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

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

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

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

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

New Algorithms for Blind Block Synchronization in Zero-Padding Systems

Blind channel identification using linear redundant filterbank precoders (LRP) has been studied extensively in the literature. Most methods are proposed based on the assumption that block synchronization is perfect. In practice, a blind block synchronization algorithm must be used to justify this assumption. This paper studies the blind block synchronization problem in systems using a zero-padding (ZP) precoder. A previously reported method is reviewed and a new approach for the problem is proposed. Generalized versions of both approaches are then developed using a parameter called repetition index. Simulation results show that when the repetition index is chosen to be greater than unity, the block synchronization error rate performance of the proposed algorithm has a significant improvement over the previously reported method

Redundancy in block coded modulations for channel equalization based on spatial and temporal diversity

Linear block codes in the complex field can be applied in spatial and/or temporal diversity receivers in order to develop high performance schemes for (almost-) blind equalization in mobile communications. The proposed technique uses the structure of the encoded transmitted information (with redundancy) to achieve equalization schemes based on a deterministic criterion. Simulations show that the proposed technique is more efficient than other schemes that follow similar equalizer structures. The result is an algorithm that provides the design of channel equalizers in low EbNo scenarios.Peer ReviewedPostprint (published version