Parthapratim De

Blind Spectrum Sensing Algorithms for Cognitive Radio Networks

In a cognitive radio network, the spectrum that is allocated to primary users can be used by secondary users if the spectrum is not being used by the primary user at the current time and location. The only consideration is that the secondary users have to vacate the channel within a certain amount of time whenever the primary user becomes active. Thus, the cognitive radio faces the difficult challenge of detecting (sensing) the presence of the primary user, particularly in a low signal-to-noise ratio region, since the signal of the primary user might be severely attenuated due to multipath and shadowing before reaching the secondary user. In this paper, a blind sensing algorithm is derived, which is based on oversampling the received signal or by employing multiple receive antennas. The proposed method combines linear prediction and QR decomposition of the received signal matrix. Then, two signal statistics are computed from the oversampled received signal. The ratio of these two statistics is an indicator of the presence/absence of the primary signal in the received signal. Our algorithm does not require the knowledge of the signal or of the noise power. Moreover, the proposed detection algorithm in this paper is blind in the sense that it does not require information about the multipath channel distortions the primary signal has undergone on its way to reaching the secondary user. Simulations have shown that our algorithm performs much better than the commonly used energy detector, which usually suffers from the noise uncertainty problem.

A calculation-efficient algorithm for decision feedback equalizers

We describe a method for decision feedback equalizers used in high speed digital receiver demodulators such as terrestrial digital television (DTV) receivers. The new algorithm uses the sparse channel characteristics of the DTV transmission. A variation of the decision feedback equalizer, namely the partial feedback equalizer, is also introduced. The sparseness of the channel is combined with the partial feedback equalizer to develop the new algorithm. Similarity with subspace based filtering is noted, which results in robust performance in the presence of noise. The new algorithm has a superior convergence speed and lower steady state mean squared error, as compared to conventional approaches.

Blind Sensing Algorithms for Cognitive Radio

In this paper, simulation results are provided for a novel blind sensing algorithm. The results are compared with that of an energy detector. Since it is difficult to estimate the noise variance accurately, the performance of the energy detector with about 1 to 2 dB uncertainty in noise variance is considered. Simulations show the algorithm to perform much better than the energy detector. The algorithm does not require an estimate of the noise power. Till date, not much work has been done on blind sensing algorithms in the low SNR regime. Algorithms based on cyclo-stationarity have been developed in previous papers. However, the performance of these algorithms at low SNR (like -10 dB) has not been investigated. Moreover, unlike the previous algorithms, the novel sensing algorithm here does not require information about the multipath channel distortions the primary signal has undergone on its way to reaching the secondary user. This blind sensing is particularly useful, if the secondary user does not have much information about the primary user (say wireless microphone user)

Low complexity data detection using fast Fourier transform decomposition of channel correlation matrix

This paper presents an efficient FFT based channel-equalization method for data detection. The data detection method is applicable to multiuser detection in the downlink, and single user detection in the uplink. It can operate for chip rate sampling as well as higher sampling rates. The FFT implementation is enabled by approximating the channel correlation matrix by a right circulant matrix. Furthermore, the circulant matrix approximation is optimized via a simple permutation procedure. The solution offers very low complexity relative to other receivers. For instance, for twelve codes with spreading factor 16 each, the complexity of the proposed solution is about 25% of the complexity of the approximate Cholesky based joint detector. The proposed FFT based solution significantly outperforms the matched filter (MF) and is comparable in performance to the approximate Cholesky based joint detector.

Subspace based decision feedback equalization

We investigate subspace based decision feedback equalizers. Efficient decision feedback equalizers are designed to exploit the sparseness of the channel. The sparseness of the channel allows subspace based approaches to be employed. The new equalizers have superior convergence speed and lower steady state mean squared error.

A delta least squares lattice algorithm for fast sampling

Most shift operator-based adaptive algorithms exhibit poor numerical behavior when the input discrete time process is obtained from a continuous time process by fast sampling. This includes the shift operator based least squares lattice algorithm. We develop a delta least squares lattice algorithm. This algorithm has a low computational complexity compared with the delta Levinson RLS algorithm and shows better numerical properties compared with the shift least squares lattice algorithm under fast sampling. Computer simulations show that the new algorithm also outperforms an existing delta least squares lattice algorithm.

Combined Linear Prediction and Subspace Based Blind Equalizers

A novel hybrid linear prediction (LP) and subspace decomposition based blind equalization algorithm, based on second-order statistics, is proposed in this paper. Previous blind equalization algorithms based on subspace decomposition and LP methods have problems when the channel order is under/over estimated. Previous subspace based algorithms exhibit significantly higher residual output mean square error if the estimation of channel length is off even by one, (Tong et al., 1994), (Li and Fan, 2000). In a practically noisy environment, accurate rank determination may be difficult. Even the linear prediction algorithms (Slock, 1994), (Liavas et al., 2000) are not robust to order over-estimation because solving the Yule Walker equation requires the computation of the pseudo-inverse of the noise free correlation matrix, for which the theoretical rank of the noise-free correlation matrix needs to be known. If the channel order is over-estimated, some of the small eigen-values (corresponding to noise) are erroneously classified in the signal subspace and are then inverted, and the LP algorithms exhibit large mean square errors (Liavas et al., 2000). In this paper, we propose a novel hybrid linear prediction and subspace based blind equalization algorithm. The superior performance of subspace based methods in low signal-to-noise ratio (SNR) is thus integrated into our method. Our algorithm is robust to channel order under/over estimation. Our algorithm is a data based (as opposed to channel based) algorithm and avoids effects of channel estimation errors. Simulations clearly indicate that our algorithm performs very well under channel order under/over-estimation, when LP and subspace based blind equalizers fail.

Linear prediction based semiblind channel estimation for multiuser OFDM with insufficient guard interval

To meet the demand of high data rate transmissions for multimedia wireless communications, orthogonal frequency division multiplexing (OFDM) systems in conjunction with multiple-input multiple-output (MIMO) signal processing have been considered one of the central techniques in advanced wireless communications. In the paper, two semiblind channel estimation algorithms are proposed for the uplink multiuser OFDM systems with insufficient guard interval, in contrast to sufficient guard interval assumed in most of the prior works. A zero-padding OFDM system, which zero-pads rather than cyclicly prefixing each block, is considered in this paper. By utilizing the relation between the linear prediction error filters (LPEFs) of the received signal with multiple prediction orders and the transmitted data sequence, the first proposed algorithm, namely the multistage LP (MLP) based algorithm, can estimate the MIMO channel coefficients, with only a single pilot OFDM block used. To reduce the sensitivity of the proposed algorithms to the channel order overestimation, it is proposed to implement the LPEFs with a QR-decomposition based approach. This QRdecomposition based approach alternatively computes the LPEFs without direct inversion of the received signal correlation matrix, thus exhibiting robustness against channel order overestimation. Some simulation results are presented to demonstrate the effectiveness and robustness of the proposed algorithms.

Robust QR Decomposition Based Blind Equalizers

This paper proposes a novel hybrid linear prediction and QR based blind equalization algorithm. The algorithm is more robust to channel order under/over estimation. The algorithm is a data based (as opposed to channel based) algorithms and is also numerically superior. Simulations clearly indicate that our algorithm performs very well under channel order under/over estimation, when LP and QRD based blind equalizers fail. In the algorithm, there is no matrix inversion involved. So small eigen values (wrongly classified in the signal subspace - in the case of channel over-modelling) are not inverted and hence there is very little performance degradation

A modified normalized lattice adaptive filter for fast sampling

Most filters, adaptive or not, formulated using the delay operator, have no limit when sampling becomes fast and therefore they will have numerical problems. We will show that one reason that the normalized lattice filter has less numerical problems is because that it has a limit as the sampling period tends to zero. The transfer function in the s-domain obtained as a limit of the normalized lattice filter will, however, have only every other power in the denominator polynomial. We propose a modified normalized lattice filter that can realize any arbitrary transfer function in the discrete (z) domain and its order-recursive limit, as the sampling period tends to zero, can realize any arbitrary transfer function in the s-domain. Various stability properties of the new lattice are also studied.