Research On The Channel Capacity And Transmission Strategies For Multi-user Networks

A system that can support many transmitters and many receivers to communicate simul-taneously is called a multi-user network.Since it captures many important aspects,such as broadcasting,cooperative,and interfere,of real-world networks,a bunch of research has been done for the type of networks.Multi-user information theory aims to establish the capacity of the network and the optimal coding schemes that achieve the capacity,it has irreplaceable theory analysis and practical guidance for the real-world communication tech-nology and system design.For example,we use vector broadcast channels to study the multi-input multi-output technology,relay networks to study cooperative communication technology,interference channels to study anti-interference technology.Although many el-egant results for multi-user networks have been developed over the past decades,the theory is far from complete.In this dissertation,we study the capacity and transmission strategies for three typical multi-user networks.Our main contributions are listed as follows.1.The ergodic sum capacity and transmission strategies for the fading Gaussian large scale multiple-input multiple-output broadcast channels are studied.We derive the scaling laws of the ergodic sum rates for the channel with dirty-paper coding and generalized zero-forcing channel inversion,the scaling law of the ergodic symmetric sum capacity,and the asymptotic behaviour of the generalized zero-forcing channel inversion scheme in the ex-treme scenario.It is shown that the singular values of the Gaussian random channel matrix approaches to a deterministic value in a large probability when the number of transmit an-tennas is much larger than the number of receivers(total number of receiver antennas).As a result,the randomness of channel matrix is fading,which makes the analysis much clear-er.Since dirty-paper coding achieves the capacity and the generalized zero-forcing channel inversion achieves the same scaling law of the ergodic sum rate with dirty-paper coding,the generalized zero-forcing channel inversion scheme is asymptotically optimal in sum rate.Furthermore,the optimal power allocation strategy for the generalized zero-forcing channel inversion approaches to equal power allocation in a large probability in the extreme scenari-o,which makes the generalized zero-forcing channel inversion with equal power allocation a simple and efficient transmission strategy to guarantee both total throughput and fairness.Since the simple strategy achieves the same rate at each receiver and is asymptotically opti-mal in sum rate,we further derive the scaling law of the ergodic symmetric sum capacity of the channel.2.The capacity and transmission strategies for the Gaussian two-hop relay networks with a common message are studied.We derive the tightest capacity lower bound on the multicast capacity of the Gaussian two-hop relay network with one source,N relays,and L destinations,and propose a partial-decode forward coding scheme with degraded message sets.This scheme improves upon a previous partial-decode forward scheme by Chern and(?).The Chern-(?) coding scheme,whereby the channel is viewed as a cascade of a broadcast channel and a multiple access channel,achieves the cutset bound within log N bits when there is only one receiver,yet has an unbounded gap from the cutset bound for L?2 destinations.The proposed coding scheme works the same as the Chern-(?) coding scheme in the first hop,where the source node broadcast the split messages to the relays using superposition coding.The relays decode the message parts according to its capability,and then forward their message parts to the L destinations using superposition coding through L multiple access channels with degraded message sets.Due to the coherent cooperative transmission in the second hop,the proposed coding scheme achieves the cutset bound within 1/2log N bits regardless of the channels gains and any number of destinations.Theoretically,the rate is improved by using coherent cooperative transmission in the second hop,however the computing complexity for finding the optimal input distributions for relays is time consuming.We propose an alternative scheme which restricts the relay inputs to mutually independent Gaussian distributions.The proposed partial decode-forward scheme achieves a slightly larger gap of log N bits from the cutset bound,however the computation of this relaxed achievable rate involves evaluating mutual information across L(N+1)cuts out of the total L2~Npossible cuts,providing a very simple linear-complexity algorithm to approximate the single-source multicast capacity of the Gaussian two-hop relay network.3.The sum capacity and transmission strategies for the Gaussian X channels are studied.We extend the sum capacity results previously obtained for the 2×2 user Gaussian X channel under noisy interference regimes to the M×M user Gaussian X channel,and derive some noisy interference regimes.The side information constructed for the analysis of the noisy interference regimes of the 2×2 user X channel is not fit anymore since the channel has been extended from 2 user pairs to M user pairs.Inspired by the analysis of interference channels with more than two users,we construct new vectors and sets side information with loop structure for the receivers,and derive some sum capacity upper bounds for the X channel with noisy-interference.It is shown that,when the channel is under the proposed noisy interference regime,operating the X channel as its underling interference channel and treating interference as noise at the receivers achieves the sum capacity,which is the same as the sum capacity of the underling Gaussian interference channel.