7

Spread spectrum signature ensembles for CDMA applications

7.1 Data transmission via spread spectrum

It is clear from the discussion of Sections 4.3–4.6 that in a CDMA network each of K users transmits or receives its individual data employing some user-specific signature, ensemble of K signatures being carefully designed to provide the best possible compatibility. In order to make the kth signature transport the datastream some sort of modulation is necessary, which—due to the spread spectrum nature of CDMA signa- tures—is often called spread spectrum modulation. There are two classical versions: direct sequence (DS) and frequency hopping (FH) modulation. The first is more typical of modern commercial wireless multiuser applications, and so the second will be considered below only briefly.

7.1.1Direct sequence spreading: BPSK data modulation and binary signatures

The general idea of direct spread spectrum is APSK modulation of the APSK signature by a datastream. To make the concept easier to grasp, let us start with the simplest case of BPSK non-spread spectrum data transmission. Let Bk(t) be the data waveform of the kth user (Figure 7.1) where positive and negative polarities during one bit interval Tb correspond to transmitting a bit equal to 0 and 1, respectively. If bk ¼ ( . . . , bk, 1, bk, 0, bk, 1, . . . ), bk, i ¼ 1, is, as it was in Chapter 4, the kth user bit (or binary symbol) stream, then Bk(t) ¼ bk, i ¼ 1, (i 1)Tb < t iTb. Transmitting Bk(t) by

Spread Spectrum and CDMA: Principles and Applications Valery P. Ipatov

2005 John Wiley & Sons, Ltd

bit at the channel output occupies time interval ((i 1)Tb þ k, iTb þ k], the correlation discussed is:

and the decision bk, i ¼ 0 or bk, i ¼ 1 is taken depending on the positive or negative sign

of zk. A possible and very popular structure of a demodulator implementing this rule is given in Figure 7.2b. It contains the correlator realized as a multiplier multiplying the observation with a locally generated CW reference cos (2 f0t þ k) and an integration- and-reset unit. At the end of every consecutive bit interval a sample is taken from the integrator output, a decision on the current bit is made according to its polarity, and the integrator is zeroed in preparation for operation over the next bit interval.

Consider now the changes that need to be done for transmitting BPSK data with BPSK DS spreading. Let sk(t) be the kth user signature, i.e. a discrete signal consisting of chips of duration D, manipulated by some user-specific binary sequence. Let there be N signature chips per one data bit. Then DS spreading of the BPSK signal just involves

Since the bandwidths of signals (7.1) and (7.3) are inverse to bit duration Tb ¼ 1/R and chip duration D ¼ Tb/N ¼ 1/RN, respectively, the DS spreading widens the spectrum N times. This explains one more name: the spreading factor for the time–frequency product or processing gain WT ¼ N. In practice, multiplications in (7.3) may be fulfilled in an arbitrary order, e.g. as Figures 7.3 (spreading by a binary m-sequence of length N ¼ 7, Tb ¼ ND) and 7.5a show, the bit stream Bk(t) may first be multiplied with a signature sk(t) to further modulate the CW carrier by the product sk(t)Bk(t). We may say in this case that the bit stream first modulates the baseband signature and then the result BPSK-modulates the carrier.

After passing the channel and acquiring delay k and phase k, the signal takes the form:

Assuming again a perfect knowledge of parameters k, k, the receiver for retrieving the current (ith) bit just needs to distinguish between the signal sk(t k) cos (2 f0t þ k) and its antipodal copy. To perform it optimally a correlation:

sk(t k) cos (2 f0t þ k) may be found and its polarity used for the decision. Interestingly, however, the same optimal operation may be realized in two stages, first removing

sk(t) t

cos(2πf0t) t

sk(t; bk) t

∆

Tb = N∆

Figure 7.3 DS spreading of BPSK data with binary signature

the spreading and then demodulating the data as though they had been transmitted directly with no spreading. Let the observation y(t) be multiplied by the local replica sk(t k) of the baseband signature synchronized accurately with the arriving signal. The useful component (7.4) of the observation after this operation changes as:

skrðt; bkÞskðt kÞ ¼ s2kðt kÞBkðt kÞ cosð2 f0t þ kÞ ¼ Bkðt kÞ cosð2 f0t þ kÞ

where the binary nature of the signature (sk(t) ¼ 1) is used, on the strength of which s2k(t) ¼ 1. As is seen, after this step the received signal has no more features of spread spectrum, coinciding entirely with the plain signal (7.2) BPSK-modulated by the datastream. Due to this, multiplying of the observation by a signature replica is called despreading. Figure 7.4 shows the procedure of transforming a DS-spread signal into a conventional BPSK data-modulated signal.

Since a despread signal is a conventional BPSK data-modulated CW carrier, further data recovery is fulfilled by an ordinary BPSK demodulator, e.g. by the one of Figure 7.2b. The entire spreading–despreading cycle is illustrated in Figure 7.5.

To support the discussion in terms of the frequency domain, consider Figure 7.6,

~ ~

which shows the power spectra densities Sb(f ), Sbs(f ) of the initial datastream Bk(t) and its spread version sk(t)Bk(t), respectively. For a sequence Bk(t) of bit-pulses of duration

pulses with independent polarities—this time of duration D—leads to a power spectrum

utilizes all the benefits of spread spectrum (see Chapters 3 and 4) but at the receiving end despreading returns the spectrum into its original bandwidth, converting the signal into narrowband and allowing use of the simplest technologies of data demodulation.