Recovering the Half-Duplex Loss via Relay Selection

Multimedia Communications Laboratory
University of Texas at Dallas


Practical wireless relays work in the half-duplex mode, i.e., they cannot receive and transmit at the same time and frequency. This is due to the difficulties in separating the transmit and receive signals that are up to 110-120dB apart in power. This practical limitation implies that any source transmission time must be split into two parts: the part where the relay listens to the source, and the part where the relay transmits. In the second part, often the source is silent to avoid interfering with the relay, thus reducing the overall spectral efficiency of the system. Therefore, it has been often the case that while relaying improves the reliability of the system, it also involves a loss of transmission rate, which is sometimes referred to as half-duplex multiplexing loss.

This problem has been recognized and attempts have been made to address it. Among others, one may name [1] which employs non-orthogonal amplify and forward, and [2] which employs alternating between decode and forward relays. In both these schemes, the source transmits continually in order to avoid the half-duplex loss. The main drawback of these methods is severely limiting assumptions on the relay channels. In [1,2] it is assumed that the relays do not interfere with each other, i.e., the inter-relay channels must be absent for these methods to work. While both [1,2] have taken important steps in the right direction, the inter-relay channel assumption limits the practicality of the results and takes an important dimension of interest out of the problem. In the present work [3], two classes of methods are considered for salvaging the half-duplex loss while allowing a completely general channel between the source, relays, and destination.

The main ideas of this work involve relay selection (Figure 1). Our system model involves a source, multiple relays, and a destination. We consider two channel conditions: (a) there is a direct link between source-destination, or (b) destination cannot hear the source directly and two-hop transmission is required. Relay selection requires a small feedback channel from the destination to the relays, which is a less stringent assumption than pre-specified channel values (zero) between the relays.

Relay Selection

Figure 1. Relay Selection: picking the best from among the relays that have decoded the source signal.

Incremental Transmission with Relay Selection

The Incremental Transmission with Relay Selection (ITRS) algorithm is designed for the case where a direct link exists between the source and destination, and relays are there to assist the source-destination communication. The algorithm is simply as follows:

  1. The source transmits a packet.
  2. If the destination correctly decodes the message, it broadcasts an ACK and system returns to Step 1. Otherwise destination broadcasts a NACK.
  3. Upon receiving the NACK, the relays that successfully decoded the packet will declare their status via a one-bit packet (RTS - Request to Send) to the destination. The RTS packet includes a pilot.
  4. The destination estimates channel gains, picks the best transmitter from among successful relays and the source, and broadcasts the index of the best node.
  5. The best node will retransmit the packet. The destination combines its two received packets and decodes. If unsuccessful, destination is in outage.
The analysis in our work [3] calculates the outage and diversity of this method, showing that this method achieves the MISO upper bound on the diversity-multiplexing tradeoff (DMT), therefore in the sense of diversity and multiplexing it is optimal and cannot be improved upon. The DMT of this method is characterized in Figure 2 below.


Figure 2. DMT of the ITRS protocol for 8 relays, and comparison with dynamic decode-forward, distributed space-time codes, and direct transmission.

Multi-Hop Relay Selection

In the case where no direct link exists between the source and destination, the previously mentioned ARQ strategy does not work. Thus a new strategy is suggested, as outlined below:

  1. The source transmits alone in the first time slot. Then, in each time slot:
  2. Relays that successfully decode the source packet, declare their status to the destination via a one-bit RTS packet (which includes a pilot).
  3. The destination picks the best relay and broadcasts its index.
  4. The best relay retransmits its decoded packet, which the destination attempts to decode. At the same time, the source transmits a new packet.
  5. The source packet and relayed packet combine at other relays. Relays attempt to decode new source packet in the presence of interference. Then continue to Step 2.

To provide good multiplexing rates, the source must transmit continually. Each relay will try to listen to the incoming signals and use interference cancellation to deduce the new signals. Any relay that is transmitting will not be able to listen, thus it will not be able to use interference cancellation in the following transmission block. Our analysis shows that due to this effect, the overall diversity available in the system will successively reduce with time, therefore the system is periodically reset so that the accumulated interference can be flushed and all the relays can start fresh. The interested reader is referred to [3] for more details of the analysis.

Figure 3 shows the DMT curves for the MHRS protocol. While we omit the details of the analysis here, we mention that two relay decoding strategies are considered in our work [3]. One of them is successive cancellation (as mentioned above), and the other is joint decoding of incoming signals. The former is better at high multiplexing gains, while the latter is better at low multiplexing gains. The overall optimal strategy adapts according to the transmission rate. We also calculate an upper bound on the DMT of this method, and it is seen that the lower and upper bounds are tight at low multiplexing gains.


Figure 3. DMT of MHRS for a two-hop network with 10 relays.


  1. S. Yang and J.-C. Belfiore, ``Towards the optimal amplify-and-forward cooperative diversity scheme,'' IEEE Trans. Inform. Theory, vol. 53, no. 9, pp. 3114-3126, Sep. 2007.

  2. Yijia Fan, C. Wang, J. Thompson and H.V. Poor, ``Recovering Multiplexing Loss through Successive Relaying Using Repetition Coding'' IEEE Trans. Wireless Comm., vol. 6, no. 12, Dec. 2007, pp. 4484 - 4493.

  3. R. Tannious and A. Nosratinia, ``Spectrally efficient relay selection with limited feedback," IEEE Journal on Selected Areas in Communication, vol. 26, no. 8, Oct. 2008, pp. 1419-1428

Last modified 2008

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