Unknown Multipath Channels Research Articles

Blind passive signal detection via dictionary learning in unknown multipath time-spreading distortion underwater channels

Blind passive signal detection is a challenging endeavor since typically there is no prior knowledge of the transmitted signal. This becomes further complicated in time-spreading distortion (TSD) underwater channels [R. Rashid, E. Zhang, A. Abdi, and Z. H. Michalopoulou, “Theoretical and experimental multi-sensor signal detection in time spreading distortion underwater channels,” Proc. Oceans (2022)], where due to the presence of multiple propagation paths, the unknown signal is convolved with an unknown channel impulse response. In this paper, we introduce and develop a blind passive signal detection method, using dictionary learning [M. Sadeghi, M. Babaie-Zadeh, and C. Jutten, “Dictionary learning for sparse representation: A novel approach,” IEEE Signal Process. Lett. (2013)]. In our blind passive signal detection method, we use the received data to estimate the unknown signal, and also to separate it from the unknown channel impulse response. We have conducted simulations and underwater experiments, to generate receiver operating characteristic curves, to study the performance of the proposed method. The high detection probabilities of the blind method, compared to the replica correlation integration method—that needs to know the transmitted signal for matched filtering—demonstrate the usefulness of the method for passive detection of unknown signals in unknown TSD channels.

Compressive Wideband Spectrum Sensing and Signal Recovery With Unknown Multipath Channels

We study the problem of joint wideband spectrum sensing and recovery of multi-band signals in a multi-antenna-based sub-Nyquist sampling framework. Specifically, the multi-band signal is composed of a number of uncorrelated narrowband signals spreading over a wide frequency band. Unlike existing works which assume the source signals impinge on the receiver via a line-of-sight (LOS) path, we consider a more practical unknown MIMO channel which results from multipath propagation. A new sub-Nyquist sampling architecture is proposed, where each antenna output passes through two channels, namely, a direct path and a delayed path with a controlled amount of time delay. The signal at each channel is then sampled by a synchronized low-rate analog-to-digital converter (ADC). We utilize the collected data samples to build a set of cross-correlation matrices with different time lags and develop a CANDECOMP/PARAFAC (CP) decomposition-based method to recover the carrier frequencies, power spectra as well as the source signals themselves. Recovery conditions of the proposed method are analyzed, and Cramér-Rao bound (CRB) results for our estimation problem are derived. Simulation results are presented to illustrate the effectiveness of the proposed method.

Deep Learning Based Nonlinear Signal Detection in Millimeter-Wave Communications

For millimeter-wave (mm-Wave) communications, signal detection in the presence of the power amplifier (PA) nonlinearity and unknown multipath channel has remained one challenging task in single-input single-output (SISO) communication system. Besides, the PA nonlinearity in multiple-input multiple-output (MIMO) communication system also has severe effects upon the signal detection in receiver-end.In this paper, firstly, we suggest a deep-learning (DL) framework, i.e. integrating feedforward neural network (FNN) and recurrent neural network (RNN), to combat both the nonlinear distortion and linear inter-symbol-interference (ISI) from a global point of view, thereby accomplishing nonlinear equalization and signal detection at the receiver-end in SISO communication system.Utilizing the powerful mapping and learning capability of DL, our new method is able to detect symbols via the received signals corrupted by both nonlinear distortion and linear ISI, avoiding both the explicit nonlinear pre-distorter in transmitter and the channel state information (CSI) estimator.Secondly, our DL-based framework can also successfully cope with the joint nonlinear distortion and space-time decoding problem in MIMO communication system, without explicitly pre-calibrating nonlinear distortion and estimating CSI.Numerical experiments demonstrate our DL-based detector is more effective in alleviating the performance degradation both from the coupled nonlinear distortion and linear ISI in SISO communication system, and the coupled nonlinear distortion and linear space-time decoding in MIMO communication system.Compared with the state-of-the-art methods, e.g. pre-distorter and post-equalizer, our DL-based scheme effectively improves the detection performance.

MOCZ for Blind Short-Packet Communication: Practical Aspects

We investigate practical aspects of a recently introduced blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ). MOCZ is suitable for a reliable transmission of sporadic and short-packets at ultra-low latency and high spectral efficiency via unknown multipath channels, which are assumed to be static over the receive duration of one packet. The information is modulated on the zeros of the transmitted discrete-time baseband signal's z- transform. Because of ubiquitous impairments between the transmitter and receiver clocks, a carrier frequency offset occurs after down-conversion to the baseband. This results in a common rotation of the zeros. To identify fractional rotations of the base angle in the zero-pattern, we propose an oversampled direct zero-testing decoder to identify the most likely one. Integer rotations correspond to cyclic shifts of the binary message, which we determine by cyclically permutable codes (CPC). Additionally, the embedding of CPCs into cyclic codes, enables additive error-correction which reduces the bit-error-rate tremendously. Furthermore, we exploit the trident structure in the signal's autocorrelation for an energy based detector to estimate timing offsets and the effective channel delay spread. We finally demonstrate how this joint data and channel estimation can be largely improved by receive antenna diversity at low SNR.

Vandermonde Constrained Tensor Decomposition Based Blind Carrier Frequency Synchronization for OFDM Transmissions

To overcome the inter-carrier interference (ICI) of orthogonal frequency division multiplexing (OFDM) transmission subject to unknown carrier frequency offset and multipath channel, Vandermonde constrained tensor decomposition based blind approach is investigated in this paper. The main idea is that signal reception model is formulated as a tensor decomposition framework involving a Vandermonde structure factor matrix. Then an efficient linear algebra algorithm is resorted to the computation of the factors for ICI suppression and symbol recovery. Taking the Vandermonde structure into account in tensor model, not only the accuracy of the estimate is increased, but also the computational cost is reduced. Compared with the existing methods reported in the literatures, theoretical analysis and simulation results illustrate that the proposed algorithm provides lower computation complexity and better performance than ESPRIT and PARAFAC algorithms for OFDM system synchronous receiving.

Blind deconvolution of extended duration underwater signals

Synthetic time reversal (STR) is a passive blind deconvolution technique for estimating the original source signal and the source-to-array impulse responses in an unknown multipath sound channel. Previous investigations of STR involved relatively short duration chirp signals (50 ms) where the assumption of a static underwater sound channel was acceptable. However, the static-channel assumption is inadequate for longer duration underwater acoustic communication signals lasting one or more seconds. Here, wave-driven changes in the ocean's surface shape and water-column sound speed lead to significant temporal variations in the source-to-array impulse responses. This presentation describes an effort to accommodate such temporal variations by decomposing a long duration signal into smaller overlapping pieces, applying STR to each piece, and then stitching the resulting sequence of signal estimates together to blindly recover the original long-duration signal. Simulations of a one-second-duration synthetic signal propagating in a static underwater sound channel to a 16-element vertical array are used to determine how the technique's performance depends on the duration and overlap of the signal pieces in relation to the signal's bit rate and the sound channel's time-delay spread. Extension of this effort to recordings from dynamic sound channels is anticipated. [Sponsored by the Office of Naval Research.]

Time-of-Arrival Estimation Based on Information Theoretic Criteria

The possibility to accurately localize tags by using wireless techniques is of great importance for several emerging applications in the Internet of Things. Precise ranging can be obtained with ultra wideband (UWB) impulse radio (IR) systems, where short impulses are transmitted, and their time-of-arrival (ToA) is estimated at the receiver. Due to the presence of noise and multipath, the estimator has the difficult task of discriminating the time intervals where the received waveform is due to noise only, by those where there are also signal components. Common low-complexity methods use an energy detector (ED), whose output is compared with a threshold, to discriminate the time intervals containing noise only from those containing signal plus noise. Optimal threshold design for these methods requires knowledge of the channel impulse response and of the receiver noise power. We propose a different approach, where ToA estimation is based on model selection by information theoretic criteria (ITC). The resulting ToA algorithms do not use thresholds, and do not require any information about the channel or the noise power level. These blind, universal ToA estimators show, for completely unknown multipath channels and in the presence of noise with unknown power, excellent performance when compared with ideal genie-aided schemes.

Non Data Aided SNR Estimation for OFDM Signals in Frequency Selective Fading Channels

This paper deals with the problem of non data aided (NDA) signal to noise ratio (SNR) estimation of OFDM signals transmitted through unknown multipath fading channel. Most of present day's SNR estimators are based on the knowledge of pilot sequences which is not applicable in some contexts such as cognitive radio for example. Moreover in Multipath fading channels SNR also depends on frequency offset which is caused by mismatch between the oscillator in the transmitter and that in the receiver. Previous NDA SNR estimation schemes assumed a perfect synchronization at reception (i.e. ? = 0 and $${\varepsilon = 0}$$ ) which results estimation of SNR with less accuracy. The frequency offset attenuates the desired signal and causes intercarrier interference, thus reducing the SNR. In this paper we propose a new NDA SNR estimator which uses periodic redundancy induced by the cyclic prefix, considering SNR degradation due to frequency offset ( $${\varepsilon}$$ ).

Investigation of blind detection mechanism for chaotic UWB system based on generalized negentrogy

A non-coherent blind detection method based on the generalized negative entropy mechanism for chaotic ultra-wideband system is proposed in this paper. In the case without knowing the transmission channel information, the chaotic impulse signals can be detected. The proposed method can overcome the practical application problem existing in the direct chaotic communication (DCC) scheme for impulse radio ultra-wideband (IR-UWB) communication system. Also, this method can overcome the complicated and unknown multipath channel effect. Analysis of simulation results show that the proposed approach has a good separating and detection performance in the case without the channel information. A new way for the noncoherent blind detection of chaotic UWB system under non-ideal unknown channel is established.

Training-Based Synchronization and Demodulation With Low Complexity for UWB Signals

In this paper, we propose a low-complexity data-aided (DA) synchronization and efficient demodulation technique for an ultrawideband (UWB) impulse radio system. Depending on the autocorrelation property of a judiciously chosen training sequence, a redundance-included demodulation template (RDT) can be extracted from the received signal by separating, shifting, and realigning two connected portions in the observation window. After constructing the RDT, two receiver designs are available. One approach is to demodulate transmitted symbols by correlating the RDT in a straightforward manner, which does not require the explicit timing acquisition and, thus, considerably reduces the complexity of the receiver. An alternative approach is accomplished with the assistance of a non-RDT (NRDT). The NRDT-based receiver is able to remove the redundant noisy component of the RDT by acquiring timing offset via a simple synchronization scheme, therefore achieving a better bit error rate (BER) performance. Both the schemes can counteract the effects of interframe interference (IFI) and unknown multipath channels. Furthermore, analytical performance evaluations of the RDT- and NRDT-based receivers are provided. Simulations verify the realistic performance of the proposed receivers in the presence of multiuser interference (MUI) and timing errors.

Joint decoding of convolution codes and estimation of multipath communication channel’s parameters on a sliding interval

Optimal and quasi-optimal non-linear recurrent algorithms of joint decoding of convolution code and estimation of unknown multipath communication channel’s parameters on a sliding interval are synthesized on the basis of mathematics technique of mixed Markov processes in discrete time. Analysis of the obtained quasi-optimal algorithm is performed using statistical modeling on PC.

Non data-aided SNR estimation of OFDM signals

This letter deals with the problem of non data aided (NDA) signal to noise ratio (SNR) estimation of OFDM signals transmitted through unknown multipath fading channel. Most of existing OFDM SNR estimators are based on the knowledge of pilot sequences which is not applicable in some contexts such as cognitive radio for instance. We show that it is possible to take advantage of the periodic redundancy induced by the cyclic prefix to get an accurate NDA SNR estimator. Numerical simulations highlight the benefit of the proposed method compared with the state of the art.

Asymptotic Performance Analysis of Blind Minimum Output Energy Receivers for Large DS-CDMA Systems

The random matrix theory is used to analyze the asymptotic performance of the blind minimum output energy (MOE) receiver in direct-sequence code division multiple-access (DS-CDMA) systems in the presence of unknown multipath channel under the condition that the spreading factor and the number of users go to infinity with the same rate. As a special case, the asymptotic properties of the blind Capon receiver are also studied and the conditions of convergence of the signal-to-interference-plus-noise ratio (SINR) of this receiver to that of the optimal minimum-mean-square error (MMSE) receiver are discussed. In particular, it is shown that the SINR performances of the Capon and MMSE receivers are nearly identical in the uplink scenario, while the performance of the Capon receiver may be considerably inferior to that of the MMSE receiver in the downlink transmission case. As the performance of the Capon receiver is closely related to the performance of the Capon channel estimator, the asymptotic properties of the latter estimator are also studied and the conditions of convergence of the Capon channel estimate to a scaled version of the channel vector of the user-of-interest are obtained.

Blind MMSE-Constrained Multiuser Detection

In this paper, blind multiuser detection is studied for a direct-sequence (DS) code-division multiple access (CDMA) system with unknown multipath channels. The receiver is designed to follow a minimum mean-square-error (MMSE) form parameterized by a channel-like constraint vector, which is then optimized by the conventional constant modulus algorithm in a much smaller dimensional space. It is analytically established that the constraint vector asymptotically converges to the channel vector of the user of interest. Correspondingly, the receiver converges to the desired user's MMSE receiver, ensuring detection of the desired signals. When the constraint vector is treated as a channel estimate, the performance of the channel estimator is analyzed using a perturbation technique. Simulation results show a satisfactory performance of the proposed approach, which is also observed to be superior to other approaches in many scenarios.

Joint Iterative Multiuser Detection and Channel Estimation for Differentially Coded Asynchronous CDMA Systems

In this paper, we propose a receiver structure that performs joint iterative multiuser detection and channel estimation for the uplink of differentially coded asynchronous direct-sequence code-division multiple-access systems in unknown multipath channels. The overall transmission scheme for each user is the serial concatenation of a recursive systematic convolutional (RSC) encoder and a differential encoder separated by an interleaver. The proposed receiver consists of two stages. The first stage performs channel estimation, soft interference cancellation, and soft-input soft-output multiuser filtering, followed by the second stage, which consists of a bank of serially concatenated single-user channel decoders and differential decoders. The single-user iterative decoder for each user consists of a powerful combination of an RSC decoder and a differential decoder, which work together in an iterative fashion. In terms of channel estimation, at the first iteration, the multipath channel is blindly estimated by exploiting the orthogonality property between the signal and noise subspaces, whereas, for the next iterations, the channel is estimated using the soft estimates of coded bits of each user provided by the single-user iterative decoders in conjunction with the output of the multiuser detector. By exchanging soft information between the different stages, the receiver performance is improved through iteration. Simulation results demonstrate that the performance of the proposed iterative multiuser detector with the integrated channel estimator approaches the single-user bound at high signal-to-noise ratio.

Estimation of channel statistics for iterative detection of OFDM signals

Maximum likelihood sequence estimation for orthogonal frequency division multiplexing (OFDM) transmissions over unknown multipath fading channels is analytically infeasible for lack of efficient methods to maximize the likelihood function. A practical solution to this problem has been recently proposed in the context of space-time block-coded OFDM by resorting to the expectation-maximization (EM) algorithm. The resulting detector operates iteratively, exploiting knowledge of the channel statistics and the operating signal-to-noise ratio (SNR). In this work, we address the problem of estimating the above quantities and propose a recursive solution based on ad hoc reasoning. Simulations indicate that the EM detector employing the estimated SNR and channel statistics has better performance than other schemes operating in a mismatched mode. Also, the performance loss with respect to a system with perfect channel knowledge is negligible at SNR values of practical interest.

Efficient semi-blind estimation of multipath channel parameters via a delay decoupling optimization approach

In this paper a parametric method for estimating the unknown multipath channel impulse response (CIR) in a semi-blind manner is proposed. The main trait of this method is that instead of seeking the whole CIR sequence, only the unknown time delays and attenuation factors of the physical channel multipath components are estimated. The technique is based on a suitable application of the sub-channel response matching (SRM) criterion. The resulting cost function is separable with respect to the two sets of unknown parameters, i.e., time delays and attenuation factors, and thus a two step optimization procedure can be applied. Concerning the first step, which is the most difficult one, it is proven that the resulting non-linear cost function can be decoupled in terms of the respective time delay parameters. Thus, only a small number of simple linear searches needs to be executed in order to estimate the time delays of the multipath channel. The new method offers significant computational savings and a lower mean square estimation error as compared to existing semi-blind channel estimation methods. It performs well even for closely-spaced delays and is quite robust to channel overmodeling.

Block spectral precoding for blind multiuser detection of DS∕CDMA signals

A new approach for blind multiuser detection of DS/CDMA signals is proposed. This approach is based on modifying the data power spectrum, uniquely for each user, through a two-stage colouring–whitening precoding scheme. This enables detection of a desired user's signal in an unknown multipath channel, regardless of the power of the interferers. The proposed precoding method does not alter the data rate or system bandwidth. Detection does not require spreading code knowledge, and consequently avoids channel estimation and the possible associated errors. The method is seen to yield reasonable performance besides being able to operate properly in nearly saturated systems, in contrast to some existing methods. Besides this, it can tolerate severe carrier frequency offsets.

Block Phase-Precoding for Blind Multiuser Detection of BPSK/DS-CDMA Signals

A new approach for blind multiuser detection of binary phase-shift keying/direct-sequence code-division multiple-access signals is proposed, based on precoding the phase of the transmitted data uniquely for each user, over a block of data. This would enable separation and detection of a desired user's signal in an unknown multipath channel without channel estimation. The method does not involve any sacrifice in data rate or system bandwidth. The proposed method exhibits good performance, compared with some existing methods.

Performance bounds for linear MMSE receivers in CDMA systems with partial channel knowledge

In code division multiple access (CDMA) systems employing linear adaptive receivers, the detector is typically estimated directly from the received signals, based on some partial knowledge about the system, e.g., signature waveforms of one or several users. We derive the Cramer-Rao lower bounds on the covariances of the estimated linear detectors, under three different assumptions on the mechanism for estimating the detectors, namely, a) finite-alphabet-based (FA) blind detectors, b) constant-modulus-based (CM) blind detectors, and c) second-order-moments-based (SO) blind detectors. These bounds translate into the upper bounds on the achievable signal-to-interference-plus-noise ratio (SINR) by the corresponding adaptive receivers. The results are asymptotic in nature, either for high signal-to-noise ratio (SNR) or for large signal sample size. The effects of unknown multipath channels on these performance bounds are also addressed. Numerical results indicate that while the existing subspace blind or group-blind detectors perform close to the SINR bound for the SO detectors, the SINR bounds for the FA and CM detectors are significantly higher, which suggests potential avenues for developing more powerful adaptive detectors by exploiting more structural information from the system.