Single-User Modulation Techniques
To discuss advanced receiver signal processing methods for
wireless, it is useful first to specify a general model for the signal received
by a wireless receiver. To do so, we can first think of a single transmitter,
transmitting a sequence or frame {b[0], b[1], ..., b[M – 1]} of channel
symbols over a wireless channel. These symbols can be binary (e.g., ±1), or they
may take on more general values from a finite alphabet of complex numbers. In
this treatment, we consider only linear
modulation systems, in which the symbols are transmitted into the channel by
being modulated linearly onto a signaling waveform to produce a transmitted
signal of this form:
Equation 1.1
where wi(·) is the
modulation waveform associated with the ith
symbol. In this expression, the waveforms can be quite general. For example, a
single-carrier modulation system with carrier frequency wc, baseband pulse shape p(·), and symbol rate 1/T is obtained by choosing
Equation 1.2
where A > 0 and f 
(-p, p) denote carrier amplitude
and phase offset, respectively. The baseband pulse shape may, for example, be a
simple unit-energy rectangular pulse of duration T:
Equation 1.3
or it could be a raised-cosine pulse, a bandlimited pulse, and
so on. Similarly, a direct-sequence spread-spectrum system is produced by
choosing the waveforms as in (1.2) but
with the baseband pulse shape chosen to be a spreading waveform:
Equation 1.4
where N is the spreading gain,
c0, c1, ..., cN-1, is a
pseudorandom spreading code (typically, cj
{+1, -1}), y(·), is the chip waveform,
and 
is the chip interval. The chip waveform may, for example, be a
unit-energy rectangular pulse of duration Tc:
Equation 1.5
Other choices of the chip waveform can also be made to lower
the chip bandwidth. The spreading waveform of (1.4) is periodic when used in (1.2), since the same spreading code is repeated in every
symbol interval. Some systems (e.g., CDMA systems for cellular telephony)
operate with long spreading codes, for which the
periodicity is much longer than a single symbol interval. This situation can be
modeled by (1.1) by replacing p(t) in (1.2) by a variant of (1.4) in which the spreading code varies from symbol to
symbol; that is,
Equation 1.6
Spread-spectrum modulation can also take the form of frequency
hopping, in which the carrier frequency in (1.2) is changed over time according to a pseudorandom
pattern. Typically, the carrier frequency changes at a rate much slower than the
symbol rate, a situation known as slow frequency
hopping; however, fast hopping, in which
the carrier changes within a symbol interval, is also possible. Single-carrier
systems, including both types of spread spectrum, are widely used in cellular
standards, in wireless LANs, Bluetooth, and others (see, e.g., [42, 131, 150, 163, 178, 247, 338, 361, 362, 392, 394, 407, 408, 449, 523, 589]).
Multicarrier systems can also be modeled in the framework of
(1.1) by choosing the signaling waveforms
{wi(·)} to be
sinusoidal signals with different frequencies. In particular, (1.2) can be replaced by
Equation 1.7
where now the frequency and phase depend on the symbol number
i but all symbols are transmitted simultaneously
in time with baseband pulse shape p(·). We can
see that (1.2) is the counterpart of this
situation with time and frequency reversed: All symbols are transmitted at the
same frequency but at different times. (Of course, in practice, multiple symbols
are sent in time sequence over each of the multiple carriers in multicarrier
systems.) The individual carriers can also be direct-spread, and the baseband
pulse shape used can depend on the symbol number i. (For example, the latter situation is used in multicarrier CDMA, in which a spreading code is used
across the carrier frequencies.) A particular case of (1.7) is OFDM, in which the baseband pulse shape is a unit
pulse pT, the intercarrier spacing is
1/T cycles per second, and the phases are chosen
so that the carriers are orthogonal at this spacing. (This is the minimal
spacing for which such orthogonality can be maintained.) OFDM is widely believed
to be among the most effective techniques for wireless broadband applications
and is the basis for the IEEE 802.11a high-speed wireless LAN standard (see,
e.g., [354] for a
discussion of multicarrier systems).
An emerging type of wireless modulation scheme is
ultra-wideband (UWB) modulation, in which data are transmitted with no carrier
through the modulation of extremely short pulses. Either the timing or amplitude
of these pulses can be used to carry the information symbols. Typical UWB
systems involve the transmission of many repetitions of the same symbol,
possibly with the use of a direct-sequence type of spreading code from
transmission to transmission (see, e.g., [569] for a basic description of UWB
systems).
Further details on the modulation waveforms above and their
properties will be introduced as needed throughout this treatment.
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