On the Persistency of Excitation for Blind Channel Estimation in Cyclic Prefix Systems

Recently, a new subspace-based blind channel estimation algorithm in cyclic prefix (CP) system was reported. A persistency of excitation (PE) property of the input signal is required for the algorithm to work. In this paper, the probability of fulfilling the PE property under different situations is studied. Four factors in the algorithm affect the PE property of the input signal: 1) signal constellation used; 2) precoder coefficients; 3) number of consecutive blocks; 4) a number called the repetition index. Theoretical derivations as well as numerical simulations are given to demonstrate the main points of this paper. Important conclusions are 1) that the probability of fulfilling the PE property increases and converges to unity when the number of received blocks increases but is always upper-bounded by a value less than unity when the repetition index increases; 2) that the probability of fulfilling the PE property is smaller when the algorithm is applied in orthogonal frequency division multiplexing (OFDM) systems than in single-carrier-cyclic-prefix (SC-CP) systems

Performance Analysis of Generalized Zero-Padded Blind Channel Estimation Algorithms

In this letter, we analyze the performance of a recently reported generalized blind channel estimation algorithm. The algorithm has a parameter called repetition index, and it reduces to two previously reported special cases when the repetition index is chosen as unity and as the size of received blocks, respectively. The theoretical performance of the generalized algorithm is derived in high-SNR region for any given repetition index. A recently derived Cramer–Rao bound (CRB) is reviewed and used as a benchmark for the performance of the generalized algorithm. Both theory and simulation results suggest that the performance of the generalized algorithm is usually closer to the CRB when the repetition index is larger, but the performance does not achieve the CRB for any repetition index

A Generalized Algorithm for Blind Channel Identification with Linear Redundant Precoders

It is well known that redundant filter bank precoders can be used for blind identification as well as equalization of FIR channels. Several algorithms have been proposed in the literature exploiting trailing zeros in the transmitter. In this paper we propose a generalized algorithm of which the previous algorithms are special cases. By carefully choosing system parameters, we can jointly optimize the system performance and computational complexity. Both time domain and frequency domain approaches of channel identification algorithms are proposed. Simulation results show that the proposed algorithm outperforms the previous ones when the parameters are optimally chosen, especially in time-varying channel environments. A new concept of generalized signal richness for vector signals is introduced of which several properties are studied

Generalized Signal Richness Preservation Problem and Vandermonde-Form Preserving Matrices

In this paper, a theoretical problem arising in digital communications, namely the generalized signal richness preservation problem, is addressed and studied. In order to solve the problem, a special class of square matrices, namely the "Vandermonde-form preserving" (VFP) matrices, is introduced and found to be highly relevant to the problem. Several properties of VFP matrices are studied in detail. The necessary and sufficient conditions of the problem have been found, and a systematic proof is also presented

Comments on “Performance Analysis of a Deterministic Channel Estimator for Block Transmission Systems With Null Guard Intervals”

In the above-mentioned paper, a Cramér–Rao bound was derived for the performance of a blind channel estimation algorithm. In this correspondence, an error in the bound is pointed out and corrected. It is observed here that the performance of the said algorithm does not achieve the Cramér–Rao bound

Blind block synchronization algorithms in cyclic prefix systems

In orthogonal frequency division multiplexing (OFDM) systems, symbol synchronization is a critical step for successful data transmission. While this task is done in most current systems by using training symbols, a few studies have been dedicated to solving the problem blindly, that is, where training symbols are not available. Blind symbol synchronization problem is especially important in many blind channel estimation algorithms in the literature which assume that OFDM symbol synchronization is perfect. In this paper, a broader version of the blind symbol synchronization problem is studied, namely, blind block synchronization in cyclic-prefix (CP) systems. The proposed algorithm for this broader problem covers the blind symbol synchronization problem in OFDM systems. Unlike previously reported algorithms which are based on obtaining sufficient statistics of received samples, the proposed algorithm is capable of identifying the correct block boundaries using much less received data in absence of noise. Simulation results of the proposed algorithm not only verify the declared property but also demonstrate improvement in accuracy of symbol synchronization over previously reported algorithms in presence of noise

New Blind Block Synchronization for Transceivers Using Redundant Precoders

This paper studies the blind block synchronization problem in block transmission systems using linear redundant precoders (LRP). Two commonly used LRP systems, namely, zero padding (ZP) and cyclic prefix (CP) systems, are considered in this paper. In particular, the block synchronization problem in CP systems is a broader version of timing synchronization problem in the popular orthogonal frequency division multiplexing (OFDM) systems. The proposed algorithms exploit the rank deficiency property of the matrix composed of received blocks when the block synchronization is perfect and use a parameter called repetition index which can be chosen as any positive integer. Theoretical results suggest advantages in blind block synchronization performances when using a large repetition index. Furthermore, unlike previously reported algorithms, which require a large amount of received data, the proposed methods, with properly chosen repetition indices, guarantee correct block synchronization in absence of noise using only two received blocks in ZP systems and three in CP systems. Computer simulations are conducted to evaluate the performances of the proposed algorithms and compare them with previously reported algorithms. Simulation results not only verify the capability of the proposed algorithms to work with limited received data but also show significant improvements in the block synchronization error rate performance of the proposed algorithms over previously reported algorithms

Subspace-Based Blind Channel Identification for Cyclic Prefix Systems Using Few Received Blocks

In this paper, a novel generalization of subspace-based blind channel identification methods in cyclic prefix (CP) systems is proposed. For the generalization, a new system parameter called repetition index is introduced whose value is unity for previously reported special cases. By choosing a repetition index larger than unity, the number of received blocks needed for blind identification is significantly reduced compared to all previously reported methods. This feature makes the method more realistic especially in wireless environments where the channel state is usually fast-varying. Given the number of received blocks available, the minimum value of repetition index is derived. Theoretical limit allows the proposed method to perform blind identification using only three received blocks in absence of noise. In practice, the number of received blocks needed to yield a satisfactory bit-error-rate (BER) performance is usually on the order of half the block size. Simulation results not only demonstrate the capability of the algorithm to perform blind identification using fewer received blocks, but also show that in some cases system performance can be improved by choosing a repetition index larger than needed. Simulation of the proposed method over time-varying channels clearly demonstrates the improvement over previously reported methods

A Semi-Blind Pilot-Assisted Channel Estimation Algorithm in OFDM Systems

In this paper we study a new semi-blind channel estimation algorithm in orthogonal frequency division multiplexing (OFDM) systems. The proposed scheme is an extension of a recently reported subspace-based blind channel estimation algorithm in cyclic prefix systems which requires very few received blocks. The semi-blind estimation algorithm is devised by using the information obtained both from the blind channel estimation method and a pure pilot-assisted method. The proposed algorithm uses a small amount of received data and can be applied to any types of communication constellations. Simulation results show that, with the same number of pilot samples, the semi-blind algorithm has a clear improvement in system performance over the pure pilot-assisted method. To achieve the same bit- error-rate performance, the proposed semi-blind algorithm uses fewer pilot samples

A golden template self-generating method for patterned wafer inspection

This paper presents a novel golden template self-generating technique for detecting possible defects in periodic two-dimensional wafer images. A golden template of the patterned wafer image under inspection can be obtained from the wafer image itself and no other prior knowledge is needed. It is a bridge between the existing self-reference methods and image-to-image reference methods. Spectral estimation is used in the first step to derive the periods of repeating patterns in both directions. Then a building block representing the structure of the patterns is extracted using interpolation to obtain sub-pixel resolution. After that, a new defect-free golden template is built based on the extracted building block. Finally, a pixel-to-pixel comparison is all we need to find out possible defects. A comparison between the results of the proposed method and those of the previously published methods is presented