# Estimation and separation of linear frequency- modulated signals in wireless communications using time - frequency signal processing.

Nguyen, Linh- Trung (2004) *Estimation and separation of linear frequency- modulated signals in wireless communications using time - frequency signal processing.* PhD thesis, Queensland University of Technology.

## Abstract

Signal processing has been playing a key role in providing solutions to key problems encountered in communications, in general, and in wireless communications, in particular. Time-Frequency Signal Processing (TFSP) provides eective tools

for analyzing nonstationary signals where the frequency content of signals varies in time as well as for analyzing linear time-varying systems. This research aimed at exploiting the advantages of TFSP, in dealing with nonstationary signals, into the fundamental issues of signal processing, namely the signal estimation and signal separation. In particular, it has investigated the problems of (i) the Instantaneous Frequency (IF) estimation of Linear Frequency-Modulated (LFM) signals corrupted in complex-valued zero-mean Multiplicative Noise (MN), and (ii) the Underdetermined Blind Source Separation (UBSS) of LFM signals, while focusing onto the fast-growing area of Wireless Communications (WCom).

A common problem in the issue of signal estimation is the estimation of the frequency of Frequency-Modulated signals which are seen in many engineering and real-life applications. Accurate frequency estimation leads to accurate recovery of the true information. In some applications, the random amplitude modulation

shows up when the medium is dispersive and/or when the assumption of point target is not valid; the original signal is considered to be corrupted by an MN process thus seriously aecting the recovery of the information-bearing frequency. The IF estimation of nonstationary signals corrupted by complex-valued zero-mean MN

was investigated in this research. We have proposed a Second-Order Statistics approach,

rather than a Higher-Order Statistics approach, for IF estimation using Time-Frequency Distributions (TFDs). The main assumption was that the autocorrelation function of the MN is real-valued but not necessarily positive (i.e. the spectrum of the MN is symmetric but does not necessary has the highest peak at zero frequency). The estimation performance was analyzed in terms of bias and variance, and compared between four dierent TFDs: Wigner-Ville Distribution, Spectrogram, Choi-Williams Distribution and Modified B Distribution. To further improve the estimation, we proposed to use the Multiple Signal Classification algorithm

and showed its better performance. It was shown that the Modified B Distribution performance was the best for Signal-to-Noise Ratio less than 10dB.

In the issue of signal separation, a new research direction called Blind Source Separation (BSS) has emerged over the last decade. BSS is a fundamental technique in array signal processing aiming at recovering unobserved signals or sources from observed mixtures exploiting only the assumption of mutual independence between the signals. The term "blind" indicates that neither the structure of the mixtures nor the source signals are known to the receivers. Applications of BSS are seen in, for example, radar and sonar, communications, speech processing, biomedical signal processing. In the case of nonstationary signals, a TF structure forcing

approach was introduced by Belouchrani and Amin by defining the Spatial Time- Frequency Distribution (STFD), which combines both TF diversity and spatial diversity. The benefit of STFD in an environment of nonstationary signals is the direct exploitation of the information brought by the nonstationarity of the signals.

A drawback of most BSS algorithms is that they fail to separate sources in situations where there are more sources than sensors, referred to as UBSS. The UBSS of nonstationary signals was investigated in this research. We have presented a new approach for blind separation of nonstationary sources using their TFDs. The

separation algorithm is based on a vector clustering procedure that estimates the

source TFDs by grouping together the TF points corresponding to "closely spaced"

spatial directions. Simulations illustrate the performances of the proposed method for the underdetermined blind separation of FM signals. The method developed in this research represents a new research direction for solving the UBSS problem.

The successful results obtained in the research development of the above two problems has led to a conclusion that TFSP is useful for WCom. Future research directions were also proposed.

Impact and interest:

**Citation counts**are sourced monthly from **Scopus** and **Web of Science®** citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the **Google Scholar™** indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

**1,324**since deposited on 03 Dec 2008

**243**in the past twelve months

**Full-text downloads**displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: | 15984 |
---|---|

Item Type: | QUT Thesis (PhD) |

Supervisor: | Boashash, Boualem& Senadji, Bouchra |

Keywords: | signal processing, wireless mobile communications, time -frequency distribution, nonstatonary signal, linear frequency - modulation, multiplicative noise(random amplitude modulation), instantaneous frequency estimation, time - frequency distribution, reduced - inteference distribution, array processing, underdetermined blind source separation, instantaneous linear mixture, spatial time - frequency distribution, vector clustering, rayleigh fading, narrowband fading channel, wideband fading channel, linear time - varying channel, wide - sense stationary uncorrelated scattering, scattering function, estimation, separation, simulation |

Divisions: | Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering Past > Schools > School of Engineering Systems |

Department: | Faculty of Built Environment and Engineering |

Institution: | Queensland University of Technology |

Copyright Owner: | Copyright Linh- Trung Nguyen |

Deposited On: | 03 Dec 2008 13:54 |

Last Modified: | 29 Oct 2011 05:41 |

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page