Professor Friedlander is doing research in the general area of statistical signal processing and its applications. Specific areas of expertise of his research group include:
Professor Friedlander's research group is currently working on the following research projects.
The goal of this project is to to improve the performance of conventional STAP processing by using linear transformations to "focus" the estimated covariance matrix for a given range. The improvements anticipated are two-fold: (i) Improve Signal to Interference-plus-Noise Ratio (SINR), especially at short ranges, (ii) Reduce the rank of the covariance matrix to further improve performance and reduce processing requirements.
In the work so far we used a technique which involves calculating the expected values of the true (optimal) covariance matrix for the range of interest and of the averaged covariance matrix which is used in conventional STAP processing, and then computing a linear transformation which converts the latter into the former. This technique apppears to work quite well, but must be considered to be a ``brute force" approach, because it does not make use of the detailed structure of the space-time covariance matrix. We have studied this technique in order to demonstrate that significant improvements can, indeed, be achieved by linear data transformation.
The main objective of the project is to develop a robust and computationally efficient version of the linear transformation approach for reducing range dependent effects in circular STAP. The work focuses on the development of techniques which are based on the temporal and spatial array response only, and do not depend on the specific clutter distribution and jammer parameters. Furthermore, we can decompose the linear transformation so that it can be applied separately in the temporal and spatial domains, which results in significantly reduced computational requirements.
References:
B. Friedlander, "A Subspace Method for Space Time Adaptive Processing", IEEE Transactions on Signal Processing, to appear.
The vast majority of modern array processing techniques are designed for point sources, i.e. spatially discrete sources of acoustic or electromagnetic energy. In many practical situations the transmitter is best modeled as a distributed, rather than a discrete source. The principal mechanism for making the source appear to be distributed in space, is diffuse (unresolvable) and specular (resolvable) multipath caused by scattering of the propagating waves. A secondary, but equally important mechanism, is transmitter motion. If the source moves significantly during the observation interval (or coherent integration time) it will appear to be distributed rather than discrete.
The goal of this project is to develop array processing techniques for distributed sources, using a parametric model for the array response. It can be shown that the vector of the signals received by an array resides in a Grassmanian manifold (or a subspace manifold) - a parametric family of subspaces. This is the natural extension of the array manifold used in the case of point sources, which can be considered to be a special (rank one) case of a subspace manifold. In other words, whereas the response of an array to discrete sources is characterized by what is commonly called the array manifold, its response to a distributed source is characterized by a subspace manifold. Algorithms will be developed to compute the subspace manifold for a given array either analytically, or from measured data. We are also developing a set of algorithms for common array processing operations such as direction finding, signal estimation and detection, and interference cancellation, designed for operation in an environment containing both discrete and distributed signal sources. These algorithms lead to improvements in future systems which make use of sensor arrays. In particular, sonar systems and communication systems are likely to be beneficiaries of this technology. However, much of the proposed work is generally applicable to a wide range of sensor arrays.
References:
Y. Jin and B. Friedlander, "Detection of Distributed Sources Using Sensor Arrays," IEEE Transactions on Signal Processing, vol. 52, no. 6, pp. 1537 - 1548, June 2004.
The objective of this project is to extend the theory of space-time array processing (STAP) to multi-antenna communication over fading channnels, using subspace models for channels and subspace methods for transceivers. Subspace models may be used to represent random fading channels, and statistical subspace methods can be used to design practical space-time transceivers for the multi-antenna, fading wireless channel.
Many of the assumptions made about fading channels for multi-antenna communication are overly pessimistic. For example, fading is often assumed to be independent from element-to-element. This assumption does not match reality for the majority of users which are not too close to the basestation (on the uplink). As a consequence, the space-time codes and transceivers designed to decode them are sub-optimum for the actual channel. On the other hand, the design of optimum transceivers that would exploit an optimistic channel can be complex, requiring real-time beamforming in uncalibrated arrays and subspace tracking for interference mitigation. Moreover, in highly nonstationary problems, the very foundations of blindly-adaptive space-time processing are called into question, for the so-called sample support required to identify subspaces is unavailable. For such nonstationary problems, the wireless literature lags the adaptive radar literature.
Prior results suggest that subspaces may be used to model the effects of a random channel on a wireless transmission. Given only the subspace, and not the detailed physics of its coordinate representation, the designer can design signals and tranceivers for space-time processing gain and diversity. Moreover, we have shown that optimum receiver statistics are just estimators of output SINR in disguise, suggesting that detection statistics for decoding data can be used to track output SINR. Estimated SINR may then be used to update the estimated network capacity, and re-allocate power and bandwidth. So, in broad outline, this work is addressed to space-time channel modelling, using subspace methods; signal and transceiver design for SINR gain and diversity, using only channel subspaces; and estimation of network capacity, using only transceiver statistics.
References:
C. Van-Rensburg and B. Friedlander, "Transmit Diversity for Arrays in Correlated Rayleigh Fading", IEEE Transactions on Signal Processing, to appear.
A fundamental assumption underlying the design of existing communication systems is that the channel variations are relatively slow so that it can be considered to be approximately constant over a sufficiently large block of symbols. Various methods such as powerful error correcting codes and spatial or temporal diversity are used post-facto to mitigate the effects of the time-varying channel. Here we study what happens when the channel changes so fast that it is invalid to assume that it is constant over a block of symbols or even over a single symbol. This forces us to confront the time-varying characteristics of the channel and to incorporate them in the design of the communication system in a more direct and fundamental manner than was done in most previous work.
References:
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Multiple-input/Multiple-output (MIMO) Radar, Waveform Diversity, Adaptive Waveform Design, Interference Avoidance, Multipath Mitigation, Clutter Rejection , multi-band, multi-modal, multi-sensor, multifunction processing from distributed platforms. Exploiting diversity in many dimensions: transmitted power, bandwidth, center frequency, pulse shape and spreading, polarization, space-time and symbol coding.Channel / propagation characterization and prediction. Synthetic Aperture Radar. Space-Time Adaptive Processing. Velocity Synthetic Aperture Radar. SAR, ISAR, VSAR, GMTI.
References:
B. Friedlander and B. Porat, "VSAR: A High-Resolution Radar System for Ocean Imaging," IEEE Transactions on Aerospace Electronic Systems , vol. 34, no 3, pp. 755--776, July 1998.
B. Friedlander and B. Porat, "VSAR -- A High Resolution Radar System for Detection of Moving Targets", IEE Proc. - Radar, Sonar, Navigation, vol. 144, no.4, August 1997, pp. 205--218.
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Wireless Communication, Broadband MIMO-OFDM, Smart Antennas, Beamforming, Maximum Ratio Combining, Correlated Fading, Diversity, Interference Suppression WLAN, Unlicensed Spectrum, CDMA, Adapative Array, Modulation, Multipath, Channel Modeling, Multi-user Diversity, Capacity, Performance Analysis, Bit-Error Rate, Transmit Diversity.
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Professor Friedlander was the Principal Investigator on a large number of research projects, primarily for the Department of Defense. Through his consulting activities he has been involved in solving problems in the the following areas:
Professor Friedlander is currently accepting full-time and part-time students, with strong preference given to Ph.D. students. To be considered for full-time position with research assistantship you need to have a strong mathematical background and interest in digital communications and statistical signal and array processing. Please send in your biography and a copy of your transcript. For those who are working full-time in a company and would like to pursue a part-time Ph.D., please contact Professor Friedlander directly to discuss your specific situation.
For more information on what is involved in a Ph.D. research program look at Ph.D. Research