In principle there exists the well known duality between TDMA and FDMA (see [Bertsekas and Gallager, 1987], p. 113 ff.). However, in the wireless environment propagation related factors have a strong influence on the comparison between FDMA and TDMA. Specifically, the duration of a transmitted symbol is much longer in FDMA than in TDMA. As an immediate consequence, an equalizer is typically not required in an FDMA based system because the delay spread is small compared to the symbol duration.
To illustrate this point, consider a hypothetical system which transmits
information at a constant rate of 50 Kbit/s.
This rate would be sufficient to support 32 Kbit/s ADPCM speech encoding, some
coding for error protection, and control overhead.
If we assume further that some form of QPSK modulation is employed the resulting symbol
duration is 40 
sec.
In relation to delay spreads of approximately 1 sec in the cordless
application and 10 sec in cellular systems this duration is large enough
that only little intersymbol interference is introduced.
In other words, the channel is frequency non-selective, i.e., all spectral
components of the signal are affected equally by the channel.
In the cordless application an equalizer is certainly not required; cellular
receivers may require equalizers capable of removing intersymbol interference
between adjacent bits.
Furthermore, it is well known that intersymbol interference between
adjacent bits can be removed without loss in SNR by using Maximum-Likelihood
Sequence Estimation (e.g. [Proakis, 1989], p. 622).
Hence, rather simple receivers can be employed in FDMA systems at these
data rates.
However, there is a flip-side to the above argument.
Recall that the Doppler spread,
which characterizes the rate at which the channel impulse response changes,
is given approximately by 
,
where v denotes the speed of the mobile user, c is the propagation speed of the
electro-magnetic waves carrying the signal, and 
is the carrier frequency.
Thus for systems operating in the vicinity of 1 GHz, 
will be less than
1 Hz in the cordless application and typically
about 100 Hz for a mobile traveling on a highway.
In either case, the
signal bandwidth is much larger than the Doppler spread and the channel
can be characterized as slowly fading.
While this allows tracking of the carrier phase and the use of coherent
receivers it also means that fade durations are long
in comparison to the symbol duration
and can cause long
sequences of bits to be subject to poor channel conditions.
The problem is compounded by the fact that the channel is frequency
non-selective because it implies that the entire signal is affected by a fade.
To overcome these problems either time diversity, frequency diversity, or spatial diversity could be employed. Time-diversity can be accomplished by a combination of coding and interleaving if the fading rate is sufficiently large. For very slowly fading channels, like in the cordless application, the necessary interleaving depth would introduce too much delay to be practical. Frequency diversity can be introduced simply by slow frequency hopping, a technique which prescribes user to change the carrier frequency periodically. Frequency hopping is a form of spectrum spreading because the bandwidth occupied by the resulting signal is much larger than the symbol rate. However, in contrast to direct sequence spread-spectrum discussed below the instantaneous bandwidth is not increased. The jumps between different frequency bands effectively emulate the movement of the portable and, thus, should be combined with the just described time-diversity methods. Spatial diversity is provided by the use of several receive or transmit antennas. At carrier frequencies exceeding 1 GHz antennas are small and two or more antennas can be accommodated even in the hand set. Furthermore, if FDMA is combined with time-division duplexing multiple antennas at the base station can provide diversity on both up-link and down-link. This is possible because the channels for the two links are virtually identical and the base station, using channel information gained from observing the portable's signal, can transmit signals at each antenna such that they combine coherently at the portable's antenna. Thus, signal processing complexity is moved to the base station extending the portable's battery life.
