An example of the MIMO relay channel in a cellular system where all nodes are equipped with multiple antennas. The mobile station (MS) is located near the cell boundary thus it receives weak direct signals from the base station (BS). A relay station (RS) is used to aid the communication between the BS and the MS.
MIMO Relay Communication
Multiple-input multiple-output (MIMO) relay systems provide the high capacity of MIMO communication with the coverage extension capability of relay transmission. Current and future generations of commercial wireless systems, such as the Third Generation Partnership Project’s Long Term Evolution-Advanced (3GPP LTE-Advanced) and the Institute of Electrical and Electronic Engineers’s (IEEE) 802.16m, will use MIMO relays for providing better coverage for high data rate services. In the future cellular deployments, MIMO relays will be joined by distributed antenna systems and femtocells creating a truly heterogenous network.
The extension of prior results either for the point-to-point MIMO channel or for the single-antenna relay channel to the MIMO relay channel is not straightforward. For example, in the point-to-point MIMO channel the source messages are transmitted directly from the source to the relay. In the MIMO relay channel, however, on the way to the destination, source messages have to travel through three channels, which are combined both in parallel and in serial. Compared to the basic single-antenna relay channel, the MIMO relay channel introduces additional degrees of freedom that make it possible to perform more sophisticated encoding and decoding techniques, thus improving system performance.
My research group has been working on several aspects of the MIMO relay channel. From an information theoretic approach, we have derived bounds on the MIMO relay channel. Note that the exact capacity of the general relay channel is still unknown. From a communication theoretic and signal processing perspective, we have developed algorithms for designing relays, e.g. for practical adaptive transmission and for multiuser transmission.
Several of our recent results and publications are summarized below.
C. Lo, S. Vishwanath and R. W. Heath, Jr., “Rate Bounds For MIMO Relay Channels,” Journal of Communications and Networks, Special Issue on Wireless Cooperative Transmission and Its Applications, vol. 10, no. 2, pp. 194-203, June 2008.
This paper finds higher achievable rates for the full-duplex MIMO relay channel than the previous proposed lower bound by Wang et. al.. The key observation is that the MIMO relay channel allows for partial cooperation between the transmitter and the relay. In addition, the message from the source can be split into two parts, only one of which will be decoded and forwarded by the relay. Given knowledge of the individual links and the codebook the relay will use, the source has two methods for choosing the codebooks for the two parts of the message: i) superposition coding and ii) precoding. In superposition coding, the codebooks are chosen independently and then added together. In precoding, they are chosen jointly and then combined using dirty paper coding. The precoding method always outperforms the superposition coding method at the cost of higher complexity.
S. W. Peters and R. W. Heath, Jr., “Nonregenerative MIMO Relaying with Optimal Transmit Antenna Selection,” IEEE Signal Processing Letters, vol. 15, pp. 421-424, 2008.
This paper proposes a method for single stream transmission via transmit antenna selection for the MIMO amplify-and-forward relay channel. The proposed method allows us to choose the best single transmit antenna at the source and at the relay that maximizes the receive signal power at the destination, taking the relay into account. The proposed antenna selection method maximizes the spatial diversity gain. Compared to other proposed relaying strategies with feedback, this method is interesting since the analysis is tractable and the implementation is relatively simple.
K. T. Truong and R. W. Heath, Jr., “Multimode Antenna Selection for Nonregenerative MIMO Relay Systems,” IEEE Trans. on Signal Processing, vol. 58, no. 11, pp. 5845-5859, Nov. 2010.
This paper proposes and analyzes the algorithms for adapting the number of data streams in the MIMO amplify-and-forward relay channel to instantaneous channel conditions. We define an antenna selection mode of operation as the number of transmit antennas at the source, the substream-to-antenna mapping at the source, the number of transmit antennas at the relay, and the substream-to-antenna mapping at the relay. A number of multimode antenna selection algorithms are developed to choose the mode that is most likely to deliver the lowest vector symbol error rate assuming the overall data rate is fixed. In addition, we derive expressions that show how the condition number of the direct and relay channels, and hence the spatial characteristics of the constituent channels, influences the choice of adaptation strategies.
C. B. Chae, T. Tang, R. W. Heath, Jr., and S. Cho, “MIMO Relaying with Linear Processing for Multiuser Transmission in Fixed Relay Networks,” IEEE Trans. on Signal Processing, vol. 56, no. 2, pp. 727-738, Feb. 2008.
This paper considers a particular type of relay channel called the multiuser MIMO relay. The idea is that MIMO is used to provide a high data rate backhaul link from the base station to the multiple antenna relay station. Then multiuser MIMO is used from the relay station to support multiple users. We propose upper and lower bounds on the sum of the achievable rates from the base station to the users assuming zero-forcing dirty paper coding at the base station and certain types of linear processing matrix at the relay. We also propose a more implementable system design where the base station deploys Tomlinson-Harashima precoding and adaptive user selection (i.e. the number of transmit streams and the QAM modulation are adapted to channel conditions). This proposed strategy performs very close to the derived sum-rate upper bound corresponding to the use of a multiple-antenna decode-and-forward relay.
We have been fortunate to have several outstanding sponsors of our work including the National Science Foundation, the Office of Naval Research under grant number N00014-05-1-0169, Samsung Electronics, Semiconductor Research Corporation, and Huawei Technologies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the aforementioned sponsor.