Performance of the MSDSD-Aided DAF-User-Cooperation Sys-

System Parameters Choice

System Two-User Cooperative OFDM

Number of Relay Nodes 1

Subcarrier BW △f =10 kHz

Number of Sub-Carriers D=1024

Modulation T-DPSK

Frame LengthLf 101

CRC CCITT-6

Normalised If it is not specified,

Doppler Frequency fd,sd= fd,sr= fd,rd=fd Channel Model typical urban, refer to Table 5.1

Channel Variances σ_sd2 =σsr2 =σrd2 =1 Power Allocation Ps=Pr1=0.5P=0.5 SNR at Relay and Destination Ps/N0=Pr1/N0

Table 5.5: Summary of system parameters used for the T-DPSK modulated two-user cooperation

5.3.4. Simulation Results 166 0 5 10 15 20 25 30 35 40 10−5 10−4 10−3 10−2 10−1 100 P/N o (dB) BER f d=0.03 f d=0.01 f d=0.001 DQPSK N wind=6 N_wind=2

Figure 5.17: BER performance improvement achieved by the MSDSD employingNwind=6 for

the DAF-aided T-DQPSK-modulated cooperative system in time-selective Rayleigh fading chan- nels. All other system parameters are summarized in Table 5.5.

As discussed in Section 5.3.2.3, the relative mobility among users imposes a performance degradation on the user-cooperation aided sysem. Thus, the multi-path MSDSD scheme proposed in Section 5.3.3, which relies on the exploitation of the correlation between the phase distortions experienced by theNwindconsecutive transmitted DPSK symbols, is employed in order to mitigate the channel-induced error floor encountered by the CDD characterized in Figure 5.17. The system parameters used in our simulations are summarized in Table 5.5.

Figure 5.17 depicts the BER performance improvement achieved by the MSDSD employed at the destination node for the DAF-aided two-user cooperative system in the presence of three dif- ferent normalized Doppler frequencies, namely fd = 0.03, fd = 0.01 and fd = 0.001. With the

aid of the MSDSD employingNwind =6 at the destination node, both the error floors experienced

in Rayleigh channels having normalized frequencies of fd =0.03 and 0.01 are significantly miti-

gated. Specifically, the BER curve corresponding to the normalized Doppler frequency fd = 0.01

almost coincides with that associated with fd = 0.001, indicating a performance gain of about 10 dB over the system dispensing with the MSDSD. Remarkably, in the scenario of a fast fading

channel having fd = 0.03, the BER curve obtained when the CDD is employed at the destination

node levels out just below10−3, as the SNR increases. By contrast, with the aid of the MSDSD the resultant BER curve decreases steadily, suffering a modest performance loss of only about4 dB at

target BER of10−5in comparison to the curve associated with fd =0.001. Hence, the more time-

selective the channel, the more significant the performance improvement achieved by the proposed MSDSD scheme.

For the sake of further reducing the detrimental impact induced by the time-selective channel on the DAF-aided user-cooperation assisted system, an observation window size ofNcand =11 is

5.3.4. Simulation Results 167 0 5 10 15 20 25 30 35 40 10−4 10−3 10−2 10−1 100 P/N 0 (dB) BER f d=0.03 f d=0.01 f d=0.001 DQPSK N wind=11 N wind=2

Figure 5.18: BER performance improvement achieved by the MSDSD scheme employing

Nwind = 11 for the DAF-aided T-DQPSK-modulated cooperative system in time-selective

Rayleigh fading channels. All other system parameters are summarized in Table 5.5.

employed by the MSDSD arrangement at the destination node at the expense of a higher detection complexity. As seen in Figure 5.18, the MSDSD using Nwind = 11 is capable of eliminating the

error floor encountered by the system employing the CDD, even when the channel is severely time- selective, namely, for fd = 0.03. In other words, the BER curve corresponding to the MSDSD-

aided system in Figure 5.18 and obtained for fd = 0.03 coincides with that of its CDD-aided

counterpart recorded forfd=0.001. Furthermore, the MSDSD-aided system with Nwind=11 in a

fast-fading channel associated withfd=0.01 is able to outperform the system employing Nwind=

2, even if the latter is operating in a slow-fading channel having fd = 0.001. Therefore, even in

the presence of a severely time-selective channel, the DAF-aided user-cooperation assisted system employing the MSDSD is capable of achieving an attractive performance by jointly differentially detecting a sufficiently high number of consecutively received user-cooperation based joint symbols Sn(n=0, 1,· · · , Nwind−1)of Eq.(5.58) by exploiting the knowledge of the equivalent channel

autocorrelation matrix_E{H ˜˜HH_}of Eq.(5.79), which characterizes the CIR statistics of both the direct and relay links.

fd,sd fd,sr fd,rd

Scenario I (S moves, R&D relatively immobile) 0.03 0.03 0.001

Scenario II (R moves, S&D relatively immobile) 0.001 0.03 0.03

Scenario III (D moves, S&R relatively immobile) 0.03 0.001 0.03

Table 5.6: Normalized Doppler frequency of three different scenarios.

All the previously described simulations were carried out under the assumption that an identical normalized Doppler frequency is exhibited by each link of the user-cooperation system, namely that we have fd,sd= fd,sr = fd,rd = fd. However, a more realistic scenario is the one where the relative

5.3.4. Simulation Results 168 0 5 10 15 20 25 30 35 40 10−4 10−3 10−2 10−1 100 P/N 0 (dB) BER Scenario I Scenario II Scenario III DQPSK MSDSD: N wind=6 f d=0.001 bound f_d=0.03 bound

Figure 5.19: The impact of the relative mobility among the source, relay and destination nodes

on the BER performance of the DAF-aided T-DQPSK-modulated cooperative system employing MSDSD at the destination node in Rayleigh fading channels. All other system parameters are summarized in Tables 5.5 and 5.6.

speeds of all the cooperative users as well as of the destination terminal are different from each other, leading to a different Doppler frequency for each link. Thus, in order to investigate the impact of different relative speeds among all the nodes on the attainable end-to-end performance of the DAF-aided system, Monte Carlo simulations were carried out for the three different scenarios summarized in Table 5.6. In all the three situations, only one of the three nodes in the two-user cooperation-aided system is supposed to move relative to the other two nodes at a speed resulting in a normalized Doppler frequency of0.03, while the latter two remain stationary relative to each

other, yielding a normalized Doppler frequency of0.001.

In Figure 5.19 the BER curves corresponding to the three different scenarios of Table 5.6 are bounded by the two dashed-dotted BER curves having no legends, which were obtained by assum- ing an identical normalized Doppler frequency of fd = 0.03 and fd = 0.001 for each link in the

user-cooperation aided system, respectively. This is not unexpected, since the two above-mentioned BER bounds correspond to the least and most desirable time-selective channel conditions consid- ered in this chapter, respectively. The channel quality of the direct link characterized in terms of its grade of time-selectivity predetermines the achievable performance of the DAF-aided user- cooperation assisted system employing the MSDSD. Hence, it is observed in Figure 5.19 that the system is capable of attaining a better BER performance in Scenario II (fd,sd = 0.001) than in

the other two scenarios (fd,sd = 0.03). However, as seen in Figure 5.19, due to the high speed of

the relay node observed in Scenario II relative to the source and destination nodes, the MSDSD employing Nwind = 6 remains unable to completely eliminate the impairments induced by the

time-selective channel, unless a higherNwindvalue is employed. Therefore, a modest performance degradation occurs in comparison to the fd = 0.001 scenario. On the other hand, the MSDSD-

5.3.4. Simulation Results 169 0 5 10 15 20 25 30 35 40 10−4 10−3 10−2 10−1 100 P/N 0 (dB) BER Destination: N wind=2 Destination: N wind=6 f d=0.001 f d=0.03 f d=0.01 Relay: N wind=6 DQPSK

Figure 5.20: BER performance improvement achieved by the multi-path based MSDSD scheme

employingNwind=6 at the destination node of the DDF-aided T-DQPSK-modulated cooperative

system in Rayleigh fading channels. All other system parameters are summarized in Table 5.5.

aided system exhibits a similar performance in Scenario I and Scenario III, since the source-relay and relay-destination links are symmetric and thus they are exchangable in the context of the DAF scheme, as observed in Eq.(5.81).