This paper derives bounds on the diversity- multiplexing tradeoff of wireless relay networks with arbitrary link connectivity between cooperating terminals. The derived bounds are applicable when there are single and multiple antennas per terminal. Two classes of relaying method are analyzed, those requiring all cooperating terminals to correctly decode the transmitted signal in order for the destination to correctly decode (comprehensive decoding), and those requiring only a subset of cooperating terminals to correctly decode the transmitted signal in order for the destination to correctly decode (destination decoding). It is shown that the diversity- multiplexing tradeoff of comprehensive decoding is constrained by the minimum number and arrangement of incident inter- terminal antenna links across all receiving terminals in the network, and that the diversity-multiplexing tradeoff of destination decoding is constrained by the minimum number and arrangement of incident inter-terminal antenna links across all cut sets in the network. Results for the complexity of the involved minimization algorithms are provided.

This paper derives bounds on the diversity order and high SNR probability of outage behavior of wireless relay networks with arbitrary link connectivity between cooperating terminals. Single and multiple antennas per terminal are considered. Two general codebook generation schemes are analyzed and compared. Common codebook generation involves the source and all relays sharing a common randomly generated codebook, and encompasses many practical encoding schemes, including both repetition coding and space-time coding. Independent codebook generation involves the source and all relays employing independent randomly generated codebooks, and provides an information theoretic lower bound on the probability of outage of all achievable codebook generation schemes. The results indicate that although independent codebook generation does not offer any diversity gain over common codebook generation, it can offer a significant probability of outage improvement under certain conditions.

This paper considers the ways that cooperating terminals can be connected to each other in wireless relay networks and the constraints imposed by the availability of different system resources. A framework is developed that exposes the relationship between constraints on available system resources and the achievable combinations of communication links between cooperating terminals. Cooperative connectivity models defined by the achievable combinations of links are derived, associated with their minimum cost constraint sets, and mapped to diversity techniques presented in the literature. The constraints considered are the available number of orthogonal relaying channels, the ability of terminals to diversity combine signals on a single common channel, the ability of terminals to diversity combine signals on orthogonal channels, the ability of terminals to transmit signals on multiple orthogonal channels, and the ability of terminals to cancel the effects of interhop interference.

The paper considers the impact of various system resource constraints on the connectivity and performance of relaying channels. This consideration is motivated by recent findings indicating that the performance of wireless relaying networks can be increased through the application of distributed spatial diversity techniques (e.g., multi-user diversity, multihop diversity, cooperative diversity) that rely on the mesh connectivity between wireless terminals. Relevant system resource constraints are introduced, constraint combinations are analyzed, and resultant system connectivity models are derived and compared via simulation. The constraints considered are the available number of orthogonal relaying channels, the ability of relays to diversity-combine signals, the ability of the destination to diversity-combine signals, the ability of receivers to diversity-combine signals on multiple orthogonal channels, and the ability of transmitters to transmit signals on multiple orthogonal channels. The analysis of these system resource constraints is applicable to both amplified (non-regenerative, amplify-and-forward) relaying and decoded (regenerative, decode-and-forward) relaying.

This paper considers the aggregate signal to noise ratio of amplified relaying channels, where the term aggregate refers to the inclusion of propagated noise terms generated as relaying terminals amplify both the information and noise portions of received signals. This consideration is motivated by recent findings for wireless relaying networks indicating that the performance of amplified relaying can approach and in some cases exceed the performance of decoded relaying. Expressions for the aggregate signal to noise ratio are developed for general amplified relaying channels with a given set of source, destination, and relaying terminals, link connectivity link attenuation, transmit power, and receiver noise. These expressions provide a method for analyzing the impact of varying the link connectivity or power allocation for a given set of terminals, and support the comparison of amplified relaying channels with decoded relaying channels.

This paper presents theoretical characterizations and analysis for the physical layer of multihop wireless communications channels. Four channel models are considered and developed: the decoded relaying multihop channel; the amplified relaying multihop channel; the decoded relaying multihop diversity channel; and the amplified relaying multihop diversity channel. Two classifications are discussed: decoded relaying versus amplified relaying, and multihop channels versus multihop diversity channels. The channel models are compared, through analysis and simulations, with the "singlehop" (direct transmission) reference channel on the basis of signal-to-noise ratio, probability of outage, probability of error, and optimal power allocation. Each of the four channel models is shown to outperform the singlehop reference channel under the condition that the set of intermediate relaying terminals is selected intelligently. Multihop diversity channels are shown to outperform multihop channels. Amplified relaying is shown to outperform decoded relaying despite noise propagation. This is attributed to the fact that amplified relaying does not suffer from the error propagation which limits the performance of decoded relaying channels to that of their weakest link.

This paper provides a theoretical characterization of the multihop wireless communications channel without diversity, wherein intermediate terminals relay information without employing spatial diversity techniques. Two channel models are proposed and developed: one where each intermediate terminal digitally decodes and re-encodes the received signal from the immediately preceding terminal and the other where each intermediate terminal simply amplifies the received signal from the immediately preceding terminal. These models are compared, through analysis and simulations, with the single-hop reference channel on the basis of probability of outage and probability of error. Both models achieve significant gains over the single-hop reference channel, with the amplified relaying model matching the performance of the decoded relaying model despite noise propagation.

This paper provides a theoretical characterization of the multihop wireless communications channel with diversity, wherein intermediate terminals relay information employing spatial diversity techniques. Two channel models are proposed and developed: one where each intermediate terminal combines, digitally decodes, and re-encodes the received signals from all preceding terminals and the other where each intermediate terminal simply combines and amplifies the received signals from all preceding terminals. These models are compared, through analysis and simulations, with the single-hop reference channel on the basis of probability of outage and probability of error. Both models achieve significant gains over the single-hop reference channel, with the amplified relaying model outperforming the decoded relaying model despite noise propagation.