despreading. In the same way, the higher-frequency term is a bandpass signal, whose complex envelope is a similar product without conjugation.

DS spreading is used in all 2G and 3G CDMA standards: IS-95 (cdmaOne), UMTS and cdma2000. Various combinations of data modulation and signature alphabets are involved there, which will be discussed in more detail in Section 11.3.

7.1.3 Frequency hopping spreading

In FH spreading FSK signatures are used and data modulation is also typically FSK. Two sorts of FH are traditionally distinguished—fast and slow—the relation between the chip D and data symbol T durations being the criterion of this classification. For a fast FH D ¼ T/l, where l > 1 is natural, while for a slow FH D ¼ lT with a natural l 1. In other words, for fast FH there are several frequency hops per data symbol, while with slow FH several data symbols may be transmitted during one frequency hop of a signature. To better imagine how it all works let us turn to an example.

Example 7.1.1. Let us take the FSK signature of Example 5.5.1 and use it for fast FH spreading in combination with a binary FSK data modulation. In this case the number of different frequencies in a signature M ¼ 5, signature length N ¼ 8 and one data symbol transmits one bit, so that T ¼ Tb . Suppose that in a fast FH scheme l ¼ N ¼ 8, i.e. there are 8 frequency hops per data bit. Then the whole sequence of FSK chips shown in Figure 5.3 is transmitted during one bit. If the data bit is zero, this frequency pattern is transmitted on the carrier frequency f0, while for the bit equal to one the carrier frequency jumps to f1. The difference between f1 and f0 should certainly be no smaller than the bandwidth occupied by the signature, i.e. MF. The transmitted frequency pattern corresponding to data bit stream 01011 is shown in Figure 7.11a.

t

T = Tb = N∆

(b)

f0 – fi

t fi + MF

(c)

fi

t

Figure 7.11 Fast FH spreading–despreading

As may be seen, the spectrum of a single data bit whose width before spreading was about 1/Tb is spread to span a bandwidth around MF M/D ¼ MN/Tb , i.e. MN times wider (see Section 5.6). At the receiving end despreading consists in down-converting the observed waveform to the intermediate frequency fi . For that the reference waveform of the carrier f0 fi is used, modulated according to a signature FSK pattern, properly delayed in time (Figure 7.11b). As a result a despread signal is an ordinary narrowband FSK data-modulated waveform, where the zero data bit is transmitted by lower frequency than the bit one (Figure 7.11c). The spectrum of an isolated data symbol is now returned to the bandwidth 1/Tb and a conventional binary FSK demodulator may be used to recover the received data.

Let us illustrate in the next example how to run slow FH spreading.

Example 7.1.2. Take the same signature in combination with, again, binary FSK data modulation and set equality between chip and symbol durations: T ¼ Tb ¼ D. This means that the current frequency remains constant over all the data bit duration and frequency hops happen only from one bit to the next. The frequency pattern of the signature is stretched in time and its length now covers N data bits (Figure 7.12a). Suppose that during a data bit number i signature frequency equals Fi . Then the transmitted frequency becomes f0 þ Fi for a zero data

f

(a)

MF

t

Tb = ∆

f1

(b)

f0

t

(c)

f0 – fi

fi + MF t

(d)

fi

t

Figure 7.12 Slow FH spreading–despreading