Kefei Liu

Semi-Blind Receivers for Joint Symbol and Channel Estimation in Space-Time-Frequency MIMO-OFDM Systems

In wireless communications, increased spectral efficiency and low error rates can be achieved by means of space-time-frequency coded MIMO-OFDM systems. In this work, we consider a MIMO-OFDM transmit signal design combining space-frequency modulation with a time-varying linear precoding technique which allows spreading and multiplexing the transmitted symbols, in both space, time and frequency domains. For this system, we propose two closed-form semi-blind receivers that exploit differently the multilinear structure of the received signal, which is formulated as a nested PARAllel FACtor (PARAFAC) model. First, we devise a least squares Khatri-Rao factorization (LS-KRF) based receiver for joint channel and symbol estimation by making an efficient use of a short frame of pilot symbols. The LS-KRF receiver provides the same performance at a lower computational complexity compared to the alternating least squares (ALS) based receiver. For further reducing pilot overhead, we develop a simplified closed-form PARAFAC (S-CFP) receiver coupled with a pairing algorithm that yields an unambiguous estimation of the transmitted symbols without the need of a pilot frame. The uniqueness conditions, spectral efficiency and computational complexity of the LS-KRF and S-CFP with pairing receivers are analyzed and compared with the ALS receiver. It is shown that the S-CFP with pairing receiver has the same order of computational complexity as the ALS receiver. Meanwhile, simulation results show that our S-CFP with pairing receiver achieves the same or very similar performance of the competing receivers with extra pilot overhead at sufficiently high signal-to-noise ratio (SNR) conditions. On the other hand, it is slightly inferior to them in terms of channel estimation accuracy and bit error rate at lower SNRs.

An Eigenvalue-Moment-Ratio Approach to Blind Spectrum Sensing for Cognitive Radio Under Sample-Starving Environment

Eigenvalue-based methods have been widely investigated for multiantenna blind spectrum sensing in cognitive radio (CR). However, most of them are formulated in the framework of maximum likelihood (ML) estimation, which is optimal only when the number of samples is much larger than the number of antennas. In relatively small-sample scenarios where the number of antennas is comparable in magnitude to the number of samples, their optimality cannot be guaranteed. Based on the random matrix theory (RMT), an eigenvalue moment ratio (EMR) approach is proposed for spectrum sensing. As the distribution of the EMR statistic in the absence of signals can be precisely determined by the RMT, this approach is able to reliably predict the theoretical threshold. Moreover, as the EMR detector is developed from the RMT perspective and utilizes all the signal eigenvalues for detection, it can be superior to state-of-the-art detection algorithms, particularly for relatively small samples. Furthermore, we derive the asymptotic distribution of the EMR statistic in the presence of signals and analyze the theoretical detection probability of the EMR approach. Additionally, the EMR statistic is calculated via the Frobenius inner product and matrix trace operations instead of the eigenvalue decomposition (EVD), which offers computational efficiency. Simulation results are presented to illustrate the superiority of the EMR approach and confirm our theoretical calculation.

A multi-dimensional model order selection criterion with improved identifiability

A novel R-dimensional (R ≥ 3) model order selection (MOS) criterion is proposed for estimating the number of sources embedded in noise. By extending the classical r-mode matrix unfolding of a Rth-order measurement tensor to multi-mode matrix unfolding, (2R-1 - 1) unfolded matrices are obtained. To maximize the identifiability, the unfolded matrix whose number of rows is closest to that of the columns is chosen. Meanwhile, as the so-obtained unfolded matrix is of large size, a sequence of nested hypothesis tests on its associated eigenvalues is utilized for MOS in the framework of the random matrix theory. The maximum number of sources the proposed enumerator able to identify is on the order of the square root of the product of all dimension sizes, whereas the identifiability of existing criteria is limited to the maximum dimension size minus one. Numerical results are included to illustrate the performance of the proposed enumerator.

Subspace techniques for multidimensional model order selection in colored noise

R-dimensional (R-D) harmonic retrieval (HR) in colored noise, where R>=2, is required in numerous applications including radar, sonar, mobile communications, multiple-input multiple-output channel estimation and nuclear magnetic resonance spectroscopy. Tensor-based subspace approaches to R-D HR such as R-D unitary ESPRIT and R-D MUSIC provide super-resolution performance. However, they require the prior knowledge of the number of signals. The matrix based (1-D) ESTimation ERror (ESTER) is subspace based detection method that is robust against colored noise. To estimate the number of signals from R-D measurements corrupted by colored noise, we propose two R-D extensions of the 1-D ESTER by means of the higher-order singular value decomposition. The first R-D ESTER combines R shift invariance equations each applied in one dimension. It inherits and enhances the robustness of the 1-D ESTER against colored noise, and outperforms the state-of-the-art R-D order selection rules particularly in strongly correlated colored noise environment. The second R-D scheme is developed based on the tensor shift invariance equation. It performs best over a wide range of low-to-moderate noise correlation levels, but poorly for high noise correlation levels showing a weakened robustness to colored noise. Compared with the existing R-D ESTER scheme, both proposals are able to identify much more signals when the spatial dimension lengths are distinct.

A closed form solution to semi-blind joint symbol and channel estimation in MIMO-OFDM systems

Due to the scarcity of the electromagnetic spectrum, multidimensional signaling schemes that take into account several signal dimensions such as space, time, frequency and constellation, are good candidates for increasing the data rate and/or improving the link reliability in future communication systems. Recently a new space-time-frequency diversity based MIMO-OFDM system has been proposed where transmit signal design combines frequency-domain Vandermonde spreading with a time-varying linear constellation precoding, while the received signal is formulated as a nested parallel factor (PARAFAC) model. A joint channel estimation and symbol decoding process has been developed for this system based on the alternating least squares (ALS) algorithm. In this paper, we propose a low-complexity blind receiver based on the least squares Khatri-Rao factorization (LS-KRF) for joint channel estimation and symbol decoding. Our proposed LS-KRF receiver is a closed-form solution which provides the same performance as that of the ALS solution while being less complex since no iteration is needed. Simulation results are included to verify the benefits of the proposed receiver.

Core consistency diagnostic aided by reconstruction error for accurate enumeration of the number of components in parafac models

Recently, the CORe CONsistency DIAgnostic (CORCONDIA) has attracted more and more attention as an effective tool for determining the number of components in parallel factor analysis (PARAFAC) or Tucker 3 models. In CORCONDIA, a proper user-defined threshold is required to ensure reliable performance. The optimal threshold increases with the signal-to-noise ratio (SNR), which results in significant probability of over-enumeration of the number of components for high SNRs under fixed threshold settings. We propose to first use a threshold interval to obtain lower and upper bounds of the estimates. The estimate takes the upper bound as its initial value and is then refined based on a sequence of hypothesis tests by exploiting the reconstruction error of the PARAFAC decomposition. The proposed scheme provides accurate detection for both low and high SNRs at almost no extra computational cost.

3-D Unitary ESPRIT: Accurate attitude estimation for unmanned aerial vehicles with a hexagon-shaped ESPAR array

Accurate estimation of the attitude of unmanned aerial vehicles (UAVs) is crucial for their control and displacement. Errors in the attitude estimate may misuse the limited battery energy of UAVs or even cause an accident. For attitude estimation, proprioceptive sensors such as inertial measurement units (IMUs) are widely applied, but they are susceptible to inertial guidance error. With antenna arrays currently being installed in UAVs for communication with ground base stations, we can take advantage of the array structure in order to improve the estimates of IMUs via data fusion. In this paper, we therefore propose an attitude estimation system based on a hexagon-shaped 7-element electronically steerable parasitic antenna radiator (ESPAR) array. The ESPAR array is well-suited for installment in the UAVs with broad wings and short bodies. Our proposed solution returns an estimation for the pitch and roll based on the inter-element phase delay estimates of the line-of-sight path of the impinging signal over the antenna array. By exploiting the parallel and centrosymmetric structure in the hexagon-shaped ESPAR array, the 3-dimensional Unitary ESPRIT algorithm is applied for phase delay estimation to achieve high accuracy as well as computational efficiency. We devise an attitude estimation algorithm by exploiting the geometrical relationship between the UAV attitude and the estimated phase delays. An analytical closed-form expression of the attitude estimates is obtained by solving the established simultaneous nonlinear equations. Simulations results show the feasibility of our proposed solution for different signal-to-noise ratio levels as well as multipath scenarios.

Efficient source enumeration for accurate direction-of-arrival estimation in threshold region

Estimation of the number of signals impinging on an array of sensors, also known as source enumeration, is usually required prior to direction-of-arrival (DOA) estimation. In challenging scenarios such as the presence of closely-spaced sources and/or high level of noise, using the true source number for nonlinear parameter estimation leads to the threshold effect which is characterized by an abnormally large mean square error (MSE). In cases that sources have distinct powers and/or are closely spaced, the error distribution among parameter estimates of different sources is unbalanced. In other words, some estimates have small errors while others may be quite inaccurate with large errors. In practice, we will be only interested in the former and have no concern on the latter. To formulate this idea, the concept of effective source number (ESN) is proposed in the context of joint source enumeration and DOA estimation. The ESN refers to the actual number of sources that are visible at a given noise level by a parameter estimator. Given the numbers of sensors and snapshots, number of sources, source parameters and noise level, a Monte Carlo method is designed to determine the ESN, which is the maximum number of available accurate estimates. The ESN has a theoretical value in that it is useful for judging what makes a good source enumerator in the threshold region and can be employed as a performance benchmark of various source enumerators. Since the number of sources is often unknown, its estimate by a source enumerator is used for DOA estimation. In an effort to automatically remove inaccurate estimates while keeping as many accurate estimates as possible, we define the matched source number (MSN) as the one which in conjunction with a parameter estimator results in the smallest MSE of the parameter estimates. We also heuristically devise a detection scheme that attains the MSN for ESPRIT based on the combination of state-of-the-art source enumerators.

Improved landing radio altimeter for unmanned aerial vehicles based on an antenna array

Unmanned aerial vehicles (UAVs) are used in various applications such as civil and military surveillance, law enforcement, and support in natural disasters as well as in hazardous environments. Approaching and landing are necessary steps for all UAVs, indicating that radio altimeters are needed. In this paper, a radio altimeter based on an antenna array is proposed. Our solution allows some improvements over the traditional radio altimeter such as more precise altitude estimation, ground imaging without the need of side looking radar, mapping the obstacles positions and detecting the ground inclination and topology. Another important contribution of this paper is a review of traditional radio altimeters along with a performance comparison between the level-crossing detection and the digital signal processing frequency detection - which is based on the fast Fourier transform algorithm.

Evaluation of Space-Time-Frequency (STF)-Coded MIMO-OFDM Systems in Realistic Channel Models

By taking into account several dimension of the transmitted signal, such as space, frequency, period and time, MIMO-OFDM systems allow an increased spectral efficiency and an improved identifiability in comparison to matrix solutions. In this paper, we evaluate MIMO-OFDM systems for geometric scenarios where the narrow band approximation is violated. To this end a new data model is proposed to better represent the behavior of the system in the presence of wide band signals. Moreover, we also relax the assumption that the amount of transmitted antennas is equal to the number of transmitted symbols.