Fundamental Properties of Wireless Relays and Their Channel Estimation
A wireless relay system involves at least three nodes: a source node, a relay node, and a destination node. The relay node assists the transmission of information from the source to the destination. The relay channels include all channels between these nodes.
Several relay processing strategies have been proposed in wireless relay channel. Basically, different strategies usually require different complexity and possess different performance. Two main strategies are amplify-and-forward (AF) strategy and decode-and-forward (DF) strategy. In AF strategy, the relay node simply amplifies the received signal and forwards it directly without decoding the messages. In DF strategy, the relay node decodes the messages from the received signals and regenerates new signals which are sent to the destination subsequently.
As the transmission protocol of the relay channel is quite different from the traditional point-to-point transmission, the corresponding physical layer techniques are greatly modified, especially the channel estimation which is used to obtain the channel state information required for physical layer designs including power allocation (Chen et al. 2017; Ma et al. 2014), precoding design (Cirik et al. 2014; Xu and Hua 2011; Yu and Hua 2010; Rong and Hua 2009; Rong et al. 2009), etc. In wireless relay channel, we generally need to estimate the channels of two-hop transmissions, i.e., from the source to the relay and from the relay to the destination. Lots of new and challenging problems are introduced. In this article, we aim to provide a brief review of the channel estimation in wireless relay channel.
According to transmission protocol, the two-hop channel estimation of wireless relay channel can be performed using the training signals received at the relay and the destination. If the relay node can perform the channel estimation and can transmit the training sequences, the two-hop channel estimation can be decoupled. For example, in the one-way relay channel, the first hop channel, i.e., the channel from the source S to the relay R, can be estimated at the relay node and the second hop channel, i.e., the channel from the relay R to the destination D, can be estimated at the destination node D separately. In this case, the overall channel estimation problem simply reduces to the two point-to-point channel estimations. In the two-way relay channel, we cannot directly decouple the two-hop channel estimation into two point-to-point channel estimation problems as it involves four independent channels. In this case, in the first hop, the channel can be considered as a multiple access channel (MAC) where received training signal at the relay node is used to estimate the channels from the source S1 to the relay node R and from the source S2 to the relay node R. While in the second hop, the channel can be treated as a broadcasting (BC) channel where the single training sequence sending from the relay node is received at the destination nodes and is then utilized to estimate the channels from the relay node R to two destination nodes S1 and S2.
In another scenario, if the relay node cannot perform channel estimation or send training sequence, the channel estimation must be conducted at the destination nodes and corresponding channel estimation problem becomes relatively more complicated. Under this setup, besides estimating the individual channels of two-hop transmission, estimating the combined channels, i.e., the cascade of two-hop channels, is an efficient way to simplify the channel estimation problems. The following brief review of the channel estimation in wireless relay channel is given from four classifications: single-antenna single-carrier case, single-antenna multi-carrier case, multi-antenna single-carrier case, and multi-antenna multi-carrier case.
Single-Antenna Single-Carrier Case
Single-Antenna Multi-Carrier Case
Regarding the single-antenna and multi-carrier two-way relay channel, the channel estimation was studied in the framework of OFDM modulation in Gao et al. (2009a). Different from Gao et al. (2011), the authors assumed that the training sequences were only transmitted from two sources while no training sequence was superposed at the relay node. Two estimation schemes, i.e., block-based and pilot-tone-based, were proposed to estimate the cascaded source-relay-destination channel and the individual channels, respectively. The block-based estimation scheme uses all carriers in one or more OFDM blocks for channel estimation and generally applies to a scenario where the training sequence is long enough. The pilot-tone estimation scheme uses several pilots residing in one OFDM block to estimate the channel and applies to the scenario with a length-limited training sequence. The estimation ambiguities of two schemes were further analyzed. In specific, the authors showed that when the length of training sequence is larger than a threshold, only the sign ambiguity can be introduced and it does not affect the finally data decoding.
Multi-Antenna Single-Carrier Case
When considering multiple antennas at each node, the channel estimation of single-carrier one-way relay channel was investigated in Rong et al. (2012) and Kong and Hua (2011). The challenge of estimating the multi-input multi-output (MIMO) channels lies in the fact that the estimation variables become unknown matrices, while not the unknown values as in the single-antenna case. In Rong et al. (2012), the MIMO channels in source-relay-destination link and the MIMO channel in direct link were estimated without knowledge of the channel statistical information. In particular, the MIMO channel in direct link was estimated using LS criterion. Regarding the source-relay-destination link, according to the parallel factor (PARAFAC) analysis, the bilinear alternating least-squares (BALS) algorithm was proposed to obtain individual MIMO channels for source-relay link and relay-destination link. It was shown that with a mild length of training sequence, the MIMO channel matrices of two hops can be estimated up to permutation and scaling ambiguities. Moreover, the authors proposed to exploit the knowledge of the relay factors to remove the permutation ambiguity. In Kong and Hua (2011), the authors assumed that the statistical channel information was known in prior, and then the linear MMSE (LMMSE) estimation method was proposed to estimate the MIMO channels. To estimate the individual MIMO channels in each hop of the source-relay-destination link, the authors proposed a two-step estimation strategy where in the first step, the MIMO relay-destination channel is estimated assuming that the relay node is able to transmit training sequences. With the estimated MIMO relay-destination channel, the MIMO source-relay channel is then estimated at the destination node utilizing the training sequence sent from the source. For the first step, the optimal structure of relay training sequence matrix was derived according to the statistical information of the relay-destination channel. While for the second step, an algorithm was developed to compute the optimal training sequence matrix used at the source and the optimal precoding matrix used at the relay.
Later on, the channel estimation of the MIMO single-carrier two-way relay channel was studied in Wang et al. (2015). Similar to Kong and Hua (2011), the authors assumed that the statistical channel information was known in prior under a Kronecker-correlation model. Additionally, the MIMO channels were estimated in a colored noise environment by considering the impact of the antenna correlation and the interference from neighboring users. To estimate each individual MIMO channel, the authors proposed to decompose the bidirectional transmission of two-way relay channel into two phases, i.e., MAC phase and the BC phase. The optimal LMMSE estimators were derived for each phase. Two iterative training design algorithms were further proposed to obtain the training sequences for the general conditions and they were verified to produce training sequences achieving near optimal channel estimation performance. For certain specific practical scenarios where the covariance matrices of the channel or disturbances are of particular structures, the optimal training sequence design guidelines were provided. To assess the estimation performance, the relationship between the estimation performance and the length of training sequences were established, which showed that when the training sequence length is shorter than the threshold, a lower bound of estimation performance exists no matter how to increase the powers.
Multi-Antenna Multi-Carrier Case
The MIMO channel estimation was extended to multi-carrier case for two-way relay channel in Kang et al. (2017). Instead of estimating the individual channels, the authors in this study proposed to estimate the convolution of two MIMO individual channels using the self-interfering link and information-bearing link under the LMMSE criterion. The training sequences were optimized with an aim to minimize the total MSE under the power constraints at the sources and the relay. To obtain the optimal training sequences, the authors derived optimal structure which then converted the training design optimization problem into a tractable convex form.
Wireless relay is one of the fundamental techniques in cellular wireless communications. It can be efficiently used to extend the wireless coverage and enhance the network throughput in harsh environments with low economy cost.