Frequency Division Multiple Access

As mentioned above, in FDMA non-overlapping frequency bands are allocated to different users on a continuous time basis. Hence, signals assigned to different users are clearly orthogonal, at least ideally. In practice, out-of-band spectral components can not be completely suppressed leaving signals not quite orthogonal. This necessitates the introduction of guard bands between frequency bands to reduce adjacent channel interference, i.e., inference from signals transmitted in adjacent frequency bands (see also Figure 1(a)).

It is advantageous to combine FDMA with time-division duplexing (TDD) to avoid simultaneous reception and transmission which would require insulation between receive and transmit antennas. In this scenario, the base station and portable take turns using the same frequency band for transmission. Nevertheless, combining FDMA and frequency division duplex is possible in principle as is evident from the analog FM-based systems deployed throughout the world since the early 1980’s.

Channel Considerations

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 μsec. In relation to delay spreads of approximately 1 μsec in the cordless application and 10 μsec 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 B_d = f_c, where v denotes the speed of the mobile user, c is the propagation speed of the electro-magnetic waves carrying the signal, and f_c is the carrier frequency. Thus for systems operating in the vicinity of 1 GHz, B_d 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 B_d 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.

Influence of Antenna Height

In the cellular mobile environment base station antennas are raised considerably to increase the coverage area. Antennas mounted on towers and rooftops are a common sight and antenna heights of 50 meters above ground are no exceptions. Besides increasing the coverage area, this has the additional effect that frequently there exists a better propagation path between two base station antennas than between a mobile and the base station (see Figure 2).

Assuming that FDMA is used in conjunction with TDD as motivated above, then base stations and mobiles transmit on the same frequency. Now, unless there is tight synchronization between all base stations, signals from other base stations will interfere with the reception of signals from portables at the base station. To keep the interference at acceptable levels it is necessary to increase the re-use distance, i.e., the distance between cells using the same frequencies. In other words, sufficient insulation in the spatial domain must be provided to facilitate the separation of signals. Notice, that these comments apply equally to co-channel and adjacent channel interference.

This problem does not arise in cordless applications. Base station antennas are generally of the same height as user sets. Hence, interference created by base stations is subject to the same propagation conditions as signals from user sets. Furthermore, in cordless telephone applications there are frequently attenuating obstacles, like walls, between base stations which reduce intra-cell interference further. Notice that this reduction is vital for the proper functioning of cordless telephones as there is typically no network planning associated with installing a cordless telephone. As a safety feature, to overcome intra-cell interference, adaptive channel management strategies, based on sensing interference levels, can be employed.

Example: CT2

The CT2 standard was originally adopted in 1987 in Great Britain and improved with a common air interface (CAI) in 1987. The CAI facilitates interoperability between equipment from different vendors while the original standard only guarantees non-interference. The CT2 standard is used in home and office cordless telephone equipment and has been used for telepoint applications [Goodman, 1991b].

CT2 operates in the frequency band 864–868 MHz and uses carriers spaced at 100 KHz. FDMA with time division duplexing is employed. The combined gross bit rate is 72 Kbit/s, transmitted in frames of 2 ms duration of which the first half carries down-link and the second half carries up-link information. This set-up supports a net bit rate of 32 Kbit/s of user data (32 Kbit/s ADPCM encoded speech) and 2 Kbit/s control information in each direction. The CT2 modulation technique is binary frequency shift keying.

Further Remarks

From the discussion above it is obvious that FDMA is a good candidate for applications like cordless telephone. In particular the simple signal processing make it a good choice for inexpensive implementation in the benign cordless environment. The possibility to concentrate signal processing functions in the base station strengthens this aspect.

In the cellular application, on the other hand, FDMA is inappropriate because of the lack of “built-in” diversity, and the potential for severe intra-cell interference between base stations. A further complication arises from the difficulty of performing hand-overs if base-stations are not tightly synchronized.

For PCS the decision is not as obvious. Depending on whether the envisioned PCS application resembles more a cordless PBX than a cellular system FDMA may be an appropriate choice. We will see below that it is probably better to opt for a combined TDMA/FDMA or a CDMA based system to avoid the pitfalls of pure FDMA systems and still achieve moderate equipment complexities.

Finally, there is the problem of channel assignment. Clearly, it is not reasonable to assign a unique frequency to each user as there are not sufficiently many frequencies and the spectral resource would be unused whenever the user is idle. Instead, methods which allocate channels on demand can make much more efficient use of the spectrum. Such methods will be discussed further during the description of TDMA systems.