Dr. Sagias research interests are in the broad area of digital communications. The man research interests are summarized, but not necessarily limited, in the following areas:

## Communication Theory

## Communication Theory

This research area includes advances in theory regarding fundamental issues of telecommunications and characterized by deep mathematical background. A number of papers provide analytical solutions to statistical theory problems, such as "*What is the distribution of the sum of random variables?*". Solutions to this kind of questions help to analyze the performance of multiple-input multiple-output (MIMO) antenna systems operating over fading channels.

Other papers in this research area propose novel multilevel correlated signaling schemes or introduce novel analytical methods, while another set of papers propose novel Gaussian-originated correlated channel models, such as the Weibull one, and analyze the performance of MIMO receivers.

It should me mentioned that this research field is explicitly supported by the Communication Theory Technical Committee of IEEE Communications Society, according to which "*of special interest is the novel use of communication theory and/or information theory to solve problems in areas that include (but are not limited to) source and channel coding, storage, modulation, detection, estimation, synchronization, multiple access, interference mitigation, and networking*".

### Representative Articles

- Ranjan K. Mallik, Nikos C. Sagias, "Distribution of inner product of complex Gaussian random vectors and its applications," IEEE Transactions on Communications, vol. 59, no. 12, pp. 3353-3362, Dec. 2011.
- Nikos C. Sagias, Ranjan K. Mallik, George S. Tombras, "Error rate performance of multilevel signals with coherent detection," IIEEE Transactions on Communications, vol. 58, no. 8, pp. 2188-2192, Aug. 2010.
- George K. Karagiannidis, Nikos C. Sagias, Theodoros A. Tsiftsis, "Closed-form statistics for the sum of squared Nakagami-
*m*variates and its applications," IEEE Transactions on Communications, vol. 54, no. 8, pp. 1353-1359, Aug. 2006. - George K. Karagiannidis, Theodoros A. Tsiftsis, Nikos C. Sagias, "A closed-form upper-bound for the distribution of the weighted sum of Rayleigh variates," IEEE Communications Letters, vol. 9, no. 7, pp. 589-591, July 2005.
- Nikos C. Sagias, George K. Karagiannidis, "Gaussian class multivariate Weibull distributions: Theory and applications in fading channels," IEEE Transactions on Information Theory, vol. 51, no. 10, pp. 3608-3619, Oct. 2005.

## Performance Analysis

## Performance Analysis

By “performance analysis” we mean the derivation of a performance metric, such as bit-error rate (BER), channel capacity, outage probability, etc., in terms of tabulated functions^{1}. Then, the performance metric is considered as being in *closed form*. Closed-form expressions have the advantage of simplicity of numerical evaluation and the characterized by the their accuracy and numerical stability. They can be also used for comparison purposes of the performance metric under consideration for different sets of parameters values, providing fast evaluating numerical results of the metric.

For example, quite generic performance evaluation results have been derived for a dual-hop plus a direct link multiple-input multiple-output (MIMO) wireless communication system using orthogonal space-time block codes (STBC). The system under consideration is based on the decode-and-forward relaying protocol and operates over spatially correlated Nakagami-*m* fading channels. The overall analysis is generic enough to account for any MIMO correlation model either from measurements or having theoretical and analytical justification. Analytical expressions for the system end-to-end outage and average symbol error probability are obtained, while critical parameters of the MIMO channel are taken into consideration such as the angle of arrival, the antenna array configuration, the wavelength, and non-isotropic scattering conditions.

In the following figure ASEP performance curves are presented of *M*-ary PSK and *M*-ary QAM constellations of dual-hop DF 2x2 MIMO relay systems with orthogonal STBCs (2 transmit and receive antennas, H_{2} STBC scheme) versus transmit SNR per symbol of the first hop, under correlated Nakagami-*m* fading.

In another contribution on the same topic, closed-form expressions are derived for the average Shannon channel capacity for generalized fading channels (Nakagami-*m*, Rice and Weibull), are derived. The following figure presents the normalized to bandwidth average channel capacity (spectral efficiency) of switched-and-stay combiners (SSC), operating at the optimum switching threshold, as a function of the average SNR in Nakagami-*m* fading with independent and identically distributed (iid) input branches and for several values of *m*.

### Representative Articles

- Kostas Peppas, Christos K. Datsikas, Nikos C. Sagias, George S. Tombras, "Dual-hop MIMO relay systems over spatially correlated Nakagami-
*m*fading channels," IET Communications, vol. 5, no. 15, pp. 2106-2115, Oct. 2011. - Nikos C. Sagias, George S. Tombras, George K. Karagiannidis, "New results for the Shannon channel capacity in generalized fading channels," IEEE Communications Letters, vol. 9, no. 2, pp. 97-99, Feb. 2005.
- Nikos C. Sagias, George K. Karagiannidis, "Effects of carrier phase error on EGC receivers in correlated Nakagami-
*m*fading," IEEE Communications Letters, vol. 9, no. 7, pp. 580-582, July 2005.

^{1. Computer simulations is another useful and accurate method to analyze the performance of wireless systems. However, in our research, simulations results are equivalently used as a verification tool for the analytical ones.↩}

## Relaying Networks

## Relaying Networks

Multi-hop relaying communications have recently attracted significant interest as they are able to provide a broad and efficient coverage in various contemporary communication networks. In multi-hop transmission, several intermediate nodes act as relays forwarding data from source to destination. Many protocols take advantage of the benefits of multi-hop transmission, including the decode-and-forward (DF) that demonstrates a reasonable trade-off between implementation complexity and error rate performance, the amplify-and-forward (AF), the store-and-forward (SF), etc. For example, the next figure shows a hybrid satellite broadcasting model, where the end-to-end reception by the mobile terminal can be achieved in two time slots, or using two different frequencies for the satellite and the terrestrial relay.

Multiple-input multiple-output (MIMO) communication systems, on the other hand, have received considerable attention in the last years due to their potential for providing significant capacity and performance enhancement over conventional single-input single-output (SISO) systems. Therefore, the application of MIMO systems in conjunction with relaying protocols has become a topic of increasing interest, due to the fact that this combination enables the design of sophisticated and high performance communication systems.

Based on all the above, the next figure presents some average symbol error probability (ASEP) curves of *M*-ary QAM for dual-hop DF MIMO relay systems with orthogonal space-time block coding (STBC) under correlated Rayleigh channels.

In another contribution on this research area some performance evaluation results are shown next, where the end-to-end (e2e) average symbol error probability of QPSK versus average SNR for a dual-hop pilot-symbol assisted system with MRC and least-squares estimation (LSE) is shown for various antenna elements.

### Representative Articles

- Nikos C. Sagias, "Pilot-symbol assisted phase-shift keying for dual-hop relaying communication networks," IEEE Transactions on Communications, vol. 62, no. 2, pp. 510-521, Feb. 2014.
- Christos K. Datsikas, Nikos C. Sagias, Fotis I. Lazarakis, George S. Tombras, "Outage analysis of decode-and-forward relaying over Nakagami-m fading channels," IEEE Signal Processing Letters, vol. 15, no. 1, pp. 41-44, Jan. 2008.
- Christos K. Datsikas, Kostas Peppas, Nikos C. Sagias, George S. Tombras, "Serial relaying communications over generalized-gamma fading channels," Wireless Communications and Mobile Computing, vol. 12, no. 13, pp. 1191-1202, Sept. 2012.

## Channel Modelling

## Channel Modelling

Multivariate statistics is a useful mathematical tool for modeling and analyzing realistic wireless channels especially in the presence of correlated fading. Correlated fading channels are usually met in contemporary multiantenna systems with not sufficiently separated antennas, where space or polarization diversity is applied (e.g., hand-held mobile terminals and indoor base stations). In such applications, the correlation among the channels results in a degradation of the diversity gain obtained.

In the open technical literature, there are several multivariate channel models, such as the Rayleigh and Nakagami-*m* ones. In this research area one key contribution is the derivation of the multivariate Weibull channel model, originated by Gaussian random variables. The Weibull distribution was first introduced by Waloddi Weibull back in 1937 for estimating machinery lifetime and became widely known in 1951. Nowadays, the Weibull distribution is used in several fields of science. For example, it is a very popular statistical model in reliability engineering and failure data analysis. It is also used in some other applications, such as weather forecasting and data fitting of all kinds, while it is widely applied in radar systems to model the dispersion of the received signals level produced by some types of clutters. Concerning wireless communications, the Weibull distribution seems to exhibit good fit to experimental fading channel measurements, for both indoor, and outdoor environments.

The next figure shows the power correlation coefficient between two Weibull random variables as a function of the power correlation coefficient of the Gaussian underline processes.

The next figure shows some results for the outage probability as a function of the first branch normalized outage threshold for a dual-branch SC, with unequal input SNRs and for different values of the Weibull fading parameter *β*.

Of great interest also is the second order statistics of the fading channels. The second order statistics are related to the average fade duration and level crossing rates that are quite useful parameters for designing the appropriate interleavers and buffers. The next figure presents the average fading duration for the Weibull channel model for different Weibull fading parameters *β*.

### Representative Articles

- Nikos C. Sagias, George K. Karagiannidis, "Gaussian class multivariate Weibull distributions: Theory and applications in fading channels," IEEE Transactions on Information Theory, vol. 51, no. 10, pp. 3608-3619, Oct. 2005.
- Nikos C. Sagias, Dimitris A. Zogas, George K. Karagiannidis, George S. Tombras, "Channel capacity and second order statistics in Weibull fading," IEEE Communications Letters, vol. 8, no. 6, pp. 377-379, June 2004.
- Petros S. Bithas, Nikos C. Sagias, P. Takis Mathiopoulos, Stavros A. Kotsopoulos, Andreas M. Maras, "On the correlated
*K*-distribution with arbitrary fading parameters," IEEE Signal Processing Letters, vol. 15, no. 2008, pp. 541-544, Dec. 2008.

## Optical Wireless Systems

## Optical Wireless Systems

Outdoor optical wireless (OW) systems have recently gained attention as a broadband alternative in niche applications including semi-permanent office interconnections and MAN implementations. Despite the inherent advantages of outdoor OW systems, the transmission of light through the atmosphere can be challenging. Apart from weather-dependent static transmission losses that may limit the system availability, atmospheric turbulence induces time-varying changes in the refractive index, which in turn affect the amplitude, phase and propagation direction of the optical signal. These changes result in time-varying power fluctuations of the received signal and when the turbulence is intense enough, the received signal decreases below the receiver sensitivity and the link is lost. This corresponds to a fade event, which affects the OW system both in terms of capacity, as well as latency. Several million bits may be lost during a msec-long fade at 10 Gb/s, while the link will be in outage for an amount of time approximately equal to the fade duration.

Our latest research focuses on the insertion of a semiconductor optical amplifier (SOA) in the receiver, prior to the photodiode, for amplification and/or equalization purposes. The proposed system model is depicted in the following figure, where the principle of operation is graphically represented:

The next figure shows some performance benefits of the use of a SOA in optical wireless receivers, where for example for a typical link length of 1km, the outage probability at the output of the photodiode can be improved up to one order of magnitude.Summarizing, this research area includes the following topics:

- Optical wireless channel modelling to accurately analyze the performance of OW systems.
- Novel fade mitigation techniques as fading channel countermeasures.
- OW relaying networks.

### Representative Articles

- Kostas Yiannopoulos, Nikos C. Sagias, Anthony C. Boucouvalas, "On the performance of semiconductor optical amplifier-assisted outdoor optical wireless links," IEEE Journal on Selected Areas in Communications, vol. 33, no. 9, pp. 1869-1876, Sept. 2015.
- Kostas Yiannopoulos, Nikos C. Sagias, Anthony C. Boucouvalas, "Fade mitigation based on semiconductor optical amplifiers," IEEE/OSA Journal of Lightwave Technology, vol. 31, no. 23, pp. 3621-3630, Dec. 2013.
- Christos K. Datsikas, Kostas Peppas, Nikos C. Sagias, George S. Tombras, "Serial free-space optical relaying communications over gamma-gamma atmospheric turbulence channels," IEEE/OSA Journal of Optical Communications and Networking, vol. 2, no. 8, pp. 576-586, Aug. 2010.