Joint maximum likelihood detection and power allocation in cooperative MIMO relay systems

Buffer-Aided Relay Selection Algorithms for Physical-Layer Security in Wireless Networks

“…where α sr is the power path loss, β sr is the log-normal shadowing (LNS) fading channel loss and n srm ∈ C Nm×1 is the Gaussian noise between the source and the relay which follows the distribution CN (0, σ 2 nsr ). According to [19], α sr is known as the distance based fading (or path loss). It is a representation of how a signal is attenuated the further it travels in the medium the system operates within.…”

“…According to [19], to approach the channel capacity, the maximum likelihood (ML) decoder can be applied at the receiver to obtain the following estimate of the transmitted data symbols:…”

Joint maximum likelihood detection and link selection for cooperative MIMO relay systems

“…The cooperative ML detector in Section 3 also makes use of a summed channel approximation in (14), and so it is logical to apply the idea of summing the channels into the link selection strategies. Therefore we define the sum of the relay to destination channels H rdt of a set of considered relays Ω c as…”

“…The original proposed cooperative ML detector is limited by the fact that it is formulated for the single relay case, with [13] extending this to the multiple relay case, but within this formulation it is required that the destination have perfect knowledge of each relays retransmission, which could not be easily obtained in the system if the relays retransmit simultaneously. In [14], the authors proposed a method for adapting the multiple relay cooperative ML detector with information which was available within the system, along with a stochastic gradient (SG) [15] power allocation technique that could optimise the global power distribution within the system to the source and relay nodes and their antennas. However, it was seen that the system performance was heavily dependent on the fact that the relays were close to the source and destination and had good channel links to both.…”

“…e − H e A e x 2 = y sd − H sd A s x 2Using the matrix S defined in(14), we can find the approximation of the equated ML rules to beye − H e A e x 2 = y sd − H sd A s x 2 + y rd − Sx 2 (41) Expanding these equations gives y H e y e + x H (H e A e ) H (H e A e )x − y H e (H e A e )x − x H (H e A e ) H y e = y H sd y sd + y H rd y rd + x H A H s H H sd H sd A s + S H S x − y H sd H sd A s + y H rd S x − x H A H s H H sd y sd + S H y rd (42) By equivalence, we can make the associations x H (H e A e ) H (H e A e )x = x H A H s H H sd H sd A s + S H S x (43) x H (H e A e ) H y e = x H A H s H H sd y sd + S H y rd (44) Starting with (43) it is clear that (H e A e ) H (H e A e ) = A H s H H sd H sd A s + S H S (45) H e A e = A H s H H sd H sd A s + S H S…”