On the Gaussian Half-Duplex Relay Channel

Abstract

This paper considers Gaussian relay networks where a source transmits a message to a sink terminal with the help of one or more relay nodes. The relays work in half-duplex mode, in the sense that they can not transmit and receive at the same time.For the case of one relay, the generalized Degrees-of-Freedom is characterized first and then it is shown that capacity can be achieved to within a constant gap regardless of the actual value of the channel parameters. Different achievable schemes are presented with either deterministic or random switch for the relay node. It is shown that random switch in general achieves higher rates than deterministic switch. For the case of K relays, it is shown that the generalized Degrees-of-Freedom can be obtained by solving a linear program and that capacity can be achieved to within a constant gap of K/2 log(4K). This gap may be further decreased by considering more structured networks such as, for example, the diamond network.

On the Capacity of the Two-Hop Half-Duplex Relay Channel

“…7 and 8, we show the upper bounds, achievable to withing 1 bit/symbol, reported in [5] and [6], given by…”

“…Given the limitations of current radio implementations, practical FD relaying suffers from self-interference. As a result, HD relaying has been widely adopted in the literature [2]- [5], [8], [9], [17]- [20].…”

“…In particular, results derived for the FD relay channel in [1] can be directly applied to the HD relay channel. Thereby, using the converse for the degraded relay channel in [1], the capacity of the discrete memoryless two-hop HD relay channel is obtained as [4], [5], [6] C = max p(x 1 ,x 2 ) min I(X 1 ; Y 1 |X 2 ) , I(X 2 ; Y 2 )},…”

“…Moreover, it was shown in [4], [5], [6] that X 2 can be represented as X 2 = [X ′ 2 , U], where U is an auxiliary random variable with two outcomes t and r corresponding to the HD relay transmitting and receiving, respectively. Thereby, (1) can be written equivalently as…”

Switched local schedules for diamond networks

“…The authors in [2], [3] approach low complexity relaying in half-duplex diamond networks by reducing the number of relaying states or using a subset of relays to approximately achieve a constant fraction of the capacity . We would like to note that the use of randomization in our work is fundamentally different from the use of random switching in [6] and [4]. In their work, the randomness in the switching sequence is used to convey additional information from the source to the destination while we use randomness to generate schedules that achieve higher rates.…”