Part IV MULTIPLE ACCESS AND ADVANCED TRANSCEIVER SCHEMES 363
22.3 Relaying with Multiple, Parallel Relays
In many situations, more than one relay is available for forwarding the information. In that case, a cooperation between the different relays can be used to greatly enhance the performance of the relaying scheme, in particular in fading channels. Essentially, the multiple relays provide diversity paths that bring better robustness with respect to fading and interference. At the same time, the cooperation between the relays necessitates the exchange of Channel State Information (CSI) and control information. There are thus a number of different schemes, which trade off the overhead with the system performance in different ways.
Also for the arrangement with multiple relays, various transmission schemes do exist – AF, DF, CF, with the various protocols discussed in the previous section. However, to keep the discussion focused, we restrict the discussion to DF (in most cases, restricted to MDF) with semi-duplex relays.
In the current section, we will only deal with two-hop networks, since in this case the relaying problem can be viewed as a physical-layer problem. Networks with more hops require, in addition, routing, and are treated in subsequent sections.
Figure 22.4 shows the fundamental setup that we consider in this section. Transmission occurs in two phases: in phase 1, the source broadcasts the information. This phase takes advantage of the broadcast effect, i.e., the signal arrives at several relays (possibly with different strengths), even though only a single node (i.e., the source) transmits. In the second phase, one or more of the relays forward the information to the destination. We see that this second phase strongly resembles a smart-antenna system, specifically the transmission from a multiantenna TX to a single-antenna destination – the main difference being that the antennas are distributed over a larger area in space.
This analogy to multiantenna systems will be helpful in the discussion below.
Phase 1 Phase 2
Source broadcasts
Destination Source
Destination
Figure 22.4 Two-phase transmission with parallel relays.
For phase 1, we always assume that thek-th relay knows the channel from the source to it (i.e., CSI at the Receiver (CSIR), is available). CSI at the Transmitter (CSIT) is only useful if the source can either adapt its power or its transmission time, in accordance to the channel states. For phase 2, we again assume CSIR (i.e., the destination knows the channels between the k-th relay and the
destination). However, we distinguish different cases with respect to knowledge of CSIT, i.e., CSI that is available at the relays. Depending on the type of CSIT, different transmission schemes can be used:
• Full CSIT available: relays know both amplitude and phase of the channel to the destination. In that case, “virtual beamforming,” similar to maximum-ratio transmission in a multiple-antenna system, can be used. This method ensures the maximum SNR at the RX for a given sum power expenditure at the relays. This case will be discussed in Section 22.3.2.
• Amplitude CSIT available: in that case, the relays know the amplitude (strength) of the channel to the destination, but not the phase. In this case, the best strategy (for a sum-power constraint) is to select a single relay that provides the best transmission quality (see Section 22.3.1).
• No CSIT available: in this case, the relays can transmit Space–Time (ST) encoded versions of the data packet – they act like antennas in a transmit-diversity system without CSIT (see Section 22.3.3). Alternatively, the relays can send out incremental-redundancy encoded bits of the same codeword (see Section 22.3.4). Note that for a sum-power constraint, the SNR for space–time codes is worse than for relay selection: transmit diversity provides an effective channel whose SNR is theaverageof the individual relay-destination channels, while relay selection provides a channel with an SNR that is themaximum of that of the individual channels.
• Average CSIT available: in this case, only the mean channel gain but not the instantaneous realization is available. This case is interesting because average CSIT can be acquired much more easily than instantaneous CSIT, particularly in fast-varying channels. Modifications of the no-CSIT schemes can be used.
22.3.1 Relay Selection
In relay selection, we simply pick the “best” of all the available relays, and then perform relaying the same way as described in Section 22.2. This approach sounds deceptively simple; the challenges are (i) defining what we mean by “best relay,” (ii) actually finding the relay for a given set of channel states.
Let us first turn to the question of defining a criterion for the “best” relay. We have to distinguish two cases: if the source has fixed transmit power and data rate, (i.e., modulation format and coding of the packet are fixed), then we cannot influence which relay will receive the packet correctly during transmission phase 1; rather, we simply consider the set of relays that do get the packet, and select the one for forwarding that has the strongest channel to the destination.
If the source can adapt to the channels, then we can make sure that a specific relay (which is selected a priori as the one that will do the forwarding) gets the message in phase 1. Choosing this relay requires a balancing between the source-relay and relay-destination channel strengths: in MDF, where the rate is given by Eq. (22.1), we should aim to avoid bottlenecks, and thus pick the relay that provides the best
ηk=min
|hs,k|2,|hk,d|2 (22.15) An alternative criterion considers a “smoothed-out” version of this criterion
ηk= 2
1
|hs,k|2 +|hk,d1|2
(22.16) It is often assumed that a central control node knows all the |hs,k|2 and |hk,d|2. In practice, this would require considerable signaling overhead, and is therefore undesirable. It is therefore preferable to use algorithms similar to the ones that used to control multiple access for packet radio systems (see Chapter 17), in a distributed manner:
Relaying, Multi-Hop, and Cooperative Communications 531
1. In a first step, the destination sends out a brief broadcast signal that allows the relays to determine the|hk,d|2(assuming channel reciprocity, see Section 20.1).
2. Next, the source sends the data packet, as well as a “Clear To Send” (CTS) message after it is finished. Each relay tries to receive the packet, and also determines its|hs,k|2,and from that, theηi,according to one of the criteria Eq. (22.15) or (22.16).
3. Each relay starts a timer with an initial value Ktimer/ηk (where Ktimer is a suitably chosen constant) and counts down, while listening for possible on-air signals from the other relays.
When the timer reaches 0, the relay starts to transmit – unless another relay has already started to transmit (and thus occupies the channel).
Clearly, the relay with the “best” channel (highest ηk)is the first – and therefore only – relay node to transmit. In practical networks, the performance is not ideal, since a second node might start to transmit between the time that the first node transmits and the time that signal actually arrives at the second node (again, compare Chapter 17), but such collisions can be resolved by repeating step 3 with differentKtimer.
Relay selection performs remarkably well, and provides the same diversity order as other, more complicated relaying schemes discussed below. This is analogous to antenna selection (see Chapter 13): antenna selection provides the same slope of the Bit Error Rate (BER) vs. SNR curve (i.e., diversity order) as the (optimum) MRC. ForK relays, the outage probability can be computed for the case of Rayleigh fading on all links as
P r[I < Rth]= K k=1
1−exp
−22Rth−1 P /Pn
1 γ2s,k + 1
γ2k,d
(22.17) whereγ2s,kandγ2k,dare the mean channel gains of the source-relay and relay-destination channels.
22.3.2 Distributed Beamforming
This protocol consists of two phases: in phase 1 the source broadcasts the information and a setD (with size|D|)receives the packet in good order. For an MDF protocol, the optimal transmission coefficient at each selected relayk in phase 2 can then be shown to be proportional to
h∗k,d (
k∈D|hk,d|2)1/2 (22.18)
once the CSIT at the relays is available. The|D|nodes cooperate, i.e., transmit coherently, to send data to the destination. This is similar to beamforming or maximum ratio transmission in transmit diversity systems.
In the case that the relays are using AF, the optimum gain applied at relayk is wk=KAF |hsk||hkd|
1+Ps|hsk|2+Pk|hkd|2 h∗sk
|hsk| h∗kd
|hkd| (22.19)
where the constantKAFis chosen such that the total power constraint
k
|wk|2(1+Ps|hsk|2)=Pr is met. The power on thek-th relay is
Pk∝ |hsk|2|hkd|2
Ps|hsk|2+1
1+Ps|hsk|2+Pk|hkd|2 2 (22.20)
Obtaining the CSIT at the relays is nontrivial: not only does each relay need to know its channel to the destination but it also needs to know the sum of the channel gains from all the relays that will be active in the forwarding of the data (i.e., the denominator in Eq. 22.18). This can be implemented through consecutive transmission of training sequences (pilots) from the relays, followed by a feedback from the destination.
The situation is, again, more complicated if the source can adjust its power, because then it determines the set of possible active relays,D.This leads to a tradeoff between the two phases in the relaying: if the source expends little energy on the broadcast, then|D| is too small, and the diversity order available in phase 2 is low – in other words, there is a risk that all the relays that received the packet have a bad channel to the destination, and thus have to expend a large amount of power to get the packet to the destination. On the other hand, spending too much energy on the broadcast is wasteful. An exact optimization of the best power allocation is somewhat complicated, but as a rule of thumb,|D|should be 3.
The above discussion assumes that the various relay nodes can co-phase their transmit signals in such a way that they superpose constructively at the intended destination. This is a very difficult endeavor in practice, since the relay nodes are not colocated, yet still have to be phase synchronous (in addition to being frequency and time synchronous). Typically, one node in the network would work as a master that periodically sends out synchronization signals and forces all other nodes to adapt their frequency and phase to this synchronization signal. Adjusting for the phase shift created by the runtime between nodes has to be done on a link-by-link case.
An alternative way of dealing with the problem of phase adjustment is the use of random beamforming (compare Section 20.1). If no special measures are taken (i.e., no specific phase adjustment), the beams created by the relays point into random directions, and by changing the relative phases of the nodes, the main direction of the beams changes. In the spirit of opportunistic beamforming, a destination node that finds itself in the main lobe of the beam sends a feedback signal, and asks for the relays to send payload data intended for this node.
22.3.3 Transmission on Orthogonal Channels
When CSI is not available at the TX, one possible solution is to have each relay transmit on an orthogonal channel. This clearly eliminates the interference between the different relay channels;
however, it also leads to a drastic reduction of the spectral efficiency. In particular, we consider a DDF scheme where every relay has a reserved channel – whether it can decode the message or not. Its capacity (or more precisely, the mutual information using Gaussian codebooks) is
I= 1 K+1log
1+γs,d+
k∈D
γk,d
(22.21) whereDis the set of the relays that can decode the message from a particular source. When all links are Rayleigh fading, the outage probability conditioned on a particular decoding set for this scheme is for high SNR
Pr[I < Rth|D]∼
2(K+1)Rth−1|D(s)|+1 1 γs,d
k∈D
1 γk,d
1
[|D| +1]! (22.22) The probability of obtaining a particular decoding set is given by
Pr[D]∼
2(K+1)Rth−1 K−|D(s)|
k∈D
1
γs,k (22.23)
Relaying, Multi-Hop, and Cooperative Communications 533
The overall outage probability is then Eq. (22.22) unconditioned by Eq. (22.23); this expression can be bounded by
2(K+1)Rth−1 γlb
K+1
k∈D
1
[|D| +1]! Pr[I < Rth]
2(K+1)Rth−1 γub
K+1
k∈D
1 [|D| +1]!
(22.24) where
1/γlbk =min{1/γs,k,1/γk,d}1/γubk =max{1/γs,k,1/γk,d}γlbs =γubs =γs,d (22.25) andγlb is the geometric mean of theγlbk, k=1...K+1, and similarly forγub. To again draw an analogy with multiple-antenna systems, transmission on orthogonal channels can be compared to antenna cycling, where only one antenna element is used (for one particular message) at each time.
We now turn to the situation where there are multiple nodes that all act as sources, as well as relays and which can transmit at different frequencies as well as times. Consider the situation depicted in Figure 22.5. Also in that case, each node is transmitting information from a particular source only for 1/(K+1) of the available time. In other words, the spectral efficiency is not improved compared to the situation discussed above.
Phase I
1 Transmits 2 Repeats 1 1 Repeats 2 1 Repeats 3
1 Repeats K +1 2 Repeats K +1 Time 2 Repeats 3 3 Repeats 2
3 Repeats 1 K +1 Repeats 1
K +1 Repeats 2 K +1 Repeats 3
K Repeats K +1 Phase II
2 Transmits 3 Transmits
Frequency
K +1 Transmits
...
...
...
...
... ...
... ... ...
Figure 22.5 Multiplexing of multiple signals on multiple relays.
Reproduced from Laneman and Wornell [2003]©IEEE.
22.3.4 Distributed Space–Time Coding
An alternative approach for the no-CSIT case is to have the relays use space–time codes during the transmission. Consider the following situation: in phase 1, the source sends the information to the relays. In phase 2, the relays now perform a space–time coded transmission to the destination.
In other words, each relay node acts as a “virtual antenna,” and sends out the signal that – in a Multiple Input Multiple Output MIMO setting – would be sent out by one of antenna elements of the transmit antenna array. For example, if two relays are used, then the used space–time code could be an Alamouti code. That means that two symbols, c1 and c2, are transmitted from the two relays at time instant 1:
s1= 1
√2 c1
c2
. (22.26)
wheresis the vector containing the symbols sent from the relays. At the second time instant, the signal vector
s2= 1
√2 −c∗2
c∗1
(22.27)
is transmitted (compare Section 20.2). Of course, the communication protocol must have a means to assign to each relay which “antenna” it is, and therefore, which sequence of data(c1 −c2∗ ....) or (c2c∗1....) it should send out.
Since the Alamouti code is a rate-1 code, the spectral efficiency of the transmission is better than for the relaying on orthogonal channels, where the rate (during the second phase of the relaying) is only 1/2 (for the case of two relays). When using more relays, the spectral efficiency of relaying with orthogonal space–time codes decreases somewhat: for K >2, no rate-1 orthogonal space–time codes exist. ForK=3 or 4, the achievable rate decreases to 3/4. Still, this is much better than orthogonal relaying, where the rate decreases as 1/K.
A further practical problem arises from the fact that the number of participating relays changes, depending on how many relays are able to decode the message from the source. Fortunately, this does not impact the operation of distributed space–time codes significantly: if a relay does not receive a message from the source, it simply does not transmit (which for the RX looks like that particular “antenna” is in a deep fade). The decoding operation of the RX is therefore not impacted.
22.3.5 Coded Cooperation
In coded cooperation, relaying and error correction coding are integrated, leading to enhanced diver- sity. A data packet from a source is encoded with a Forward Error Correction FEC code (see Chapter 14), and different parts of the codewords are sent via two (or more) different paths in the network.
To give more details, let us consider the example of Figure 22.6. At node 1, a source data block is encoded with an FEC, and the resulting codeword is split up into two parts, with N1 and N2 bits, respectively. It is important that it is possible to reconstruct the source data from the firstN1
bits alone. For example, the FEC can be a rate 1/3 convolutional code, which is then punctured to result in a rate 2/3 code that is transmitted in the first N1 bits; the bits that are punctured out are transmitted in the secondN2 bits. A similar encoding and splitting is done for a different block of source data at node 2.
Now the transmission interval available for one block of source data is divided into two parts during the first interval, node 1 broadcasts the firstN1 bits. They are received by the destination, as well as by node 2. At the same time, node 2 transmits (on an orthogonal channel, e.g., a different frequency channel) its firstN1 bits. If node 1 can successfully decode the source word of node 2 (this is checked with a Cyclic Redundancy Check CRC), then it computes the second N2 bits associated with that source data of node 2 and transmits it in the second time interval. If it cannot decode successfully, then it sends the N2 bits associated with its own codeword. Node 2 behaves in a completely analogous way. Since there is no feedback between nodes 1 and 2, the four situations depicted in Figure 22.7 can arise. Summarizing, each node always sendsN1+N2
bits; if the channel between the two nodes is good, then part of the transmitted bits are helping a partner node; this is the case that we will consider in the following (the other case, where each node just transmits N1+N2 of its own data, is a regular coded Frequency Division Multiple Access (FDMA) transmission of two users to an RX, see Chapter 17).
Since the different parts of the codeword are transmitted from different locations, the transmission has a diversity order of 2 (if the two nodes 1 and 2 are sufficiently widely separated, they might pro- vide macrodiversity as well as microdiversity (see Chapter 13)). The diversity order is reflected in the asymptotic expressions for the outage probability. Assuming that all channels are Rayleigh fad- ing, and the channels from node 1 to node 2 and node 2 to node 1 are independent (as is usually the case in a frequency duplexing), the outage probability is approximated in the high-SNR regime by
Pr[I < Rth]= (22Rth−1)2
γA,dγA,B +Rthln(2)22Rth+1−22Rth+1
γA,dγB,d . (22.28)
For the case of reciprocal inter-user channels (i.e., if transmission from node A to node B and node B to node A is done on the same frequency channel, e.g., using Time Division Multiple
Relaying, Multi-Hop, and Cooperative Communications 535
Frame 1 N1
Frame 2 user 1 bits N2 user 2 bits
User 2 User 1
Base station
To TX
Puncture (N2) bits RCPC
CRC check Viterbi
decoder Partner
received Own
bits CRC RPPC
Coded, punctured to (N1) bits Punctured (N2) bits
No Yes N1 user 2 bits
Frame 1 Frame 2 N2 user 1 bits
Figure 22.6 Principle of coded cooperation. Solid (dashed) lines: bits associated with the payload user 1 (2) has generated.
Reproduced from Nosratinia et al. [2004]©IEEE.
Access (TDMA)), the outage probability is Pr[I < Rth]= (2Rth−1)(22Rth−1)
γA,dγA,B +Rthln(2)22Rth+1−22Rth+1
γA,dγB,d . (22.29) The transmission of the data packet for one particular user can be considered as DF relaying with incremental redundancy; this is more efficient than conventional DF, where the relay repeats the originally transmitted bits, as discussed in Section 22.2 above. This is also visible in Figure 22.8, which compares the block error rate of coded cooperation with rate 1/4 encoding to AF and DF with rate 1/2 encoding (i.e., all schemes have the same spectral efficiency).
22.3.6 Fountain Codes
The virtual-MIMO techniques described in the previous section suffer from a number of drawbacks, including the necessity to coordinate simultaneous transmissions to achieve cooperative gain, and comparatively low efficiency of the collaboration (RXs accumulate energy from the cooperating