Henrik Sahlin

MIMO signal separation for FIR channels: a criterion and performance analysis

Signal separation for a general system of an arbitrary number of signals is investigated. The signal separation research area deals with the problem of separating unknown source signals that are mixed in an unknown way when only these mixtures are available. A criterion, based on second-order statistics, is formulated to be used in estimating the mixing system. This estimate of the mixing system is used in a separation structure with a parameterization that minimizes the number of parameters to be estimated. Formulae for the gradient and Hessian of the criterion are derived. A formula for the lower bound for the variance of the estimated parameters of the mixing matrix is derived. This lower bound is the asymptotic (assuming the number of data samples to be large) Cramer-Rao lower bound (CRLB). The proposed algorithm is tested with simulations and compared with the CRLB.

Source separation: a TITO system identification approach

Abstract The blind source separation problem is studied in this paper using a system identification approach. Two unmeasurable source signals are mixed by means of a channel system resulting in two measurable output signals. The measurable signals can be used in a two-inputs two-outputs system identification approach in order to extract the sources. The system to be identified can be described by two parts, namely a model of the source generating filters and a model of the mixing channels. Both the source generating filters and the mixing channels are modeled as ARMA-filters. It is shown that the system, under various weak conditions, is identifiable using second-order statistics only. These conditions are presented along with identifiability results. Furthermore, with some minor additional restrictions, the sources can be recovered. One method to perform this system identification is by using the prediction error method (PEM). PEM is a general method which is statistically efficient under the Gaussian hypothesis. To be able to perform the separation in an on-line manner, a recursive version of PEM is used. Simulation results using this approach are presented, both with computer generated and real-world signals.

Aspects of MIMO Channel Estimation for LTE Uplink

The use of MIMO (Multiple Input Multiple Output) in current and future mobile communications relies on accurate channel estimates. In OFDM based systems such as LTE (Long Term Evolution), the channel estimation can be successfully designed with processing in a transform domain, both for uplink and downlink. One such popular transform is to use the IDFT (Inverse Discrete Fourier Transform), window the channel estimate in the time domain and then use DFT to transform back to the frequency domain again. This channel estimate is distorted in the band edges leading to a biased channel estimate. One suggested solution to this problem is to use a DCT (Discrete Cosine Transform) based channel estimator, such that this distortion is reduced. However, as discussed in the current paper, the DCT based channel estimate suffers more from cyclically shifted reference signals, as used for MIMO in LTE for uplink, than the DFT based channel estimator. In order to overcome band edge problems with the DFT based channel estimate, a method is proposed of de-biasing over-sampled DFT based channel estimate by using digital sinc functions. Simulation results indicate that the de-biased DFT based channel estimate is more robust against interference from cyclic shifted reference signals than DCT based channel estimates.

The asymptotic Cramer-Rao lower bound for blind signal separation

This paper considers some aspects of the source separation problem. Unmeasurable source signals are assumed to be mixed by means of a channel system resulting in measurable output signals. These output signals can be used to determine a separation structure in order to extract the sources. When solving the source separation problem the channel filter parameters have to be estimated. This paper presents a compact and computationally appealing formula for computing a lower bound for the variance of these parameters, in a general many inputs many outputs scenario. This lower bound is the asymptotic (assuming the number of data samples to be large) Cramer-Rao lower bound. The CRLB formula is developed further for the two-input two-output system and compared with the results from a recursive prediction error method.

Channel Prediction for Link Adaptation in LTE Uplink

Link adaptation is the process of selecting Modulation and Coding Scheme (MCS) and Precoder Matrix Index (PMI) based on channel quality measures. Here a Signal to Interference and Noise Ratio (SINR) estimate is used as quality measure, which is calculated from channel and noise covariance estimates. An SINR expression is derived within the current paper which is designed for a Minimum Mean Square Error (MMSE) equalizer with a single tap channel model, which is an equalizer suitable for uplink Long Term Evolution (LTE). Channel estimates from Sounding Reference Signal (SRS) are used for this link adaptation. Illustrations are given in the current paper of the performance impact of the time delay between transmissions of SRS to the time instant when the result of the link adaptation is used. Furthermore, a channel predictor is proposed in order to reduce the impact of this delay. Simulations results indicate the benefits of using the proposed channel predictor, in terms of link level throughput.

Statistical analysis of a signal separation method based on second-order statistics

This correspondence explores a method for separation of dynamically mixed sources, which is based on second-order statistics. Here, a statistical analysis is given of a generalized version of the original algorithm. The generalized method includes a weighting matrix, and a result of the statistical analysis is that the best possible weighting is found. In cases where the sources have similar color, the weighted algorithm significantly improves the estimates of the mixing parameters. The problem of model validation is discussed as well.

Random access preamble format for systems with many antennas

The computational complexity of FFT (Fast Fourier Transform) processing in an OFDM (Orthogonal Frequency Division Multiplex) based receiver is large with a large amount of receiver antennas. In LTE (Long Term Evolution) release 8, FFTs of different size are used for user data and random-access preambles [1] requiring additional FFTs to be implemented for random-access reception. Within the current paper, a 5G random-access preamble format is proposed based on a short sequence of the same length as the length of the OFDM symbols that are used for other uplink physical channels, such as user data, control signaling, and reference signals. The preamble sequence is constructed by repeating the short sequence multiple times. A corresponding preamble detector in which FFTs of the same size as for other uplink channels and signals are used is also described. In this way, the amount of special random-access related processing and hardware support is significantly reduced for multi-antenna systems with frequency-domain beamforming. This preamble detector is also robust against inter-carrier interference from other uplink channels and signals. Furthermore, the proposed preamble detector scheme can be used in 5G scenarios with a high amount of phase noise and frequency errors. For time-domain beamforming, the beamforming weights can be changed during preamble reception such that the number of spatial directions is increased for which preamble detection is done. Simulation results are used to compare preamble formats for different lengths of the sequences.

Blind separation of images

The problem of separating two uncorrelated images from two observed mixtures of these images is considered in this paper. Each observed image is modeled as the sum of one original image and another original image filtered through a two dimensional FIR filter. An algorithm, to estimate these filters, is presented from a separation structure and a minimization of a criterion based on second order statistics. This separation structure can be used in order to extract two uncorrelated images. Simulation results are also presented.

Statistical analysis of a signal separation method based on second order statistics

This paper explores an existing method for signal separation, which is based on second order statistics. Here, statistical analysis of a generalized version of the original algorithm is given. The generalized method includes a weighting matrix, and a result of the statistical analysis is that the best possible weighting is found. The problem of initialization of the involved non-linear optimization is also discussed.

Time-of-Arrival Estimation in Block-IFDMA Systems for LTE in Unlicensed Spectrum

Time-of-arrival estimation is a critical aspect of wireless systems, both for initial access and ongoing communications. The timing estimates are needed in uplink and downlink, where the initial timing estimation in LTE uplink is based on a physical random access channel (PRACH) preamble transmitted by the user. Block Interleaved Frequency Division Multiple Access (B-IFDMA) is a transmission scheme that recently emerged as an attractive choice for LTE operation in unlicensed spectrum due to its benefits in allowing increased power levels under unlicensed band regulations. In this paper, we introduce a new PRACH preamble format suitable for unlicensed operation based on B-IFDMA. In addition, we present a receiver structure for the PRACH preamble together with simulation results on its timing estimation performance. We show that the PRACH preamble design is robust against possible aliasing effects caused by frequency-domain properties of B-IFDMA and provides accurate timing estimates. We also propose non-uniform frequency interleaving for the PRACH preamble that further improves timing estimation performance.