Telecommun Syst DOI 10.1007/s11235-017-0278-3 On the diversity analysis of symbol remapping in cooperative BICM–OFDM scheme for frequency selective Rayleigh fading channels Ali Jamshidi 1 · Maede Zolanvari 1 © Springer Science+Business Media New York 2017 Abstract In this paper, diversity analysis of a symbol remapping scheme in cooperative systems is considered. We employ Bit Interleaved Coded Modulation and Orthogonal Frequency Division Multiplexing, which are widely used at wireless networks. In this paper, at the cooperative scheme, relays operate in DF mode and the effect of their erroneous detection will be considered. We present a closed form of the asymptotic worst-case pairwise error probability at the des- tination for our proposed scheme. It will be shown that this scheme exploits full spatial and frequency diversities. After that, we work on designing a new precoder matrix. Moreover, we propose two new subcarrier allocations for the proposed scheme. All new methods have been suggested to achieve the available diversities with a better performance than current state of the art. Finally, the simulation results reveal the ana- lytical derivations and confirm the obtained diversity gain of the proposed systems. Keywords Bit-interleaved coded modulation · Orthogonal frequency division multiplexing · Cooperative commu- nications · Modulated symbol remapping · Decode and forward 1 Introduction Channels in wireless systems suffer from severe attenuation caused by path loss and fading; therefore, the main objec- B Ali Jamshidi jamshidi@shirazu.ac.ir Maede Zolanvari maede-zolanvari@shirazu.ac.ir 1 Electrical and Computer Engineering School, Shiraz University, Shiraz, Iran tive for current research is the technique which increases its reliability and capacity. One of the most effective solutions to combat this negative effect is the use of diversity. Regard- ing the spatial diversity exploited by multiple antennas in multiple input multiple output (MIMO) systems, cooperative scheme has an increasing interest in which single-antenna users in multiple-user environment can share their own antenna and build up a virtual MIMO system [1–3]. Thus, these kind of systems can exploit the advantages of multi- ple paths between the source node and the destination node with no need to multiple physical antennas which results in complexity [4, 5]. Most of cooperation relaying schemes employs AF (Amplify-Forward) or DF (Decode-Forward) strategy. Each scheme has its own advantages over the other. Although, DF relaying does not amplify the additive noise, it does not achieve the performance of AF relaying [6–8]. This reason is due to the possible decision errors at relays. Therefore, using cooperative maximum-ratio combining (C-MRC) pro- posed in [9] can fairly improve the error rate performance in cooperative DF relaying protocols, as was shown in [10]. On the other hand, as it has been declared in [11], the capacity of BICM scheme proposed by Zehavi in [12], along with Gray labeling is close to the capacity of multilevel codes (MLC) [13]. Furthermore, the purpose of BICM by using interleaver is to break the correlation of fading channels; therefore, the errors within a codeword appear to be inde- pendent and subsequently gain the coding diversity at symbol level. Thus, BICM can be used as a bandwidth efficient tech- nique to combat the impairments of fading channels. Symbol mapping in systems using BICM has a significant impact on the system’s error performance. Finding the most efficient mapping and demapping scheme in the BICM technique has been suggested in [14, 15]. 123