Combining Coded Signals with Arbitrary Modulations in Orthogonal Relay Channels

We consider a relay channel for which the following assumptions are made : 1. The source-destination and relay-destination channels are orthogonal (frequency division relay channel) ; 2. The relay implements the decode-and-forward protocol ; 3. The source and relay implement the same channel encoder namely a convolutional encoder ; 4. They can use arbitrary and possibly different modulations. In this framework, we derive the best combiner in the sense of the maximum likelihood (ML) at the destination and the branch metrics of the trellis associated with its channel decoder for the ML combiner and also for the maximum ratio combiner (MRC), Cooperative-MRC (C-MRC) and the minimum mean square error (MMSE) combiner. I. MOTIVATIONS AND TECHNICAL BACKGROUND We consider orthogonal relay channels for which orthogonality is implemented in frequency [1]. Since the source-destination channel is assumed to be orthogonal to the relay-destination channel the destination receives two distinct signals. In order to maintain the receiver complexity at a low level, the destination is imposed to combine the received signals before applying channel decoding. The relay is assumed to implement the decode-andforward (DF) protocol. We have at least two motivations for this choice. First, in contrast with the well-known amplify-andforward (AF) protocol, it can be implemented in a digital relay transceiver. More importantly, whereas the AF protocol imposes the source-relay channel to have the same bandwidth as the relay-destination channel, the DF protocol offers some degrees of freedom in this respect. This is a critical point when the cooperative network has to be designed from the association of two existing networks. For instance, if one wants to increase the performance of a Digital Video Broadcasting (DVB) receiver or reach some uncovered indoor areas, a possible solution is to use cell phones, say Universal Mobile Telecommunications System (UMTS) cell phones as relaying nodes. The problem is that DVB signals use a 20 MHz bandwidth (source-relay channel) while UMTS signals have only a bandwidth of 5 MHz (relay-destination channel). The AF protocol cannot be used here. But the DF protocol can be used, for instance, by adapting the modulation of the cooperative signal to the available bandwidth. In this case, the destination has to combine two signals with different modulations. In this context, one of the issues that needs to be addressed is the design of the combiner. A conventional MRC cannot be used for combining signals with different modulations (except for special cases of modulations). Even if the modulations at the source and relay are identical, the MRC can severely degrade the receiver performance because it does not compensate for the decoding noise introduced by the relay [2]–[6]. This is why the authors of [2][4] proposed a maximum likelihood detector (MLD) for combining two BPSK-modulated signals coming from the source and relay. The authors of [6] proposed an improved MRC called C-MRC which aims at maximizing receive diversity. The authors of [3] proposed a linear combiner for which the weights are tuned to minimize the raw bit error rate (BER). The main issue is that one is not always able to explicit the raw BER as a function of the combiner weights whereas the likelihood calculation is more systematic. Additionally, when some a priori knowledge is available, the ML metric can be used to calculate an a posteriori probability (APP). In the context of orthogonal N−relay channels the authors of [4] derived two new combiners : 16 février 2009 DRAFT ha l-0 03 61 51 8, v er si on 1 16 F eb 2 00 9 Author manuscript, published in "EURASIP Journal on Wireless Communications and Networking 2008, Article ID 287320, 4 pages (2008)" DOI : 10.1155/2008/287320