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In this section, a perfect CSI is assumed to be known at the receiver side in order to

neglect the channel estimation effect. Noting that 1024 sub-carriers are used and no

CP and pilot symbols are inserted. The oversampling factor in this section is set to be

0 500 1000 1500 2000 104 105 106 107 108 N log(Number of operations) Turbo−General Turbo−OFDM Turbo−SEFDM

Figure 3.21: Complexity comparisons of different systems.

2 4 6 8 10 12 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 Eb/N0 BER α=0.55, v=4 α=0.55, v=7 α=0.6, v=4 α=0.67, v=4 α=0.8, v=4 α=1 (OFDM), v=4

Figure 3.22: Performance of 4QAM-SEFDM in AWGN channel with N=1024 and ρ=2 at various α. The number of iterations is denoted as v.

Simulation results are given in Fig. 3.22. In this case study, 1024 sub-carriers and

can be increased or decreased according to performance requirements. It is clearly seen

that curves with α=0.8, 0.67, 0.6 converge at 7dB. The Eb/Nodifference at BER=10−6

between α = 1 and α = 0.6 is approximately 1 dB, and reduces to 0.5 dB with α = 0.8.

On the other hand, for α ≤ 0.55, with the same iteration number, curves cannot reach

the same performance as others at 7dB. This is due to the fact that too much ICI is

introduced with small bandwidth compression factors. However, this performance gap

can be reduced by increasing the number of iterations. With 7 iterations, considering

α=0.55, the performance gap at BER=10−6 is reduced to 2 dB compared to α = 1.

It is proved that this new system can save 45% of bandwidth with slight performance

degradation. It also indicates that the new detector is suitable for 1024 sub-carrier

SEFDM system; the highest number of sub-carriers to be considered.

2 4 6 8 10 12 14 10−6 10−5 10−4 10−3 10−2 10−1 100 Eb/N0 BER α=0.55, no iteration α=0.6, no itertion α=0.8, no iteration α=0.55, v=4 α=0.55, v=7 α=0.6, v=4 α=0.8, v=4 α=1 (OFDM), v=4

Figure 3.23: Performance of 4QAM-SEFDM in the presence of frequency selective channel with N=1024 and ρ=2 at various α. The number of iterations is denoted as v.

The performance of Turbo-SEFDM is examined in the presence of static frequency

selective channel [147]. The channel impulse response is shown as

h(t) = 0.8765δ(t) − 0.2279δ(t − Ts) + 0.1315δ(t − 4Ts)−0.4032e jπ

This channel model is reserved as the default frequency selective channel for the

following simulations and experiments. Assuming perfect CSI is known at the receiver.

For time-varying channels, preambles can be periodically inserted to obtain accurate

channel estimates. Results in Fig. 3.23 indicate that 4 iterations are sufficient to ap-

proach OFDM performance while saving up to 40% of bandwidth. As for the smaller

α = 0.55, with the same iteration number, it cannot reach the converged performance.

This is due to the fact that too much ICI is introduced by using small bandwidth

compression factors. However, this performance gap can be reduced by increasing the

number of iterations. It is clear seen that the convergence is achieved by 7 iterations.

Thus, considering a reasonable iteration number, in a multipath channel scenario, this

new system can save up to 45% of bandwidth with slight performance degradation. It

also indicates that the new detector is applicable for 1024 non-orthogonal sub-carrier

SEFDM systems; the highest number of sub-carriers to be considered so far. In ad-

dition, it should be noted that for systems in the frequency selective channel, the

performance gap is much smaller compared with systems in an AWGN channel. This

can be observed by comparing Fig. 3.22 and Fig. 3.23. It is proved that our technique

performs well in multipath channel scenarios.

Higher modulation schemes in the presence of AWGN and frequency selective chan-

nels are investigated in this work. Fig. 3.24(a) and Fig. 3.24(b) present the performance

of SEFDM and OFDM in different channel scenarios. In the case of 16QAM modu-

lation scheme, each symbol carry more bits than 4QAM, making it more difficult to

demap accurately the symbols to the corresponding constellation. In a normal 4QAM

SEFDM, the curve with α=0.8 approaches the OFDM curve. However, as the level of

modulation increases, a performance degradation appears in SEFDM. It is clearly seen

that the curve with α=0.8 no longer converges to the one with α=1 in both AWGN

and frequency selective channels. This is because high level interference is introduced

in 16QAM.

1 2 3 4 5 6 7 8 9 10 10−6 10−5 10−4 10−3 10−2 10−1 100 Eb/N0 BER α=0.67, v=4 α=0.8, v=4 α=1 (OFDM)

(a) AWGN channel.

2 4 6 8 10 12 14 16 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 Eb/N0 BER α=0.8, v=4 α=1 (OFDM)

(b) Frequency selective channel.

Figure 3.24: Performance of 16QAM-SEFDM in the presence of different channel con- ditions with N=1024 at various α. The number of iterations is denoted as v.

channels are plotted in Fig. 3.25. It is observed that the performance of both scenarios

is significantly improved at the first 3 iterations. By further increasing the number to

4, the performance remains stable. It can be concluded that 4 iterations are sufficient

to obtain optimal performance, showing a significant improvement on the work in [52]

where a large number of iterations are required.

In Fig. 3.26, we investigate effects of different interleaving sizes for 4QAM-SEFDM

systems. Both 2048 bits and 10 × 2048 bits are considered. The 16QAM performance

is included as a reference. The performance gap between the two interleavers are very

small. Considering BER=10−3, by using 7 iterations, the difference is only 0.5 dB.

Increasing further the iteration number to 12, the difference reduced to 0.25 dB. We note

that for any iteration numbers, 2048-bit interleaver and 10 × 2048-bit interleaver have

very similar BER performance, proving that the interleaver size has negligible effects

on the performance. Therefore, it is concluded that 2048-bit interleaver is sufficient to

decode symbols.

4QAM-SEFDM technique can reach the same spectral efficiency with 16QAM-

1 2 3 4 5 6 7 8 10−6 10−5 10−4 10−3 10−2 10−1 100 Eb/N0 BER no iteration v=1 v=2 v=3 v=4 v=5

(a) AWGN channel.

2 4 6 8 10 12 14 10−6 10−5 10−4 10−3 10−2 10−1 100 Eb/N0 BER no iteration v=1 v=2 v=3 v=4 v=20

(b) Frequency selective channel.

Figure 3.25: Convergence behaviour of 4QAM-SEFDM in the presence of different channels at α = 0.6 with various iterations.

Fig. 3.27(a) and Fig. 3.27(b), α = 0.5 4QAM-SEFDM is compared with the spectral

efficiency equivalent 16QAM-OFDM. It is apparent that the performance of 4QAM-

SEFDM has the same performance with 16QAM-OFDM. However, this is achieved at

the cost of large number of iterations. In Fig. 3.27(a), when 4 iterations are used,

the performance of α = 0.5 SEFDM is much worse than that of OFDM. The perfor-

mance is improved by increasing it to 19. This is attributable to the fact that more

efforts are required to eliminate ICI. Fig. 3.27(b) shows comparisons in frequency se-

lective channels. 4 iterations are also not sufficient for SEFDM to approach OFDM

performance. However, in this situation, only 10 iterations are required to obtain a

converged performance. No performance improvement is observed with higher number

of iterations.