There are many functions of the degree sequence of a graph which give lower bounds on the independence number of the graph. In particular, for every graph G, α(G) ≥ R(d(G)), where R is the residue of the degree sequence of G. We consider the precision of this estimate when it is applied to semi-regular degree sequences. We show that the residue nearly always gives the best possible estimate on ...

This study studies the performance of multihop free-space optical systems using the subcarrier binary phase-shift keying modulation over atmospheric turbulence channels. The authors propose a modified relaying strategy, termed ‘amplify– decode-and-forward’, realised by using avalanche photodiode (APD) receivers. The outage probability of the proposed system is analytically derived considering t...

This paper studies the performance of multihop free-space optical (FSO) systems using the subcarrier binary phase-shift keying modulation (BPSK) over atmospheric turbulence channels. We propose a modified relaying strategy, termed amplify-decode-and-forward (ADF), realised by using avalanche photodiode (APD) receivers. The outage probability of the proposed system is analytically derived consid...

The problem of finding the optimal number of data streams to transmit in a multi-user MIMO scenario, where both the transmitters and receivers are equipped with multiple antennas is considered. Without channel state information at any transmitter, with a zero-forcing receiver each user is shown to transmit a single data stream to maximize its own outage capacity in the presence of sufficient nu...

This paper investigates the impact of relay selection (RS) on the performance of cooperative non-orthogonal multiple access (NOMA), where relays are capable of working in either full-duplex (FD) or half-duplex (HD) mode. A number of relays (i.e., K relays) are uniformly distributed within the disc. A pair of RS schemes are considered insightfully: 1) Single-stage RS (SRS) scheme; and 2) Two-sta...

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...