TENDENCIA DE LA DEMANDA DE AGUA POTABLE

The bandwidth of a communication system is the spectrum between the upper and lower cutoff frequencies. For a baseband signal, the bandwidth equals to the upper cut- off frequency. To avoid interferences suffering from the bandwidth overlap, the band- width of each communication standard and protocol is regulated by some forums such as International Telecommunication Union (ITU), European Conference of Postal and Telecommunications Administrations (CEPT), etc.. For instance, the GSM-Railway system in UK is licensed in two operating bands: 876-880 MHz for uplink, and 921-925 MHz for downlink [74]. While for an IMT system (UMTS-FDD system, regulated under Ofcom in UK), the uplink and downlink bands are 1,920-1,980 MHz and 2,110-2,170 MHz, respectively. However, the limited bandwidth in each standard may not satisfy the demands of data service from the growing number of customers in the future, and this concern is called ‘spectrum scarcity’ [75]. While, there are still a few bands which are not allocated to any commercial or governmental usage, such as 47-47.2 GHz, and 77.5-78 GHz [74]. Hence, some literatures put the focuses on the application of un- licensed bands [76] [77] [78] [79]. In [76], the authors analysed the performance of a modification of the multiple frequency shift system in the unlicensed 2.4 GHz band. To

avoid the interference with other sources and keep low power density, direct sequence and frequency hopping were considered in the application. In [77], a method was devel- oped for examining the wireless services coexistence between wireless local area network (WLAN) and WPAN, where the closed-form solution for the probability of collision was derived. A spectrum sharing problem was studied in [78] for the coexistence of multiple systems, where the self-forcing protocol must correspond to an equilibrium of a game. It was proved that the repeated game is more appropriate than the one shot game to model the interaction. In [79], a unified framework was presented for interference characterisations in the unlicensed frequency bands, where a new spatial-spectral inter- ference model was introduced. In this model, interferences can be any power spectral density and are distributed according to Poisson process in space and frequency do- mains. In Chapter 5, the unlicensed 60 GHz wireless communication in a short-range scenario is considered.

At the transmission end, the length of the antenna should be comparable with the wavelength in order to deliver the EM wave efficiently,i.e., a quarter of the wavelength [80]. While in the early wireless communication system, human voice is the only infor- mation source needed to be transmitted. The spectrum of human voice in telephony system is usually limited between 300 and 3,000 Hz [81], so the minimum size of the antenna should be around 25 km, which is incredibly long. To solve this problem, the baseband signal needs to be up-converted to a radio frequency (RF) waveform [24], which allows the contained information to be transmitted out by small-sized antennas. Fig. 3.1 shows the relationship between the passband and its baseband of a complex modulated signal in the frequency domain, whereB is the bandwidth,fc is the central carrier frequency. Defining Xb(f) as the frequency response of the baseband signal

xb(t), the passband signalx(t) [24] can be written as

x(t) =√2R [

xb(t)ej2πfct

]

(3.1)

where R[·] is the real part of a complex number, and ej2πfct _{is the carrier waveform.}

Applying Fourier transform F{·}, the frequency response of x(t) can be defined as

X(f) =F{x(t)}= √1

2{Xb(f−fc) +X

∗

b(−f −fc)} (3.2) Since the frequency response of the carrier ej2πfct _{is an impulse function, X(f) keeps}

the same shape ofXb(f) when f >0 as shown in Fig. 3.1. Hence, all the information of the source is preserved in the RF waveform x(t) without any loss, which largely reduces the length of antenna. To avoid the distortion by the overlap of frequency bands between the positive and negative spectrum parts of the passband signal, the carrier frequency is required asB < 2fcat least. For instance, the central frequency of IMT standard in downlink is around 2,140 MHz, while the bandwidth is only 60 MHz. If the transmit power and the distance are fixed, the data rate is determined by the bandwidth and central carrier frequency. According to (2.5), it is obvious that

f c f c f fc B 2 B 2 B 2 fc B 2 fc B 2 2 c f B 2 1 2 ( ) X f Passband Spectrum Baseband Spectrum

Figure 3.1: Illustration of the relationship between a passband spectrum and its base- band equivalent

the carrier central frequency affects the PL, and further affects the received SNR. The higher fc is, the lower the received SNR will be. From (2.39) it is easy to observe that once the fc is fixed, the data rate for transmission is mainly determined by the bandwidth. In other words, ultra high frequency transmission can provide ultra wide band, but it also brings serious attenuation on the strength of signals.