Cyclic-prefix code division multiple access (CP-CDMA) has been shown to be effective in combating frequency selective fading channels. However, this effectiveness can be leveraged only with accurate channel impulse response (CIR) estimate and proper compensation for the carrier frequency offset (CFO). In this paper, we formulate a subspace-based joint CFO and CIR estimator without using any pilot symbols. The users' spreading codes are selected following the steps in. We show that the selected users' spreading codes must also satisfy an additional requirement in order to have the signal subspace dimension to be independent of users' CFO and CIR. For high signal to noise ratio, we show that the proposed CFO estimator is unbiased and derive the theoretical mean square error for CFO estimate. Computer simulation results show that the proposed estimator's performance is close to Cramer-Rao lower bound.

In the uplink of multi-user multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems, there are multiple carrier frequency offsets (CFO's) from the multiple users. In this paper, we study algorithms to estimate these multiple CFO values. We first derive the maximum likelihood (ML) estimator and show that the complexity of the ML estimator increases exponentially with the number of users so that the estimator is not suitable for practical implementations. To reduce the complexity, we propose a sub-optimal algorithm using constant amplitude zero autocorrelation (CAZAC) sequences. The complexity of the proposed method increases only linearly with the number of users. Using computer simulations, we compare the performance using CAZAC training sequences with that using the m sequence and the short training field (STF) of the IEEE 802.11n systems. The results show that in the low to medium SNR regions, the performance using CAZAC sequences is very close to the single-user Cramer-Rao bound. For high SNR regions, an error floor exists due to multiple access interference (MAI). The error floor using CAZAC sequences is more than 10 times smaller compared to the error floor using the other two sequences.

The aim of this letter is twofold: 1) to stabilize a fast adaptive noise subspace algorithm, which was proposed earlier in the literature under the name of FRANS algorithm and 2) to present a low computational cost version that is free from any square root and division operations, which is very suitable for VLSI implementation. A stability analysis and simulation results are also given in order to assess the performance of this algorithm.

Subspace-based channel impulse response (CIR) estimators have been proposed for multi carrier code division multiple access (MC-CDMA) systems. Channel identifiability conditions have been formulated for blind (non-data-aided) CIR estimators. These identifiability conditions require the channel filtering matrix to satisfy certain rank conditions. In this paper, the generalized uplink MC-CDMA system model is analyzed in detail. It will be shown that each user's signal subspace dimensionality is independent of the user's spreading code and CIR. Furthermore, for any realization of the users' CIR, the channel identifiability is established by only imposing a simple rank condition on the users' spreading codes.

Signal detection is a crucial phase in building a cognitive radio system. However, energy detection, as well as other 'moment detector', has been shown to exhibit considerable performance degradation in the presence of noise power uncertainty. In this paper, we discuss another method that employs fast Fourier transform (FFT) and max-to-mean ratio (MMR) to detect weak narrowband signals. An analytical approximation of the threshold used is derived, and compared with the empirically simulated constants to assess the degree of accuracy of the former. Simulation results are then presented to illustrate the impact of different parameters on the performance of the detector. Finally, comparisons with energy detector are drawn to highlight some important advantages of the MMR method, i.e. noise power independence and lower sample size requirement.

Block Iterative - generalized decision feedback equalizer (BI-GDFE) is an iterative receiver using previously made hard decisions to cancel out the multiple access interference (MAI) and inter-symbol interference (ISI). In this paper, we formulate the BI-GDFE for downlink multi-carrier code division multiple access (MC-CDMA) system under time varying channel conditions. The time varying coefficients of each channel tap over a data block is a finite length sequence whose maximum bandwidth depends on the Doppler bandwidth. This sequence can be represented using basis expansion models proposed for time varying channels. In this paper, Slepian basis expansion is used because the number of basis vectors required to represent the time varying channel is less compared with other basis expansion models and hence the number of parameters to be estimated is less. Thus less number of pilot symbols are required for channel estimation. BI-GDFE for fully loaded downlink MC-CDMA system can be formulated as a one-tap equalizer which is simple for implementation. Furthermore, the computation of the signal to interference noise ratio (SINR) value for each iteration of BI-GDFE can be simplified using matrix manipulations for the downlink MC-CDMA system. Computer simulations show that the BER performance of BI-GDFE with channel estimation is close to the single user matched filter bound (MFB).

In this paper, we propose a new optimal diagonal-matrix step-size strategy for some noise subspace estimation algorithms. The proposed step-sizes control the decoupled subspace vectors individually as compared to conventional methods where all the subspace vectors are multiplied by the same step-size value. Simulation results show that this optimal diagonal- matrix step-size strategy outperforms the original algorithms as it offers faster convergence rate, smaller steady state error and similar orthogonality error simultaneously. Finally, the algorithms with the proposed step-size strategy are used for blind channel estimation in MC-CDMA system.

In this letter, we propose a new adaptive algorithm for the generalized symmetric eigenvalue problem, which can extract the principal and minor generalized eigenvectors, as well as their corresponding subspaces, at a low computational cost. A comparison with other adaptive algorithms from the literature, including the batch generalized singular value decomposition (GSVD) technique, is also given to show the superiority of the proposed algorithm in terms of convergence performance and computational complexity.

In this paper we propose a non-data aided estimator for joint time delay, carrier frequency offset (CFO) and channel estimation for uplink asynchronous CDMA system. The cost function for CFO estimation is a determinant of a matrix, which is a function of the CFO. The CFO estimator does the estimation by performing a linear search and the search point which minimizes the determinant is the estimated CFO. The matrix corresponding to the estimated CFO is used for channel estimation, where the channel impulse response (CIR) is obtained as the eigenvector corresponding to the minimum eigenvalue of that matrix. Time synchronization is inherently done along with the channel estimation, assuming the maximum channel order for all user channels is known. We also modify the existing estimator based on generalized eigenvalue problem (GEVP) and show the performance improvement through computer simulations. The performance of the proposed method is compared with the modified generalized eigenvalue problem method (MGEVPM). Computer simulations show that the proposed estimator performs better than MGEVPM and has wider CFO acquisition range than MGEVPM. Using Taylor's series approximation, we reformulate the proposed estimator in order to reduce the computational complexity. Through computer simulations we show that the performance of the reformulated estimator improves with increase in the order of Taylor's series and performs better than MGEVPM.

Combining orthogonal frequency division multiplexing (OFDM) and multiple input and multiple output (MIMO) technologies enables high spectral efficiency data transmission over frequency selective fading channels. However, carrier frequency offset (CFO) and channel estimation become more complex for MIMO-OFDM systems. In this paper, we propose a class of efficient shift-orthogonal training sequences to assist joint CFO and channel estimation. We show that with the proposed training sequence, the CFO estimation touches Cramer- Rao bound (CRB) at practical SNR values. Such sequences are efficient as the overhead used for channel estimation can be significantly reduced compared to using conventional training sequence designs. We also derive a tight lower bound on the MSE of the channel estimation in the presence of the residual CFO.

In Liu and Toreli (1998), a blind carrier frequency offset (CFO) estimation method was proposed for orthogonal frequency multiplexing (OFDM) systems. This method makes use of the fact that in practical OFDM systems, there are some subcarriers that do not carry any data. However, the computation complexity of the method is rather high. In this paper, based on practical considerations, we propose a low complexity blind CFO estimation method. We derive an approximate closed-form solution for the CFO estimate. We show that the proposed algorithm achieves similar performance as the method in Liu and Toreli (1998) with significantly reduced computational complexity. For relatively large CFO values, we show that we could use the iterative algorithm in Wu et al. (2005) to improve the performance of the proposed algorithm.

In this paper we propose a two-stage carrier frequency offset (CFO) estimator for frequency synchronization in the uplink of MC-CDMA system. The proposed approach is non-data-aided and uses only the second order statistics (SOS) of the received signal. In the first stage, determinant of a matrix which is a function of the CFO is used as a cost function. A linear search is performed and the search point which minimizes the determinant value is taken as the estimated CFO. This is called coarse synchronization. In the second stage, adaptive LMS algorithm is used to estimate the CFO. The LMS algorithm is initialized with the estimated CFO from the first stage. The application of the gradient type algorithm is due to the local convexity of the cost function. The performance of the proposed estimator is evaluated through computer simulations.

The presence of residual carrier frequency offset (CFO) in an orthogonal frequency division multiplexing (OFDM) system leads to a loss of orthogonality between the subcarriers. This introduces inter-subcarrier interference and degrades the system performance significantly. In the literature, Liu and Tureli proposed a blind CFO estimation method based on the observation that in a typical OFDM system not all the subcarriers are used for data transmission. However, the computational complexity of such a method is very high. Based on practical considerations, we propose an approximate closed-form solution for the blind estimation of CFO that is easily implementable at a very low cost. We also propose a successive CFO estimation and compensation procedure, which reduces the performance degradation of the proposed algorithm as compared with the method of Liu and Tureli when relatively large CFO values are assumed. In addition, a decision-directed extension of the successive algorithm, which further improves the CFO estimation at a slightly higher complexity, is also given.

In Gao and Nallanathan (IEEE Signal Process. Lett., vol.13, no.2, p.73-6, Feb. 2006), a polynomial rooting-based carrier frequency offset (CFO) estimator for OFDM systems was proposed. It is essentially based on the idea of rooting the first-order derivative of the cost function derived in Liu and Tureli (1998). We discuss the connection of this work with some earlier work in the literature (Attallah, 2004)

A blind carrier frequency offset (CFO) estimation algorithm using the null subcarriers for orthogonal frequency diversity multiplexing (OFDM) systems was proposed in [1]. The optimal null subcarrier placement that minimizes the Cramer Rao bound (CRB) was studied in [3]. In this paper, we study the optimal null subcarrier placement from an SNR maximization point of view. We first derive the relationship between the SNR of the CFO estimation and the placement of null subcarriers. Based on that, we formulate the optimization problem and find the optimal solution using convex optimization for small CFO values. We also discuss the optimality of the null subcarrier placement in practical OFDM systems where guard bands are required at both ends of the spectrum.

This paper addresses the problem of blindly estimating the carrier offset and channel response in the uplink of multi-user CDMA systems having large variation in carrier offset. Two blind subspace-based estimation methods, namely Exact Determinant Minimization Method (EDMM) and Approximate Determinant Minimization Method (ADMM) are proposed, which exploit the orthogonality between the signal and noise subspaces. The performance of the proposed methods is compared with the available solution using Generalized Eigenvalue Problem Method (GEVPM). Simulation results are given to show that the proposed methods give better performance than the GEVPM and have a wider acquisition range for the carrier offset.

In this paper, we propose new adaptive algorithms for the extraction and tracking of the least (minor) eigenvectors of a positive Hermitian covariance matrix. The proposed algorithm is said fast in the sense that its computational cost is of order O(np) flops per iteration where n is the size of the observation vector and p < n is the number of minor eigenvectors we need to estimate. This algorithm is based on a stochastic gradient technique and a fast orthogonalization procedure that guarantees the algorithm stability and the orthogonality of the weight matrix at each iteration. Despite its low computational cost, the proposed algorithm is quite efficient as shown by simulation experiments and performs better than other existing methods of higher computational complexity

In orthogonal frequency division multiplexing (OFDM) systems, the loss of orthogonality between the subcarriers due to carrier offset can degrade the performance of the system. In the literature, Liu and Tureli proposed a blind, music-like method to solve such a problem. The latter has a good performance as compared to the Cramer-Rao bound, but can have a very high computational complexity. In this letter, based on practical considerations, we present a new implementation of the previous method that reduces significantly the cost without sacrificing the performance.

A high peak-to-average power ratio is a major problem that is inherent in all multicarrier communication systems. Clipping the high-peak power samples introduces (extra) clipping noise, which degrades the system performance in terms of bit-error rate (BER). Measuring the BER usually requires a very long simulation time, as clipping occurs very rarely. We propose a method called clipping noise injection, which allows BER estimation (due to clipping) in discrete multitone-based systems in a fast and quite precise way. Savings of as great as 90% or more are observed in some simulations that are reported. Higher savings are expected when lower BER cases have to be studied.

We investigate the problem of CDMA multiuser detection in the presence of a small residual carrier offset. We propose, in particular, a method based on the generalized eigenvalue problem for efficiently estimating the channel response and the carrier offset. A closed-form solution is obtained without any knowledge of the transmitted symbols. Simulation results are given to verify the validity of the proposed method. It is shown that the proposed method can achieve a similar or better performance but with a reduced computational complexity as compared to a previous algorithm which uses a polynomial matrix projection property.

We consider a bootstrap-based approach to enhance the performance of RAKE receivers in multi-user CDMA systems over a multipath frequency selective slowly fading channel. A training based strategy is proposed to identify a low order channel. In this approach we use an FIR filter model with unknown length, estimating the model directly with low complexity in the time domain. Based on the estimates, bootstrap-based multiple hypothesis tests are applied to identify the non-zero coefficients of the FIR filter; in other words low order estimates of the channel. Simulation results demonstrate the power of using this technique in RAKE receivers in unknown noise environments.

High peak to average power ratio (PAR) is a major problem that is inherent to all multi-carrier communication systems. Clipping the high peak power samples introduces (extra) clipping noise, which degrades the system performance in terms of bit error rate (BER). Measuring BER usually requires very long simulation time, as clipping occurs very rarely. In this paper, we propose a method called clipping noise injection, which allows us to estimate BER (due to clipping) in DMT-based systems in a fast and quite precise way. Savings of as great as 90% or more are observed in some simulations that are reported in this paper. Higher savings are expected when lower BER cases have to be studied.

This paper analyses the fast subspace tracking algorithm recently proposed by Attallah and Abed-Meraim. Specifically, the associated Ordinary Differential Equation is derived and its properties studied in detail. Partial comparisons with other subspace tracking algorithms are made.

The problem of CDMA multiuser detection in the presence of a small residual carrier is considered in this paper. Subspace-based approaches are employed for channel estimation and signal demodulation. The channel response and carrier offset are estimated separately in order to avoid the computational complexity of joint estimation of two parameters. The simulation results show that the separate estimation approach results in lower BER than a previous subspace-based joint estimation algorithm does for a large range of carrier offsets which are generally considered in practical applications. Adaptive channel estimation in a time-variant channel is also considered. A novel adaptive algorithm for subspace estimation, namely the normalized orthogonal Oja (NOOja) algorithm, is used to track the channel variations with time. The NOOja algorithm is applicable for both signal and noise subspace tracking and offers advantages of better orthogonality and numerical stability than previous tracking algorithms without any significant increase in computational complexity. It is shown that the NOOja algorithm exhibits good tracking performance in a time-variant channel.

We propose a new adaptive algorithm for subspace estimation and tracking that is based on Rayleigh's quotient. This algorithm allows the estimation of the signal subspace of a vector sequence. It has a number of interesting properties such as a low computational complexity, a fast convergence, orthogonality of the subspace vectors which is ensured at each iteration and a good numerical stability. The proposed algorithm outperforms Oja's algorithm.

Clipping the peak power samples in the DMT signal introduces clipping noise which degrades the system performance. A previous report proposed the spectrum shaping method in which clipping noise is shifted to the high frequency subcarriers that can tolerate higher noise levels. We propose two new clipping noise reduction schemes, one of which is used in conjunction with the spectrum shaping method, to efficiently reduce the clipping noise in ADSL transceivers. The second scheme reduces the clipping noise through a signal randomization, transparent to the receiver. We also study the reduction in clipping noise by combining the two proposed schemes.

We present two normalized versions of Oja's (1992) algorithm (NOja and NOOja), which can be used for the estimation of minor and principal subspaces of a vector sequence. The new algorithms offer, as compared to Oja, a faster convergence, orthogonality, and a better numerical stability with a slight increase in computational complexity.

In this letter, we propose an orthogonalized version of the Oja algorithm (OOja) that can be used for the estimation of minor and principal subspaces of a vector sequence. The new algorithm offers, as compared to Oja, such advantages as orthogonality of the weight matrix, which is ensured at each iteration, numerical stability, and a quite similar computational complexity.