## Final Report Summary - TRADENET (Transceiver Design for Distributed Wireless Networks)

In this project we developed advanced signal processing techniques for the design of distributed wireless schemes that are robust to asynchronism among network nodes, focusing specially on distributed space-time coding, physical layer network coding, low-complexity receivers that incorporate channel uncertainty at different nodes in the network, and appropriate power/frequency allocation schemes. This was achieved through the determination of relevant distributed optimization criteria, development of a novel methodology to obtain practical optimal schemes, and real-time evaluation of the proposed schemes to demonstrate their quality.

Specifically, motivated by the recent increased interest in large-scale multiple-input multiple-output (MIMO) systems, combined with the cost of analog radio-frequency (RF) chains that necessitates the use of efficient antenna selection (AS) schemes, we considered the maximum-SNR joint beamforming-AS problem at the transmitter side for a MIMO system that consists of a large number of transmit antennas. Capacity or signal-to-noise ratio (SNR) optimal AS has been considered to require an exhaustive search among all possible antenna subsets. In this project, we proved that, under a total power constraint on the beamformer, the maximum-SNR joint beamforming transmit AS problem with two receive antennas and an arbitrary number of transmit antennas is polynomially solvable and developed an algorithm that solves it with quartic complexity, independently of the number of selected antennas. The algorithm identifies with quartic complexity a cubic-size collection of antenna subsets that contains the one that maximizes the post-processing receiver SNR. From a different perspective, for any given two-row complex matrix, our algorithm computes with quartic complexity its two-row submatrix with the maximum principal singular value, for any number of selected columns. In addition, our method also applies to receive AS with two transmit antennas. Finally, if we enforce a per-antenna-element power constraint on the beamformer (i.e., constant-envelope transmission), then the set of transmit AS subsets that contains the optimal one is the same as in the total power constraint case. Therefore, our algorithm offers a practical solution to the maximum-SNR antenna selection problem when either the transmitter or the receiver consists of a large number of antennas. An important extension of that work, that was motivated by the requirement of significant front-end hardware savings for massive-MIMO, was the implementation and fine-tuning of the algorithm to solve, with appropriate modifications, the problem of SNR-optimal subarray selection with reduced complexity with respect to the problem of full array selection.

In addition, we considered two-way relay (TWR) systems with physical-layer network coding (PNC) under unknown channel state information. In noncoherent scenaria, relay systems usually operate with differential or orthogonal modulation. In either case, due to channel-induced memory, the optimal receiver at both the relay and source nodes takes the form of a sequence detector. Such a receiver has exponential (in the sequence length) complexity, when implemented through an exhaustive search among all possible sequences. Hence, many works in the literature consider single-symbol or short-block noncoherent PNC. In this project, we considered transmission of frequency-shift keying (FSK) signals in a TWR system and presented an algorithm that performs generalized-likelihood-ratio-test (GLRT) and maximum-likelihood (ML) optimal noncoherent PNC with polynomial (in the sequence length) complexity. Although presented in the context of FSK, our developments hold for other orthogonal modulation techniques as well. As a low-cost alternative, we also presented a quadratic-complexity suboptimal detector that attains near-optimal performance. Simulation studies indicate that the proposed noncoherent PNC scheme attains near-coherent-PNC performance with affordable complexity when the sequence length is on the order of 64, offering a 2-4dB gain over conventional noncoherent PNC approaches that can handle only short values of the sequence length.

In addition to the aforementioned major project results that enhanced the Researcher’s knowledge and ability to deal with multi-disciplinary problems, the Researcher spent significant time to get trained on the programming of software-defined-radio, get experience with hands-on experimentation, and, hence, enhance her knowledge of communications systems. She learned how to program the B210 USRP SDR platform of the Return Host and implement on it various physical-layer protocols and communication algorithms. This stage of training involved time spent on both fundamental and advanced programming skills. The Researcher learned how to synchronize in time and frequency a pair of a transmitter and a receiver and gave emphasis to fully-blind time and frequency synchronization because of the nature of the project. She also studied the pros and cons of real-time experimentation in conjunction with communications principles, such as carrier frequency, sampling frequency, signal bandwidth, sequence duration, and channel coherence time. Through this training, she became able to develop a real-time fully noncoherent communication system using orthogonal modulation and validate the observations that she had made through theoretical and simulation studies.

The training and the knowledge the Researcher received during the duration of this project is interdisciplinary and combines combinatorial optimization, detection, statistical signal processing, coding, linear algebra, and hands-on experimentation. Combinatorial optimization is met in many engineering problems where partial information is available to the designer and is a growing field not only in distributed transmission systems but also in other engineering fields such as networking, signal processing, and multimedia to name a few. In addition, hands-on training and experience is a strong complementary skill that becomes necessary in today’s research in communications. Therefore, the training and research performed, although concentrated on distributed wireless networks, is by nature interdisciplinary and has impact in a wider area of engineering applications where noncentralized optimization is of high interest. The training and experience the Researcher received from both the Outgoing and the Return Hosts have boosted the Researcher's career, professional maturity, and independence.

Project Coordinator: Prof. Aggelos Bletsas (http://www.telecom.tuc.gr/~aggelos/)

Project Researcher: Dr. Maria Gkizeli (http://www.telecom.tuc.gr/~mgkizeli/)

Specifically, motivated by the recent increased interest in large-scale multiple-input multiple-output (MIMO) systems, combined with the cost of analog radio-frequency (RF) chains that necessitates the use of efficient antenna selection (AS) schemes, we considered the maximum-SNR joint beamforming-AS problem at the transmitter side for a MIMO system that consists of a large number of transmit antennas. Capacity or signal-to-noise ratio (SNR) optimal AS has been considered to require an exhaustive search among all possible antenna subsets. In this project, we proved that, under a total power constraint on the beamformer, the maximum-SNR joint beamforming transmit AS problem with two receive antennas and an arbitrary number of transmit antennas is polynomially solvable and developed an algorithm that solves it with quartic complexity, independently of the number of selected antennas. The algorithm identifies with quartic complexity a cubic-size collection of antenna subsets that contains the one that maximizes the post-processing receiver SNR. From a different perspective, for any given two-row complex matrix, our algorithm computes with quartic complexity its two-row submatrix with the maximum principal singular value, for any number of selected columns. In addition, our method also applies to receive AS with two transmit antennas. Finally, if we enforce a per-antenna-element power constraint on the beamformer (i.e., constant-envelope transmission), then the set of transmit AS subsets that contains the optimal one is the same as in the total power constraint case. Therefore, our algorithm offers a practical solution to the maximum-SNR antenna selection problem when either the transmitter or the receiver consists of a large number of antennas. An important extension of that work, that was motivated by the requirement of significant front-end hardware savings for massive-MIMO, was the implementation and fine-tuning of the algorithm to solve, with appropriate modifications, the problem of SNR-optimal subarray selection with reduced complexity with respect to the problem of full array selection.

In addition, we considered two-way relay (TWR) systems with physical-layer network coding (PNC) under unknown channel state information. In noncoherent scenaria, relay systems usually operate with differential or orthogonal modulation. In either case, due to channel-induced memory, the optimal receiver at both the relay and source nodes takes the form of a sequence detector. Such a receiver has exponential (in the sequence length) complexity, when implemented through an exhaustive search among all possible sequences. Hence, many works in the literature consider single-symbol or short-block noncoherent PNC. In this project, we considered transmission of frequency-shift keying (FSK) signals in a TWR system and presented an algorithm that performs generalized-likelihood-ratio-test (GLRT) and maximum-likelihood (ML) optimal noncoherent PNC with polynomial (in the sequence length) complexity. Although presented in the context of FSK, our developments hold for other orthogonal modulation techniques as well. As a low-cost alternative, we also presented a quadratic-complexity suboptimal detector that attains near-optimal performance. Simulation studies indicate that the proposed noncoherent PNC scheme attains near-coherent-PNC performance with affordable complexity when the sequence length is on the order of 64, offering a 2-4dB gain over conventional noncoherent PNC approaches that can handle only short values of the sequence length.

In addition to the aforementioned major project results that enhanced the Researcher’s knowledge and ability to deal with multi-disciplinary problems, the Researcher spent significant time to get trained on the programming of software-defined-radio, get experience with hands-on experimentation, and, hence, enhance her knowledge of communications systems. She learned how to program the B210 USRP SDR platform of the Return Host and implement on it various physical-layer protocols and communication algorithms. This stage of training involved time spent on both fundamental and advanced programming skills. The Researcher learned how to synchronize in time and frequency a pair of a transmitter and a receiver and gave emphasis to fully-blind time and frequency synchronization because of the nature of the project. She also studied the pros and cons of real-time experimentation in conjunction with communications principles, such as carrier frequency, sampling frequency, signal bandwidth, sequence duration, and channel coherence time. Through this training, she became able to develop a real-time fully noncoherent communication system using orthogonal modulation and validate the observations that she had made through theoretical and simulation studies.

The training and the knowledge the Researcher received during the duration of this project is interdisciplinary and combines combinatorial optimization, detection, statistical signal processing, coding, linear algebra, and hands-on experimentation. Combinatorial optimization is met in many engineering problems where partial information is available to the designer and is a growing field not only in distributed transmission systems but also in other engineering fields such as networking, signal processing, and multimedia to name a few. In addition, hands-on training and experience is a strong complementary skill that becomes necessary in today’s research in communications. Therefore, the training and research performed, although concentrated on distributed wireless networks, is by nature interdisciplinary and has impact in a wider area of engineering applications where noncentralized optimization is of high interest. The training and experience the Researcher received from both the Outgoing and the Return Hosts have boosted the Researcher's career, professional maturity, and independence.

Project Coordinator: Prof. Aggelos Bletsas (http://www.telecom.tuc.gr/~aggelos/)

Project Researcher: Dr. Maria Gkizeli (http://www.telecom.tuc.gr/~mgkizeli/)