A Distributed Polarizing Transmission System for Frequency Selective Fading Channels
Tinuola Olayinka Coker · IOSR Journal of Computer Engineering · 2013
Motivated by Arikan's channel polarization that shows the occurrence of capacity-achieving code sequences, we address the scheme design issues by switching to polarizing frequency selective fading channels while transmitting information symbols in a source-relay-destination MIMO-OFDM relay communication system.A simple polar-and-forward (PF) MIMO relay scheme, with source node polar coding and relay nodes polar coding, is proposed to provide an alternative solution for transmitting with higher reliability than the conventional decode-and-forward/amplify-and-forward (DF/AF) relay schemes.In the proposed scheme, OFDM modulator is implemented at source node, some simple operations, namely time reversion, complex conjugation and polarization, are implemented at relay nodes, and the cyclic prefix (CP) removal is performed at destination node.It is divided into two symmetrical polarizing relay systems, i.e., the down-polarizing system and the up-polarizing system, which result in different capacities for the polar system.We analyze the bit error rate (BER) performance with the fixed polar system equipped with four OFDM blocks, which is an idea approach to select signal sequences that tend to polarize in terms of the reliability under certain combining and splitting the transmitted OFDMs in the frequency selective fading (FSF) channels.The polar system has a salient recursiveness feature, and thus the transmitted information signals embedded in the polar code can be decoded with a low-complexity decoder.scaled signals without any attempt to decode the original information [21], [22].In the light of superiority of these relay strategies with the availability of CSI, we consider the coding design of the MIMO-OFDM relay system for the FSF channels with the fixed gain relaying scheme using the polar-and-forward (PF) relay technique, in which each relay node encodes and retransmits the partial signals with the fixed power constraint.A key feature of this scheme is that we do not require relays to decode.Only a simple processing operation is done at each relay, which makes the transmission much simple and hence can avoid imposing bottlenecks on the data rate.Recently, significant efforts have been related to the increasing capacity [23] or the optimal design of the relay system [24] in terms of the DF/AF relay schemes based on a scenario equipped with single or multiple antennas.However, further improvement should be sought in these relay systems, in which the loss of the signal rate is boosted as the number of relay nodes along with antennas increases.While a key component relay design is to optimize the precoding of source and relay in benefits of multiple antennas and multiple OFDM symbols, how to design the MIMO-OFDM relay system to achieve high reliability with low-decoding complexity via a coding approach becomes a challenge.The problem with the previous relay system is the data rate loss as the number of relay nodes increases.This leads to the use of polar coding sequences in MIMO-OFDM system, where relay nodes are allowed to simultaneously transmit the same OFDM systems over the FSF channels.We consider a simple design of the relay system that achieves the fascinating symmetric capacity of the FSF channels based on polar coding with a successive interference cancellation (SIC) decoder at destination node, which is motivated by the fascinating Shanon's channel coding theorem [25].It is an extension of work where OFDM combining and splitting are used for recursive code construction with the SIC decoding, which are essential characters of the polar coding sequences [1]-[6].This is an idea approach to construct code sequences as combining and splitting OFDM for the FSF channels to increase its reliability.Furthermore, we establish an analytical framework that illustrates the potential bit error rate (BER) performance to be achieved from the polar MIMO-OFDM relay system.We argue that the present system may increase the symmetric capacity under a low computation complexity of the SIC decoding due to the fact that a large number OFDM symbols may be equipped for the polarizing FSF channels that tend to polarize under certain OFDM combining and splitting operations.This paper is or ganized as follows.In Section II, we describe the polar MIMO relay system with two switching communication model, the down-polarizing system and the up-polarizing system.In Section III, we systematically study the design of an simple PF scheme with space-time-frequency (STF) transmission for down-polarizing and up-polarizing FSF channels.Some simulation results are also depicted in order to show the BER performance behavior and robustness of this polar MIMO-OFDM relay system.Finally, conclusions are drawn in Section IV. a) Down-polarizing OFDM Blocks for Distributed System b) Up-polarizing OFDM blocks for Distributed System