Gsr = µdsd
drd
¶2
. (2.95)
2.3.2 Cooperation Types
In this section, we only consider a conventional single-relay-aided cooperative scenario, where two orthogonal phases are employed in order to avoid interference. These phases may be created by either in TDMA or FDMA.
• In phase 1, the SS broadcasts information to both the RS and the DS.
• In phase 2, the RS can assist the SS by forwarding or retransmitting the information to the DS.
Figure 2.30: Conventional single-relay-aided network.
Fig. 2.30 depicts a general relay channel, where the source transmits at a power of PS and the relay transmits at a power of PR. During the first phase, the source broadcasts its signal, x, to both the destination and to the relay. Hence, the signals ySD and ySR received at the destination and the relay, respectively, may be written as
ySR = p
PSGSRhSRx + nSR, (2.96)
ySD = p
PSGSDhSDx + nSD, (2.97)
where GSD and GSR are the path-loss-related-power gains detailed in Section 2.3.1, while hSR and hSD represent the coefficients of the SR and SD links’ fading processes associated with a variance of σf2, while nSD as well as nSR represent the AWGN noise associated with a zero mean and a variance of σ2n.
In phase 2, the relay forwards a processed version of the source’s signal to the destination, which may be modelled as
yRD =p
PRGRDhRDΦ(ySD) + nRD, (2.98) where the function Φ(·) defines the operation carried out at the relay. Again, hRD represents the coefficients of the RD link’s fading process having a variance of σf2, while nRD represents the AWGN noise having a zero mean and a variance of σn2.
2.3.2.1 Amplify-and-Forward
In AF relaying, the RS amplifies the signal received from the SS and forwards it to the DS, while aiming for eliminating the effects of the channel fades between the SS and the RS. This can be achieved
2.3.2. Cooperation Types 72 by simply scaling the received signal by a factor that is inversely proportional to the received power.
When the channel coefficients are available at the RS, the associated |hSD|-dependent gain may be expressed as [109]
β = 1
pPSGSR|hSD|2+ σn2. (2.99)
By contrast, when only the variance of the fading process is known at the RS, the |hSD|-independent gain may be expressed as [108]
β = 1
q
PSGSRσ2f+ σn2. (2.100)
Subsequently, the signal received at the DS during the second phase is given by yRD = βp
If the noise terms nSD and nRD are independent, then the equivalent noise nRD is a zero-mean, complex-valued Gaussian random variable having a variance of
σn20= (β2PRGRD|hRD|2+ 1)σ2n=
µ PRGRD|hRD|2 PSGSR|hSR|2+ σn2 + 1
¶
σ2n. (2.103) As seen in Eq. (2.103), the unwanted noise is also amplified at the relay, imposing a degraded performance at the destination, when compared to the corresponding co-located MIMO. According to [23,129], the relay should be close to the source in order to reduce the effects of noise amplification.
The destination receives two versions of the transmitted signal x through the SD and RD links.
As discussed in Section 2.2.1.1, various diversity combining techniques may be employed at the des-tination. If the channel knowledge is available at the destination, the optimal MRC technique may be employed for maximizing the overall signal-to-noise ratio. By contrast, the SC or EGC combining should be considered, when no channel information is available.
Given the knowledge of the channel coefficients hSD and hRD, the output of the MRC detector at the destination may be expressed as
y = w1ySD+ w2yRD, (2.104)
where w1 and w2 represent the weighting factor of the MRC. As optimized in [130], the weighting factors w1 and w2 are given by
w1 =
√PSh∗SD
σ2n w2= βPRPSh∗SRh∗RD
(β2PRGRD|hRD|2+ 1)σn2. (2.105) Therefore, the instantaneous SNR of the MRC’s output is expressed as
γ = γ1+ γ2, (2.106)
2.3.2. Cooperation Types 73 where we have
γ1 = |w1PSGSDhSD|2
|w1|2σn2 = PSGSD|hSD|2
σn2 (2.107)
γ2 = |w2β√ PS√
PRhSRhRD|2
|w2|2σn20 = 1 σn2
PSPRGSDGRD|hSR|2|hRD|2
PSGSD|hSR|2+ PRGRD|hRD|2+ σn2. (2.108)
2.3.2.2 Decode-and-Forward
In contrast to simply amplifying and forwarding data to the destination as in AF relaying, in DF relaying the relay fully decodes the received signal, before re-encoding and forwarding it to the desti-nation. Assuming that ˆx is the decoded signal at the relay, the signal received at the destination via the RD link may be expressed as
yRD =p
PRGRDhRDx + nˆ RD. (2.109) Consequently, given the knowledge of the channel coefficients hSD and hRD, the output of the MRC detector at the destination may be expressed as
y = w1ySD+ w2yRD, (2.110)
where we have
w1 =
√PSh∗SD
σ2n w2=
√PRh∗RD
σ2n . (2.111)
The the instantaneous SNR at the MRC output is obtained as
γ = γ1+ γ2, (2.112)
where we have
γ1 = |w1PSGSDhSD|2
|w1|2σ2n = PSGSD|hSD|2
σ2n (2.113)
γ2 = |w2PRGRDhRD|2
|w2|2σ2n = PRGRD|hRD|2
σ2n . (2.114)
As seen in Eq. (2.114), DF relaying has an advantage over AF relaying, since it is capable of reducing the effects of noise at the relay. However, if the relay incorrectly decodes and forwards the signal to the destination, then it imposes error propagation that may degrade the performance of the system. In this case, the DF scheme achieves a spatial diversity order of one, since the performance of the system is limited by the worst link in the set of the SR and SD links.
2.3.2.3 Compress-and-Forward
In contrast to AF and DF relaying, in compress-and-forward relaying the relay transmits a quantized and compressed version of the received signal. Therefore, the DS will combine the message received from the SS and its quantized as well as compressed version received from the RS. The quantization and compression process invoked at the relay node is reminiscent of the process of source encoding.
2.3.3. Relaying Protocols 74