Showing papers on "Signal-to-noise ratio published in 2008"

Gaussian Interference Channel Capacity to Within One Bit

Abstract: The capacity of the two-user Gaussian interference channel has been open for 30 years. The understanding on this problem has been limited. The best known achievable region is due to Han and Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a very simple and explicit Han-Kobayashi type scheme can achieve to within a single bit per second per hertz (bit/s/Hz) of the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high signal-to-noise ratio (SNR) regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

Nonlocal Image and Movie Denoising

Abstract: Neighborhood filters are nonlocal image and movie filters which reduce the noise by averaging similar pixels. The first object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other filter classes. A CCD noise model will be presented justifying the involvement of neighborhood filters. A classification of neighborhood filters will be proposed, including classical image and movie denoising methods and discussing further a recently introduced neighborhood filter, NL-means. In order to compare denoising methods three principles will be discussed. The first principle, "method noise", specifies that only noise must be removed from an image. A second principle will be introduced, "noise to noise", according to which a denoising method must transform a white noise into a white noise. Contrarily to "method noise", this principle, which characterizes artifact-free methods, eliminates any subjectivity and can be checked by mathematical arguments and Fourier analysis. "Noise to noise" will be proven to rule out most denoising methods, with the exception of neighborhood filters. This is why a third and new comparison principle, the "statistical optimality", is needed and will be introduced to compare the performance of all neighborhood filters. The three principles will be applied to compare ten different image and movie denoising methods. It will be first shown that only wavelet thresholding methods and NL-means give an acceptable method noise. Second, that neighborhood filters are the only ones to satisfy the "noise to noise" principle. Third, that among them NL-means is closest to statistical optimality. A particular attention will be paid to the application of the statistical optimality criterion for movie denoising methods. It will be pointed out that current movie denoising methods are motion compensated neighborhood filters. This amounts to say that they are neighborhood filters and that the ideal neighborhood of a pixel is its trajectory. Unfortunately the aperture problem makes it impossible to estimate ground true trajectories. It will be demonstrated that computing trajectories and restricting the neighborhood to them is harmful for denoising purposes and that space-time NL-means preserves more movie details.

Analysis and comparison of several simple impulsive noise mitigation schemes for OFDM receivers

Abstract: In this paper, we analyze and compare the performance of OFDM receivers with blanking, clipping and combined blanking-clipping nonlinear preprocessors in the presence of impulsive noise. Closed-form analytical expressions for the signal-to-noise ratio at the output of three types of nonlinearity are derived. Simulation results are provided that show good agreement with theory.

Signal Synthesis and Receiver Design for MIMO Radar Imaging

Abstract: Multiple-input-multiple-output (MIMO) radar is an emerging technology that has significant potential for advancing the state-of-the-art of modern radar. When orthogonal waveforms are transmitted, with M+N (N transmit and M receive) antennas, an MN-element filled virtual array can be obtained. To successfully utilize such an array for high-resolution MIMO radar imaging, constant-modulus transmit signal synthesis and optimal receive filter design play critical roles. We present in this paper a computationally attractive cyclic optimization algorithm for the synthesis of constant-modulus transmit signals with good auto- and cross-correlation properties. Then we go on to discuss the use of an instrumental variables approach to design receive filters that can be used to minimize the impact of scatterers in nearby range bins on the received signals from the range bin of interest (the so-called range compression problem). Finally, we present a number of numerical examples to demonstrate the effectiveness of the proposed approaches.

Rician Noise Removal by Non-Local Means Filtering for Low Signal-to-Noise Ratio MRI: Applications to DT-MRI

Abstract: Diffusion-Weighted MRI (DW-MRI) is subject to random noise yielding measures that are different from their real values, and thus biasing the subsequently estimated tensors The Non-Local Means (NLMeans) filter has recently been proposed to denoise MRI with high signal-to-noise ratio (SNR) This filter has been shown to allow the best restoration of image intensities for the estimation of diffusion tensors (DT) compared to state-of-the-art methods However, for DW-MR images with high b-values (and thus low SNR), the noise, which is strictly Rician-distributed, can no longer be approximated as additive white Gaussian, as implicitly assumed in the classical formulation of the NLMeans High b-values are typically used in high angular resolution diffusion imaging (HARDI) or q-space imaging (QSI), for which an optimal restoration is critical In this paper, we propose to adapt the NLMeans filter to Rician noise corrupted data Validation is performed on synthetic data and on real data for both conventional MR images and DT images Our adaptation outperforms the original NLMeans filter in terms of peak-signal-to-noise ratio (PSNR) for DW-MRI

Optimizations of a MIMO Relay Network

Abstract: Relay networks have received considerable attention recently, especially when limited size and power resources impose constraints on the number of antennas within a wireless sensor network. In this context, signal processing techniques play a fundamental role, and optimality within a given relay architecture can be achieved under several design criteria. In this paper, we extend recent optimal minimum-mean-square-error (MMSE) and signal-to-noise ratio (SNR) designs of relay networks to the corresponding multiple-input-multiple-output (MIMO) scenarios, whereby the source, relays and destination comprise multiple antennas. We investigate maximum SNR solutions subject to power constraints and zero-forcing (ZF) criteria, as well as approximate MMSE equalizers with specified target SNR and power constraint at the receiver. We also maximize the transmission rate between the source and destination subject to power constraint at the receiver.

On the Importance of the Pearson Correlation Coefficient in Noise Reduction

Abstract: Noise reduction, which aims at estimating a clean speech from noisy observations, has attracted a considerable amount of research and engineering attention over the past few decades. In the single-channel scenario, an estimate of the clean speech can be obtained by passing the noisy signal picked up by the microphone through a linear filter/transformation. The core issue, then, is how to find an optimal filter/transformation such that, after the filtering process, the signal-to-noise ratio (SNR) is improved but the desired speech signal is not noticeably distorted. Most of the existing optimal filters (such as the Wiener filter and subspace transformation) are formulated from the mean-square error (MSE) criterion. However, with the MSE formulation, many desired properties of the optimal noise-reduction filters such as the SNR behavior cannot be seen. In this paper, we present a new criterion based on the Pearson correlation coefficient (PCC). We show that in the context of noise reduction the squared PCC (SPCC) has many appealing properties and can be used as an optimization cost function to derive many optimal and suboptimal noise-reduction filters. The clear advantage of using the SPCC over the MSE is that the noise-reduction performance (in terms of the SNR improvement and speech distortion) of the resulting optimal filters can be easily analyzed. This shows that, as far as noise reduction is concerned, the SPCC-based cost function serves as a more natural criterion to optimize as compared to the MSE.

On the degrees-of-freedom of the MIMO interference channel

Abstract: The high signal-to-noise ratio capacity of the symmetric MIMO interference channel is characterized as a function of the interference-to-noise ratio. This work is a multiple antenna extension of the degrees of freedom expressions derived by Etkin et al. for the single antenna case. This characterization considers the case where the number of receive antennas is greater than or equal to the number of transmit antennas and shows the number of degrees of freedom available for communication as a function of log(INR)/log(SNR).

Blindly Combined Energy Detection for Spectrum Sensing in Cognitive Radio

Abstract: In this letter, a method is proposed to optimally combine the received signal samples in space and time based on the principle of maximizing the signal-to-noise ratio (SNR). After the combining, energy detection (ED) is used. However, optimal combining needs information of the source signal and channel, which is usually unknown. To overcome this difficulty, a method is proposed to blindly combine the signal samples. Similar to energy detection, blindly combined energy detection (BCED) does not need any information of the source signal and the channel a priori. BCED can be much better than ED for highly correlated signals, and most importantly, it does not need noise power estimation and overcomes ED's susceptibility to noise uncertainty. Also, perfect synchronization is not required. Simulations based on wireless microphone signals and randomly generated signals are presented to verify the methods.

Iterative Hard Thresholding for Compressed Sensing

Abstract: Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when applied to the compressed sensing recovery problem. We show that the algorithm has the following properties (made more precise in the main text of the paper) - It gives near-optimal error guarantees. - It is robust to observation noise. - It succeeds with a minimum number of observations. - It can be used with any sampling operator for which the operator and its adjoint can be computed. - The memory requirement is linear in the problem size. - Its computational complexity per iteration is of the same order as the application of the measurement operator or its adjoint. - It requires a fixed number of iterations depending only on the logarithm of a form of signal to noise ratio of the signal. - Its performance guarantees are uniform in that they only depend on properties of the sampling operator and signal sparsity.

Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence

Abstract: It is well know that free-space laser system performance is limited by atmospheric turbulence. Most theoretical treatments have been described for many years by Kolmogorov's power spectral density model because of its simplicity. Unfortunately, several experiments have been reported recently that show that the Kolmogorov theory is sometimes incomplete to describe atmospheric statistics properly, in particular, in portions of the troposphere and stratosphere. We present a non-Kolmogorov power spectrum that uses a generalized exponent instead of constant standard exponent value 11/3, and a generalized amplitude factor instead of constant value 0.033. Using this new spectrum in weak turbulence, we carry out, for a horizontal path, an analysis of long-term beam spread, scintillation index, probability of fade, mean signal-to-noise ratio (SNR), and mean bit error rate (BER) as variation of the spectrum exponent. Our theoretical results show that for alpha values lower than =11/3, but not for alpha close to =3, there is a remarkable increase of scintillation and consequently a major penalty on the system performance. However, when alpha assumes a value close to =3 or for alpha values higher than =11/3, scintillation decreases, leading to an improvement on the system performance.

Audio Denoising by Time-Frequency Block Thresholding

Abstract: Removing noise from audio signals requires a nondiagonal processing of time-frequency coefficients to avoid producing ldquomusical noise.rdquo State of the art algorithms perform a parameterized filtering of spectrogram coefficients with empirically fixed parameters. A block thresholding estimation procedure is introduced, which adjusts all parameters adaptively to signal property by minimizing a Stein estimation of the risk. Numerical experiments demonstrate the performance and robustness of this procedure through objective and subjective evaluations.

Noise Removal From Hyperspectral Images by Multidimensional Filtering

Abstract: A generalized multidimensional Wiener filter for denoising is adapted to hyperspectral images (HSIs). Commonly, multidimensional data filtering is based on data vectorization or matricization. Few new approaches have been proposed to deal with multidimensional data. Multidimensional Wiener filtering (MWF) is one of these techniques. It considers a multidimensional data set as a third-order tensor. It also relies on the separability between a signal subspace and a noise subspace. Using multilinear algebra, MWF needs to flatten the tensor. However, flattening is always orthogonally performed, which may not be adapted to data. In fact, as a Tucker-based filtering, MWF only considers the useful signal subspace. When the signal subspace and the noise subspace are very close, it is difficult to extract all the useful information. This may lead to artifacts and loss of spatial resolution in the restored HSI. Our proposed method estimates the relevant directions of tensor flattening that may not be parallel either to rows or columns. When rearranging data so that flattening can be performed in the estimated directions, the signal subspace dimension is reduced, and the signal-to-noise ratio is improved. We adapt the bidimensional straight-line detection algorithm that estimates the HSI main directions, which are used to flatten the HSI tensor. We also generalize the quadtree partitioning to tensors in order to adapt the filtering to the image discontinuities. Comparative studies with MWF, wavelet thresholding, and channel-by-channel Wiener filtering show that our algorithm provides better performance while restoring impaired HYDICE HSIs.

Low noise superconducting single photon detectors on silicon

Abstract: We have fabricated superconducting nanowire single photon detectors made of NbTiN on a silicon substrate. This type of material reduces the dark count rate by a factor of 10 compared to identical NbN detectors, enabling single photon detection with unprecedented signal to noise ratio: we report a noise equivalent power of 10−19 W Hz−1/2 at 4.2 K. The compatibility of our superconducting device with silicon enables its integration with complex structures.

Robust signal-to-noise ratio estimation based on waveform amplitude distribution analysis.

Abstract: In this paper, we introduce a new algorithm for estimating the signal-to-noise ratio (SNR) of speech signals, called WADA-SNR (Waveform Amplitude Distribution Analysis) In this algorithm we assume that the amplitude distribution of clean speech can be approximated by the Gamma distribution with a shaping parameter of 04, and that an additive noise signal is Gaussian Based on this assumption, we can estimate the SNR by examining the amplitude distribution of the noise-corrupted speech We evaluate the performance of the WADA-SNR algorithm on databases corrupted by white noise, background music, and interfering speech The WADA-SNR algorithm shows significantly less bias and less variability with respect to the type of noise compared to the standard NIST STNR algorithm In addition, the algorithm is quite computationally efficient Index Terms : SNR estimation, Gamma distribution, Gaussian distribution 1 Introduction The estimation of signal-to-noise ratios (SNRs) has been extensively investigated for decades and it is still an active field of research (

Reconstructing Green's function by correlation of the coda of the correlation (C3) of ambient seismic noise

Abstract: Analysis of long-range correlation of the microseisms has been shown to provide reliable measurements of surface wave speeds that can be used for seismic imaging and monitoring. In the case of an even distribution of noise sources, it has been theoretically demonstrated that the correlation is the exact Green's function, including all types of waves. This method is limited in its application by the actual source distribution. In practice, the azimuthal distribution of energy flux of the noise is dominated by some particular directions resulting in a clear azimuthal dependence of the quality of the reconstruction of Rayleigh waves, with a poor reconstruction in some azimuths. To solve this problem, we use noise correlations measured on the entire network. We consider two stations, A and B, for which the Rayleigh waves could not be discerned in the in the correlation of continuous records of ambient noise. We computed all correlations between the station A (respectively B) and all the 150 other stations located at regional distances. Theoretically, these virtual seismograms contain direct waves and coda, although they are clearly contaminated by the influence of the imperfect ambient noise field and most are inadequate for direct analysis. We used these correlation functions as equivalents to seismograms produced by sources acting at the 150 stations locations and recorded in A (respectively B). We select time windows in those virtual seismograms that correspond to coda and compute correlations between them. This metacorrelation is found to exhibit the surface wave part of the Green's function that was not visible in the raw correlation of ambient noise. We illustrate the legitimacy of the reconstruction by comparison with raw noise correlations. This procedure can be used to assess seismic velocity between stations, even in presence of a directive and poorly oriented ambient noise. The result shows that in spite of the small signal-to-noise ratios often seen in correlations of ambient noise, especially at large lag time corresponding to coda, their codas are better equipartitioned than was the ambient noise upon which they were based. They are therefore presumably multiply scattered and contain information on both direct surface waves and also on more complex travel paths.

Radio Transmitter Fingerprinting: A Steady State Frequency Domain Approach

Abstract: We present a novel technique for radio transmitter identification based on frequency domain characteristics. Our technique detects the unique features imbued in a signal as it passes through a transmit chain. We are the first to propose the use of discriminatory classifiers based on steady state spectral features. In laboratory experiments, we achieve 97% accuracy at 30 dB SNR and 66% accuracy at OdB SNR based on eight identical universal software radio peripherals (USRP) transmitters. Our technique can be implemented using today's low cost high-volume receivers and requires no manual performance tuning.

MIMO multichannel beamforming: SER and outage using new eigenvalue distributions of complex noncentral Wishart matrices

Abstract: This paper analyzes MIMO systems with multichannel beamforming in Ricean fading. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel. We first present new closed-form expressions for the marginal ordered eigenvalue distributions of complex noncentral Wishart matrices. These are used to characterize the statistics of the signal to noise ratio (SNR) on each eigenmode. Based on this, we present exact symbol error rate (SER) expressions. We also derive closed-form expressions for the diversity order, array gain, and outage probability. We show that the global SER performance is dominated by the subchannel corresponding to the minimum channel singular value. We also show that, at low outage levels, the outage probability varies inversely with the Ricean A*-factor for cases where transmission is only on the most dominant subchannel (i.e. a singlechannel beamforming system). Numerical results are presented to validate the theoretical analysis.

Transmitter Noise Effect on the Performance of a MIMO-OFDM Hardware Implementation Achieving Improved Coverage

Abstract: This paper presents analysis of performance measurements from a MIMO-OFDM IEEE 802.11n hardware implementation at 5.2 GHz using four transmitters and four receivers. Two spatial multiplexing systems are compared; one which uses a zero-forcing (ZF) detector and the other a list sphere detector (LSD). We show that the measured results do not align with standard prediction based on simulation assuming uncorrelated receiver noise. We show that the discrepancy can be explained by the inclusion of transmitter noise into the channel model. This effect is not included in existing MIMO-OFDM channel models. The measured results from our hardware implementation show successful packet transmission at 600 Mb/s with 15 bits/s/Hz spectral efficiency at 73% coverage for ZF and 84% coverage for LSD with an average receiver signal to noise ratio (SNR) of 26 dB.

Coordinated beamforming for the multi-cell multi-antenna wireless system

Abstract: In a conventional wireless cellular system, signal processing is performed on a per-cell basis; out-of-cell interference is treated as background noise. This paper considers the benefit of coordinating base-stations across multiple cells in a multi-antenna beamforming system, where multiple base-stations may jointly optimize their respective beamformers to improve the overall system performance. This paper focuses on a downlink scenario where each remote user is equipped with a single antenna, but where multiple remote users may be active simultaneously in each cell. The design criterion is the minimization of the total weighted transmitted power across the base-stations subject to signal-to-interference-and-noise-ratio (SINR) constraints at the remote users. The main contribution is a practical algorithm that is capable of finding the joint optimal beamformers for all base-stations globally and efficiently. The proposed algorithm is based on a generalization of uplink-downlink duality to the multi-cell setting using the Lagrangian duality theory. The algorithm also naturally leads to a distributed implementation. Simulation results show that a coordinated beamforming system can significantly outperform a conventional system with per-cell signal processing.

Three dimensional visualization by photon counting computational Integral Imaging

Abstract: In this paper, we present three dimensional (3D) object reconstruction using photon-counted elemental images acquired by a passive 3D Integral Imaging (II) system. The maximum likelihood (ML) estimator is derived to reconstruct the irradiance of the 3D scene pixels and the reliability of the estimator is described by confidence intervals. For applications in photon scarce environments, our proposed technique provides 3D reconstruction for better visualization as well as significant reduction in the computational burden and required bandwidth for transmission of integral images. The performance of the reconstruction is illustrated qualitatively and compared quantitatively with Peak to Signal to Noise Ratio (PSNR) criterion.

Error probability of digital communications using relay diversity over Nakagami-m fading channels

Abstract: The (lower-bound) symbol error rate (SER) performance of cooperative digital communication schemes is investigated, where multiple dual-hop relays are invoked for achieving the cooperative diversity with the aid of the maximal ratio combining (MRC). A range of closed-form expressions are obtained for the probability density functions (PDFs) of the relay-channels' output signal-to-noise ratio (SNR). Accurate and approximated closed-form expressions are derived for computing the SER. Our study shows that, with the aid of the closed-form expressions obtained in this contribution, the SER performance of the relay-assisted digital communications schemes, which may employ various classes of coherent modulations, can be readily evaluated in the context of a variety of fading scenarios that the cooperative signals might experience.

Joint Source–Channel Codes for MIMO Block-Fading Channels

Abstract: We consider transmission of a continuous amplitude source over an L-block Rayleigh-fading Mt x Mr multiple-input multiple-output (MIMO) channel when the channel state information is only available at the receiver Since the channel is not ergodic, Shannon's source-channel separation theorem becomes obsolete and the optimal performance requires a joint source-channel approach Our goal is to minimize the expected end-to-end distortion, particularly in the high signal-to-noise ratio (SNR) regime The figure of merit is the distortion exponent, defined as the exponential decay rate of the expected distortion with increasing SNR We provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths For the lower bounds, we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital/analog transmission In each case, by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio We prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom, that is L = 1, and min{Mt ,Mr} =1 When we have more degrees of freedom, our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio We demonstrate that our results, which were derived for a complex Gaussian source, can be extended to more general source distributions as well

High-Resolution Through-the-Wall Radar Imaging Using Beamspace MUSIC

Abstract: The MUSIC algorithm is a high-resolution direction finding technique which has been successfully applied to enhance radar imaging in inverse synthetic aperture radar (ISAR). Although this signal subspace-based method has proven effective when dealing with point targets and high signal-to-noise ratio (SNR), it may fail to work when directly applied to extended targets or target returns of low SNR. The Beamspace MUSIC (BS-MUSIC), in which the MUSIC algorithm is applied to multiple beams, is capable of locating spatially extended targets in low SNR environments. In this paper, we consider BS-MUSIC as an image formation method for indoor radar imaging problems and sensing through-the-wall applications. We compare BS-MUSIC performance to conventional beamforming and element-space MUSIC. Imaging results, using both synthesized and real data, demonstrate the advantages of the proposed algorithm in depicting targets behind walls.