Computer Simulations

, ,

f f nocoop f u

P ≈P P (3.47)

Note the difference between (3.43) and (3.47). The probability that users go back to no cooperation mode is much lower comparing to the probability in non-adaptive scheme, thus provides a better performance. Simulations of the adaptive scheme will be presented in Fig. 3-5 in next Section.

3.3 Computer Simulations

In this Section we simulate the proposed space-time coded cooperation protocols and compare with other protocols mentioned in Chapter 2. All systems are with equal code rate R and hence equal data rate. We use a rate-1/4 base code with generator [15

17 13 15] used by [18]. For the conventional coded cooperation and the proposed ST-coded cooperation, the puncture patterns are [1 1 0 0] for the broadcast sub-codeword, [0 0 1 1] for the relay sub-codeword. Binary phase-shift keying (BPSK) modulation is used. The frame size is 260 bits. We consider the case that both nodes communicate with the same destination. Each user and the destination are equipped with a single antenna. The channel is slow Rayleigh fading channel with AWGN.

Fig. 3-3 plots the analytical bound and simulation results of FER as a function of the transmit SNR. Similar results could be obtained in terms of BER. Perfect inter-user channel is assumed so there is no data exchange failure. Investigating the FER at high SNR region and comparing with the analytical bounds (dash line with diamonds), it is clear that the proposed ST-coded cooperation (line with diamonds) achieves full diversity as we expected in Section 3.2. Comparing the performance of the proposed protocol with conventional coded cooperation (line with squares) at FER of 10⁻³, the proposed ST-coded cooperation using Alamouti code achieves nearly 4dB gain over the conventional coded cooperation. If more users join the cooperation, higher order space-time code can be used to gain more diversity. For the case of four users (line with down triangles), additional gain of 2.5dB is achieved comparing to 2-user case.

0 2 4 6 8 10 12 14 16 18 20

Conventional coded cooperation (union bound) Conventional coded cooperation

Proposed ST-coded (Alamouti)(union bound) Proposed ST-coded (Alamouti)

Proposed ST-coded (4x4 OSTBC)(union bound) Proposed ST-coded (4x4 OSTBC)

Fig. 3-3. Simulations and bounds of frame error rate (FER) in ST-coded cooperation. Equal uplink SNR, base code [15 17 13 15]

Fig. 3-4 shows the impact of data exchange failure to the overall FER. We assume that the rate of data exchange failure between users is 0.1. Analytical bounds based on Section 3.2.3 are shown in the figure. It can be seen that the simulation result is consistent with the analytical bound.

Lines with diamonds and down triangles are the same as the simulation results in Fig. 3-3, that is, ST-coded cooperation with no data exchange failure. Diamonds and down triangles with no lines are the simulation result when data exchange failure is considered. From the figure we can see that the proposed ST-coded cooperation protocols lose their diversity at high SNR region. At that region, they seem to have diversity of order 2 because the two sub-codewords still experience independent

channels in broadcast and relay phase.

Despite the loss in diversity, the proposed 2-user ST-coded cooperation still has advantages over the conventional one. But the performance of 4-user scheme is even worse than 2-user case. As mentioned in Section 3.2.3, cooperation among four users with imperfect inter-user channel experiences severe performance degradation since the data exchange between 4 users is hardly all successful. To this problem, we’ll show in Fig. 3-5 the performance improvements of 4-user cooperation with adaptive protocol.

Conventional coded cooperation (failure rate=0.1) ST-coded (4x4 OSTBC) (failure rate=0.1) (union bound)

ST-coded (4x4 OSTBC) (failure rate=0.1) ST-coded (Alamouti) (failure rate=0.1) (union bound)

ST-coded (Alamouti) (failure rate=0.1) ST-coded (Alamouti) (perfect cooperation) ST-coded (4x4 OSTBC) (perfect cooperation)

Fig. 3-4. Frame error rate (FER) with imperfect inter-user channels. Equal uplink SNR, generator [15 17 13 15], inter-user FER=0.1

Comparing the performance of 4-user case (down triangles) in Fig. 3-4 and Fig.

3-5, we can see clearly the improvement by applying adaptive protocol mentioned in

Section 3.2.3. The algorithm assures the performance under 4-user scheme not worse than the case when only 2-user Alamouti code is applied. Meanwhile, it still benefits from the use of 4 4× OSTBC when the data is exchanged successfully. For the case of data exchange failure rate=0.1, the average probability of 4-user cooperation is about 0.531, 2-user cooperation is about 0.468 and the probability of no cooperation is only 0.001.

Conventional coded cooperation (inter-user FER=0.1) ST-coded (Alamouti) (failure rate=0.1)

ST-coded (Alamouti) (perfect cooperation) ST-coded (4x4 OSTBC) (failure rate=0.1) (union bound)

ST-coded (4x4 OSTBC) (failure rate=0.1) ST-coded (4x4 OSTBC) (perfect cooperation)

Fig. 3-5. Frame error rate (FER) with imperfect inter-user channels. Equal uplink SNR, generator [15 17 13 15], inter-user FER=0.1, adaptive algorithm

3.4 Summary

In this Chapter we give a detailed description of the proposed space-time coded

cooperation protocol. We show the diversity gain in the case of 2-user coded cooperation with Alamouti space-time code by evaluating the pairwise error probability. Extension to other space-time code is straightforward. The proposed protocol can utilizes full diversity gain from the used space-time code. Tight union bounds for the BER as well as the FER are given by using the weight enumerating function and the limit-before-averaging technique. Both analytical and simulation results have been shown to prove the performance gain. We also consider the impact of imperfect inter-user channel to the proposed protocol and give an adaptive way to reduce the performance loss.

Chapter 4

Spectrally Efficient Multi-user Coded Cooperation using Code Partitioning

In this Chapter we introduce the second modification of coded cooperation:

code-partition (CP) coded cooperation. The proposed protocols still achieve great system reliability while maintaining equal spectral efficiency as non-cooperation protocols. The CP-coded cooperation has similar performance to the protocols in Chapter 3. Besides, it has the advantages of less complexity and lower requirements for inter-user channel.