For simplicity reason, systems in this chapter have only two relay groups and two relay nodes in every relay group.
transmit one of their two BPSK signals simultaneously to the next relay group. After the first two BPSK signals reach the receiver, the second two BPSK signals will be transmitted by relay group one. Finally, two relays in relay group two transmit their received signals to the receiver via different time slots.
Transformation Mechanism
This mechanism takes place at the relays in relay groups one to separate the received QPSK signal to two BPSK signals.
The relay node divides all signals on the constellation into two groups according to the information they carry (signal carries bit 1 as its first bit and signal carries bit 0 as its first bit will be separate into different group). After a QPSK signal is received, the relay node will find one signal from each group who is closest (has the minimum distance) to the received signal. Assuming the distances between the received signal and its closest two points from each group whose first bit is 1 and 0 are d11 and d10, the log likelihood-ratio of the first bit is
LLR1= −d 2 11+ d102
2σ2 (3.12)
Applying the same procedure to the second bit of the received signal, the log likelihood-ratio of the second bit is
LLR2= −d 2 21+ d202
2σ2 (3.13)
In order to constrain the transmit power, hyperbolic function tanh() is used. Finally, the two transformed BPSK signals are
tanh(LLR1) (3.14)
and
tanh(LLR2) (3.15)
At high SNR, because of the small noise variance σ2 and large distance between different
points, LLR becomes large. Consequently, tanh(LLR) is close to or almost equals to 1, so this mechanism produces a signal very similar to standard BPSK with average transmit power to 1. The advantage of this transformation mechanism is that it applies soft decision which will give better BER performance than the hard decision system used in the decode-and-forward system.
3.7.2
Simple Amplify-and-Forward System
The original system and soft-decoding-and-forward system provide only first order diversity; in order to achieve higher order diversity we develop a new system in which the transmitter first broadcasts one QPSK signal to relays in relay group one. The relays amplify and forward the received signals to relays in relay group two where the received signals are stored. Next, the another QPSK is sent by the transmitter and received by relay group two via relay group one using the same procedure as the first QPSK signal does. In relay group two, the received signals are combined with the previously stored signals and transmitted to the receiver.
Combining Mechanism
The signals received by every relay node in the last relay group consist of two QPSK signals superposed together which contain the same information but via different rout.
The QPSK constellation the transmitter use has unity transmit power, so if we scale the power of one received signal by half and add it to the other one, a 16 QAM signal with average transmit power 2.5 will be formed.
Note that the combining mechanism here also affects the diversity of the system. If we use the same combining style on every relay node in the last relay group, the system will not have full receive diversity. For example, if on one relay node the first signal is scaled down by half and added to the second signal, then on the other relay node the procedure must be performed the other way around. This prevent the situation in which the weaker signal is scaled down on both relay nodes.
Figure 3.5 is the comparison between different combining styles. The system has two relay groups with three relay nodes each. The blue line which approaches third order diversity corresponds to the combining style that weights each received signal differently in every relay node, the red line which is second order diversity corresponds to the combining style that weights each received signal in the same way in every relay nodes.
3.7.3
Performance Comparison
In order to make these three systems comparable, we set the average transmit energy per bit in every phase across these three systems equal to 0.5. We assume every system uses the same symbol period T to transmit one signal, so the through-put of these three systems are: the original system uses 5 symbol periods to transmit 4 bits (two QPSK signals), the soft-decode- and-forward system uses 6 symbol periods to transmit 4 bits (two QPSK signals ), the simple amplify-and-forward system uses 6 symbol periods to transmit 4 bits (two QPSK signals). Note that the number of symbol periods the original system uses does not match those used by the other two systems, but the difference is not very significant.
Figure 3.6 shows the BER performance of the original system (blue), the soft-decode-and- forward system (red) and the simple amplify-and-forward system (green). It is obvious that the simple amplify-and-forward system outperforms other two significantly due to its higher diversity order.
Figure 3.7 shows the throughput of these three systems, every block is one symbol period, phase one is the transmission from transmitter to relay group one, phase two is from relay group one to relay group two, phase three is from relay group two to the receiver.
−5 0 5 10 15 20 25 30 35 10−6 10−5 10−4 10−3 Eb/N0 (dB) BER
same combining style at all realys different combining style at each relay
Figure 3.5: performances of different combining mechanisms in section 3.7.2