Sub-Band TR Transmission Scheme

The TR signal has a very large bandwidth. In our case, it has a bandwidth of 2GHz with a center frequency of 1.7 GHz. Fig. 4.21 shows the power spectral density (PSD) of a TR transmitted signal normalized to a constant power. The PSD is calculated using Welch’s method [71]. The PSD of the TR transmitted signal depends on the effects of the propagation channel including path loss and the antenna effects.

Therefore, PSD has a descending shape. The components of the signal at higher frequencies are attenuated as compared to the components at lower frequencies. This inherent property of the TR signal makes it difficult to employ efficiently to a UWB system. Thus, the transmitted signal must be attenuated so that it respects the UWB

0 1 2 3 4

−80

−60

−40

−20 0 20

Frequency (GHz)

PSD (dBm/MHz)

Modified TR

Figure 4.23: PSD of a modified TR transmitted signal

spectral mask (imposed by the Federal Communication Commission (FCC) [3]) over the whole band resulting in a poor spectral efficiency. However, if the PSD of the transmitted signal is flat, the TR system will then respect the UWB spectral mask with a better spectral efficiency. To achieve a flat PSD, total bandwidth of the time reversed signal is divided into N sub bands of equal power [88]. We call the scheme as Sub-Band TR Transmission Scheme (SB-TRTS). The power of each sub-band is normalized using equal power control (EPC) so that each sub-band contributes equally to the PSD. Letx_i be the signal for thei_thsub-band. Using EPC, it can be normalized as:

|xi(t)|EP C = xi(t)

kx_i(t)k (4.22)

where k.k is the Frobenius norm operation.

In our case, the TR signal is divided into 10 sub bands of 200 M Hz. The block diagram of the SB-TRTS is shown inFig. 4.22. The filtering is achieved by transform-ing the signal in the frequency domain (FFT), then filtertransform-ing the signal by band-pass filters, and transforming the signal back into the time domain (IFFT). In this way, the signals with precise bands are achieved. Once the signals are filtered with N sub bands, the signal of each sub-band is normalized to have an equal power using EPC.

The normalized signals are then added together to form the transmitted signal for the SB-TRTS. The added signal must be again normalized so that it respects the UWB spectral mask. Fig. 4.23 shows the PSD of the TR signal of the SB-TRTS having a

1 -0.14 75

2 2.24 37.4

4 5.97 18.7

8 11.83 9.35

16 17.10 4.67 32 20.05 2.33 64 26.60 1.16

Table 4.2: Comparison of SIR for differentT_sin the indoor channel forSN R= 15 dB with SB-TRTS

power normalized to a constant. As expected, PSD is flat and it is easier to respect the spectral mask.

The received signal with the SB-TRTS has a better SSR as compared to the classic TR, but it has a lower peak power as well for the same transmitted power [88]. We have used this scheme to achieve a better BER performance for a high data rate TR communication system. The experiments are performed with the SB-TRTS in the same way as were performed with the classic TR scheme.

4.3.3.1 Experimental Results with SB-TRTS

Table4.2shows the SIR at the instants of decision for differentT_swith the SB-TRTS.

SIR is computed by following the same procedure adopted for the classic TR scheme.

Comparing Table 4.1 and Table 4.2, it can be seen that the SB-TRTS has improved the SIR of the TR system forT_s≥8 nsin an indoor environment.

Fig. 4.24shows the BER performance of the SB-TRTS in an indoor environment.

Comparing Fig. 4.19 and Fig. 4.24, it can be seen that the performance of the system has significantly improved with the SB-TRTS. For instance, SB-TRTS gives a 3 dB better performance than the classic TR scheme for a fixed BER of 10⁻⁴ for a data rate of 125 M bps. The SB-TRTS gives a 2.4dB better performance than the classic TR scheme for the data rate of 62.5 M bps for a fixed BER of 10⁻⁶. Thus, the flattening of the spectrum has worked as equalization and has improved the BER performance with the SB-TRTS. However, the performance has not improved for the data rates ≥250 M bps where the curves reach a plateau for both the schemes.

With the validation of high data rate communication, TR can be thought of a po-tential transmission scheme for realistic applications, for example, WLAN and wireless streaming applications etc. The SB-TRTS has furthered improved the performance of the TR system. For the future work, study can be done by using an equalizer at the receiver but it will be a performance complexity trade off. The performance of

5 10 15 20 10⁻⁶

10⁻⁵ 10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

SNR

BER

1000 Mbps 500 Mbps 250 Mbps 125 Mbps 62.5 Mbps 31.25 Mbps 15.62 Mbps

Reverberation Chamber Tx

R_x

3.7m

16m

Corridor Office Office Office

10m

8.7m

Figure 4.24: BER performance of TR system for 1 ns ≤ T_s ≤ 64ns in an indoor environment with sub-band filtering

the TR system can also be compared by using pulse position modulation scheme with classic TR and the SB-TRTS.

4.4 Conclusion

In this chapter, high data rate TR communication is discussed with two approaches.

In the first approach, a novel modulation scheme is proposed for a time reversal (TR) ultra wide-band (UWB) communication system. The proposed modulation scheme adds a new level of modulation to the existing modulation scheme like bipolar pulse amplitude modulation (BPAM). Multiple bits are transmitted simultaneously by shifting the transmitted signal and packing them in the same time slot. The BER

shown that for negligible interference and quasi orthogonal signals, the data rate of the modulation scheme increases linearly whereas the transmitted power must only be increased logarithmically. The validation of the modulation scheme is carried out with the help of two separate measurement campaigns. For the first measurement campaign, the frequency responses of a typical indoor channel are measured with a vector network analyzer and TR communication is simulated for the new modulation scheme. The bit error rate performance of the new modulation scheme is analyzed for different modulation orders. It is shown that for an optimal shift, theoretical and simulation performances of the modulation scheme are in strong agreement to each other. In the second measurement campaign, time domain instruments are used to measure the channel impulse response and the new modulation scheme is validated experimentally. It is shown that the experimental and the simulative results are in good agreement with each other. For high data rate communication, large number of bits must be added in the same symbol duration and the introduced shift will degrade the performance of the system. However, this scheme can be very useful for multi-user TR communication system where the shift is introduced on the signals of different users. Multi-user TR communication by using the proposed shift operation has been investigated in the next chapter.

In the second part of the chapter, results of high data rate communication exper-iments without any shift introduction are presented using BPAM. Experexper-iments have been done in a typical indoor environment and in a reverberation chamber for dif-ferent data rates (R_b) ranging from 15.62 M bps to 1 Gbps. Signal, Interference and Noise components are separated from the measured received signal and are compared for differentT_s at a fixed SNR. It is observed that inter symbol interference increases with the decrease in T_s and saturates the BER performance. It is shown that the BER performance in the indoor channel is better than the reverberation chamber.

Furthermore, experiments are performed using a sub-band TR transmission scheme (SB-TRTS) which divides the total bandwidth of the transmitted signal into multiple sub bands, each contributing equally to the power spectral density (PSD) and there-fore improves the spectral efficiency of the system. This process helps to achieve a flat PSD. It is shown that the modified TR scheme performs a sort of equalization and significantly improves the BER performance. For instance the SB-TRTS gives a 2.4 dB better performance than the classic TR scheme for R_b = 62.5 M bps and a fixed BER of 10⁻⁶.