Cascaded orthogonal space–time block codes for wireless multi-hop relay networks

Vaze and Heath EURASIP Journal on Wireless Communications and Networking 2013, 2013:113 http://jwcn.eurasipjournals.com/content/2013/1/113 R ESEA R CH Open Access Cascaded orthogonal space–time block codes for wireless multi-hop relay networks Rahul Vaze1* and Robert W Heath Jr.2 Abstract Distributed space–time block coding is a diversity technique to mitigate the effects of fading in multi-hop wireless networks, where multiple relay stages are used by a source to communicate with its destination. This article proposes a new distributed space–time block code called the cascaded orthogonal space–time block code (COSTBC) for the case where the source and destination are equipped with multiple antennas and each relay stage has one or more multiple antenna relays. Each relay stage is assumed to have receive channel state information (CSI) for all the channels from the source and all relays from previous stages to itself, while the destination is assumed to have receive CSI for all the channels. To construct the COSTBC, multiple orthogonal space–time block codes (OSTBCs) are used in cascade by the source and each relay stages. In the COSTBC, each relay stage separates the constellation symbols of the OSTBC sent by the preceding relay stage using its CSI, and then transmits another OSTBC to the next relay stage. COSTBCs are shown to achieve the maximum diversity gain in a multi-hop wireless network with linear decoding complexity thanks to the connection to OSTBCs. Several explicit constructions of COSTBCs are also provided, and their performance is simulated in different relay configurations. 1 Introduction Distributed space–time block coding (DSTBC) is a technique to improve reliability in relay-assisted communication, where one or more relays help the source to communicate with its destination. Relay-assisted communication is likely to occur in large wireless networks, such as ad-hoc or sensor network, where the destination is possibly out of the source’s communication range. Relay-assisted communication is also used in a cellular wireless networks to improve the performance of cell edge users, and has been incorporated in modern wireless standards such as IEEE 802.16j, and 3GPP LTE Advanced. In DSTBCs, relay antennas are used together with the source antennas in a distributed manner to transmit a space–time block code (STBC) [1] to the destination. By introducing redundancy in space and time, DSTBCs increase the reliability of the communication by increasing the diversity gain, defined as the negative of the exponent of the signal-to-noise ratio (SNR) in the pairwise error probability expression at high SNR [1]. *Correspondence: 1 School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai 400005, India Full list of author information is available at the end of the article In prior work, maximum diversity gain achieving DSTBC constructions have been proposed for the twohop network [2-21], and for the multi-hop network [22-24]. Even though these DSTBC constructions [2-24] achieve the maximum diversity gain, the decoding complexity of most of them, except [14-21], is very high, thereby limiting their use in practical deployment. Construction of DSTBCs with low decoding complexity is practically important as highlighted by the fact that the Alamouti code is the most practically used code not only because it achieves the maximum diversity gain, but also because it requires minimum decoding complexity. Moreover, the DSTBC constructions with low decoding complexity [14-21] are limited to two-hop network with single antenna equipped source, destination, and the relay nodes. In this article, we design maximum diversity gain achieving DSTBCs with low-decoding complexity for a multi-hop wireless network where the source, the destination, and the relay nodes are equipped with multiple antennas. In the proposed DSTBC, called the cascaded orthogonal space–time block code (COSTBC), an orthogonal space-time code (OSTBC) [25] is used by the source, and subsequently by each relay stage to communicate with its adjacent relay stage. OSTBCs are considered because © 2013 Vaze and Heath; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Vaze and Heath EURASIP Journal on Wireless Communications and Networking 2013, 2013:113 http://jwcn.eurasipjournals.com/content/2013/1/113 of their single symbol decodable property [25,26], i.e., with the maximum likelihood decoding each constellation symbol of the OSTBC can be decoded independently of other constellation symbols. We assume that each relay has receive channel state information (CSI) for all the channels from the source to itself, while the destination is assumed to have receive CSI for all the channels. With COSTBCs, in the first time slot, the source transmits an OSTBC to the first relay stage. Using the orthogonality property of the OSTBC and the available CSI, each relay of the first relay stage separates the different OSTBC constellation symbols from the received signal, and transmits a codeword vector in the next time slot, such that the matrix obtained by stacking all the codeword vectors transmitted by the different relays of the first relay stage is an OSTBC. These operations are repeated by subsequent relay stages. With COSTBCs, no signal is decoded at any of the relays, therefore COSTBC construction with single antenna relays is equivalent to COSTBC construction with multiple antenna relays. Thus, without loss of generality, in this article, we only consider COSTBC construction for single antenna relays. We note that for the code construction each relay is required to have receive CSI for all the channels from the source and all relays from previous stages to itself, while the destination is assumed to have receive CSI for all the channels. 1.1 Our contributions • We show that COSTBCs achieve the maximum diversity gain in a multi-hop wireless network when each symbol of the code is decoded independently (non- maximum-likelihood decoding), resulting in linear decoding complexity similar to single symbol decodable codes. • We prove that for a two-hop network and when the destination has a single antenna, by adding channel coefficient-dependent noise terms to the received signals, COSTBCs have the single symbol decodable property for any number of source and relay antennas. Thus, by paying a penalty in terms of coding gain because of extra noise, COSTBCs provide significant decoding complexity gain. A part of this article has been presented at [27,28]. Due to space limitation, the studies [27,28] contain only the results of this article without any proofs. In this article, detailed proofs of the results, together with explicit code construction, and some simulation resul (...truncated)