronous DS-CDMA UWB with the following specifications. All users have equal power with Gold sequence of spreading gain 31 as spreading code. Binary phase shift keying with sampling frequency of 50 GHz, chip time of 0.5 nsec and second derivative of the Gaussian pulse of width 0.5 nsec used. Random binary data is generated for each user; the data is spread with the respective spreading code followed by modulation with second derivative of the Gaussian pulse. Each user undergoes a different UWB channel. Channel models CM1, CM2, and CM3 from IEEE P802.15  are used. Channel model parameters are listed in [Table 1] and their impulse response is shown in [Figure 4]. Proposed adaptive MMSE Rake receiver and conventional adaptive MMSE Rake (C-Rake) receiver use training signals of 500 bits followed by decision directed operation. Proposed MMSE Rake receiver does not require spreading code of any user, whereas, it is assumed that C-Rake receiver knows spreading code of the user of interest.
To study the convergence of C-Rake and proposed Rake, we plotted Mean Square Error (MSE) vs. number of bits. MSE is averaged over 200 channels with 1000 bits/channel. Step size μ = 0.001 is considered. [Figure 5] shows MSE plot for E b /N 0=20 dB in CM1 for K=1 and 5. It is observed that proposed Rake receiver converges at a faster rate (100 bits) as compared to C-Rake (≈200 bits) in both the cases. It is also observed that in the presence of MAI, MSE of the proposed Rake receiver increased by a value of 0.0038, whereas MSE of the C-Rake increased by a value of 0.0862. This indicates that the proposed Rake receiver effectively cancel MAI in multi-user scenario.
Diversity gain and Bit error probability is averaged over 500 realizations for each user with 2000 bits/channel. Initial value of tap weight vector w = [0, 0, 0….0] T and r =[0, 0, 0….0] T . Step size μ = 0.001 and 0.001 are considered, as these values are found to give best performance for C-Rake and proposed Rake receivers respectively.
In order to assess the diversity gain of C-Rake and proposed Rake receiver, we define the Rake diversity gain as the ratio of the Rake output SNR to SNR of an arbitrary chosen single MPC, so that the Rake diversity gain can be given by 
Diversity gain is defined as the increase in the received power due to the diversity system, which corresponds to SNR gain when the noise is uncorrelated and zero-mean Gaussien distributed.
[Figure 6] and [Figure 7] show diversity gain as a function of L in CM3 for K=1 and 5 respectively. It is observed that with increase in L there is sharp increase in Δr for proposed Rake receiver as compared to C-Rake receiver. However, gain saturates as L increases. The decline in gain is well known for diversity combining systems  , due to which suboptimal implementations find favor in practical systems. It is also observed that in the presence of MAI diversity gain of the C-Rake decreased by 2 dB, whereas, for the proposed Rake receiver diversity gain increased by an amount of 1.8 dB for large L (L>10). Proposed Rake receiver gives an average improvement of 2 dB as compared to C-Rake receiver in the absence of MAI, and 4 dB in the presence of MAI.
[Figure 8] and [Figure 9] show BER performance as a function of L in CM3 for K=1 and 5 respectively. In the absence of the MAI, C-Rake receiver BER decreases at a rate 10-1 for every addition of 6 Rake fingers in the range (1≤L≤20). Further increase in L does not give much improvement; for proposed Rake, much better BER (10 -3 ) is achieved with L=5. The desired BER performance can be achieved with proposed Rake receiver with half the number of Rake fingers as required for C-Rake receiver.
To verify and investigate receiver performance, bit error probability vs. E b /N 0 for K=5, L=5, 10, 15, and 20 is considered. [Figure 10],[Figure 11] and [Figure 12] shows simulation results in channel models CM1, CM2, and CM3 respectively. In CM1, for L=5, at a BER of 10 -3 the proposed Rake receiver gives an improvement of 9 dB as compared to C-Rake receiver. Further, for every addition of 5 Rake fingers, proposed Rake receiver gives an average improvement of 0.1 dB and C-Rake receiver gives an average improvement of 2 dB. For large values of L (i.e. L=20) and E b /N 0 (i.e. ≥ 14 dB), MAI does not completely cancelled in C-Rake receiver, as a result BER saturates. Whereas, in the proposed Rake receiver MAI is completely cancelled for E b /N 0 =12 dB.
In the case of CM2, the BER performance in comparison with CM1 degrades by an amount of 0.5 dB and 3 dB for proposed Rake and C-Rake receiver respectively. This degradation in BER performance is due to the presence of more number of multipaths. C-Rake fails to cancel MAI and multipath effect even at higher values of E b /N 0 (14 dB), whereas, with 1 dB penalty proposed Rake receiver completely cancels MAI and multipath effect. In CM3, further degradation in BER performance is observed, this is once again due to presence of large number of multipaths. It is to be noted that the proposed Rake receiver completely cancels MAI and multipath effect with a penalty of 4 dB in comparison with CM1 performance.
[Figure 13],[Figure 14],[Figure 15] show bit error probability vs. number of users' performance with E b /N 0 =20 dB in CM1, CM2, and CM3 respectively. It is observed that the proposed Rake receiver BER performance is much better than C-RAKE receiver even for large number of users. This improved performance is once again due to better MAI cancellation capability of the proposed Rake receiver in multipath environment. The number of users supported by the above discussed receivers is summarized in [Table 2]. It is to be noted that, in all three channel models, for a BER ≥ 10 -3 , the number of users supported in proposed Rake receiver is twice the number of users supported by C-Rake receiver, whereas, for a BER ≤ 10 -4 , the number of users supported in proposed Rake receiver is four times the number of users supported by C-Rake receiver. This increased number of user capacity is once again attributed to complete cancellation of MAI in multipath environment.
| 5. Conclusion|| |
We have derived and proposed the chip equalized adaptive MMSE Rake receiver for DS-CDMA UWB multipath channels. The mean square error, diversity gain, and BER as performance index have been used and compared with the C-Rake receiver in multi-user environment. It is observed that proposed Rake receiver converges at a faster rate (< 100 bits) than C-Rake receiver (≈200 bits), and also observed that in the presence of MAI, proposed Rake receiver has lower MSE as compared to C-Rake receiver. The diversity gain of proposed Rake receiver gives an average improvement of 2 dB in single user case and 4 dB in the presence of multi-user case.
BER vs. E b /N 0 performance of the proposed Rake receiver is found to be better in comparison with conventional Rake receiver for all three channel models (CM1-CM3). Proposed receiver gives an improvement of 2 dB at BER of 10-2 and substantial improvement at BER of 10 -3 . Further, it offers significant improvement in MAI cancellation in multipath channels. The number of users supported by the proposed Rake receiver at a BER of 10 -3 is found to be two times that of the conventional Rake receiver with E b /N 0 =20 dB. Further at a BER of 10 -4 , the number of users supported by the proposed Rake receiver is four times the conventional Rake receiver with the same computational complexity.
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| Authors|| |
G. S. Biradar received his Bachelor of Engineering degree in Electronics and Communication from Gulbarga University Gulbarga in 1990 and M.Tech in Telecommunication Systems Engineering from IIT Kharagpur, India in 2002. From 1992 onwards he is working as a lecturer is P. D. A. College of Engineering Gulbarga. He worked on multiuser detectors for 3 rd generation wireless communication. Currently he is working towards his doctoral thesis at IIT Bombay, India. His research interests are in wireless communication and adaptive signal processing.
S. N. Merchant received his B.Tech, M.Tech, and Ph.D degrees all from Department of Electrical Engineering IIT Bombay, India. He has more than 20 years of experience in teaching and research. He has made significant contributions in the filed of signal processing and its applications. His noteworthy contributions have been in solving state of art signal and image processing problems faced by Indian defence. His broad area of research interests are signal and image processing, multimedia communication, wireless sensor networks and wireless communications, and has published extensively in these areas. He has been a chief investigator for number of sponsored and consultancy projects. He has served as a consultant for both private industries and defence organization. He is a reviewer for many leading international and national journals and conferences. He was chair of local organization committee for IEEE International Conference on Computer Vision, 1998 (ICCV 98). He is fellow of IETE. He is a recipient of 10th IETE Prof. SVC Aiya Memorial award for his contribution in the field of detection and tracking.
U. B. Desai received the B. Tech. degree from Indian Institute of Technology, Kanpur, India, in 1974, the M.S. degree from the State University of New York, Buffalo, in 1976, and the Ph.D. degree from The Johns Hopkins University, Baltimore, U.S.A., in 1979, all in Electrical Engineering. From 1979 to 1984 he was an Assistant Professor in the Electrical Engineering Department at Washington State University, Pullman, WA, U.S.A., and an Associate Professor at the same place from 1984 to 1987. Since 1987 he has been a Professor in the Electrical Engineering Department at the Indian Institute of Technology - Bombay. He has held Visiting Associate Professor's position at Arizona State University, Purdue University, and Stanford University. He was a visiting Professor at EPFL, Lausanne during the summer of 2002. From July 2002 to June 2004 he was the Director of HP-IITM R and D Lab. at IIT-Madras. His research interest is in wireless communication, wireless sensor networks and statistical signal processing. He is the Editor of the book "Modeling and Applications of Stochastic Processes" (Kluwer Academic Press, Boston, U.S.A. 1986). He is also a co-author of two books "A Bayesian Approach to Image Interpretation" and "Multifractal based Network Modeling", both from Kluwer Academic Press. Dr. Desai is a senior member of IEEE, a Fellow of INSA (Indian National Science Academy), Fellow of Indian National Academy of Engineering (INAE). He is on the Executive Committee (EC) for the All India Council of Technical Education (AICTE). He was an associate editor of IEEE Transactions on Image Processing from Jan 1999 to Dec.2001. He is Vice-President of the Indian Unit for Pattern Recognition and Artificial Intelligence. He is on the Technology Advisory Board of Microsoft Research Lab. India. He was associate Vice Chair for PHY/MAC for IEEE International Conference for Wireless Communication and Networking (WCNC) 2005, TPC Chair for WPMC 2007, and TPC Co-Chair for COMSWARE 2008. He is the Chair for IEEE Bombay Section. He is also on the Visitation Panel for University of Ghana.
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15]
[Table 1], [Table 2]