Part IV MULTIPLE ACCESS AND ADVANCED TRANSCEIVER SCHEMES 363
17.2 Frequency Division Multiple Access
17.2.1 Multiple Access via Frequency Division Multiple Access
FDMA is the oldest, and conceptually most simple, multiaccess method. Each user is assigned a frequency (sub)band – i.e., a (usually contiguous) part of the available spectrum (see Figure 17.1).
The assignment of frequency bands is usually done during call setup, and retained during the whole call. FDMA is usually combined with the Frequency Domain Duplexing (FDD) (see Section 17.5), so that two frequency bands (with a fixed duplex distance) are assigned to each user: one for downlink (BS-to-MS) and one for uplink (MS-to-BS) communication.
Power-spectral density
Frequency Time
Figure 17.1 Principle of frequency division multiple access.
Pure FDMA is conceptually very simple, and has some advantages for implementation:
• The transmitter (TX) and receiver (RX) require littledigital signal processing. However, this is not so important in practice anymore, as the costs for digital processing are continuously decreasing.
• (Temporal) synchronization is simple. Once synchronization has been established during the call setup, it is easy to maintain it by means of a simple tracking algorithm, as transmission occurs continuously.
However, pure FDMA also has significant disadvantages, especially when used for speech communications. These problems arise from spectral efficiency considerations, as well as from sensitivity to multipath effects:
• Frequency synchronization and stability are difficult: for speech communications, each frequency subband is quite narrow (typically between 5 and 30 kHz). Local oscillators thus must be very
Multiple Access and the Cellular Principle 367
accurate and stable; jitters in the carrier frequency result in adjacent channel interference. High spectral efficiency also requires the use of very steep filters to extract the desired signal. Both accurate oscillators and steep filters are expensive, and thus undesirable. If they are not admissible, guard bands can be used to mitigate filter requirements. This, however, reduces the spectral efficiency of the system.
• Sensitivity to fading: since each user is assigned a distinct frequency band, these bands are narrower than for other multiaccess methods (compare TDMA, CDMA) – i.e., 5–30 kHz. For such narrow subbands, fading is flat in practically all environments. This has the advantage that no equalization is required; the drawback is that there is no frequency diversity. Remember that frequency diversity is mainly provided by signal components that are more than one channel coherence bandwidth apart (see Chapters 13 and 16).
• Sensitivity to random Frequency Modulation (FM): due to the narrow bandwidth, the system is sensitive to random FM: the Bit Error Rate (BER) due to random FM is proportional to(νmaxTS)2 (see Chapter 12). Thus, it is inversely proportional to the square of the bandwidth. On the positive side, appropriate signal-processing schemes can not only mitigate these effects but even exploit them to obtain time diversity. Note that the situation here is dual to wideband systems, where delay dispersion can be a drawback, but equalizers can turn them into an asset by exploiting frequency diversity.
• Intermodulation: the BS needs to transmit multiple speech channels, each of which is active the whole time. Typically, a BS uses 20–100 frequency channels. If these signals are amplified by the same power amplifier, third-order modulation products can be created, which lie at undesirable frequencies – i.e., within the transmit band. We thus need either a separate amplifier for each speech channel, or a highly linear amplifier for the composite signal – each of these solutions makes a BS more expensive.
It is for these reasons that FDMA is mostly used for the following applications:
• Analog communications systems: here, FDMA is the only practicable multiple access method.
• Combination of FDMA with other multiple access methods: the spectrum allocated for a service (or a network operator) is divided into larger subbands, each of which is used for serving a groupof users. Within this group, multiple access is done by means of another multiple access method – e.g., TDMA or CDMA. Most current wireless systems use FDMA in that way (see Chapters 24–28).
• High-data-rate systems: the disadvantages of FDMA are mostly relevant if each user requires only a small bandwidth – e.g., 20 kHz. The situation can be different for wireless Local Area Networks (LANs), where a single user requires a bandwidth on the order of 20 MHz, and only a few frequency channels are available.
17.2.2 Trunking Gain
We will now compute how many subscribers can be covered with an FDMA system by one BS.
This seemingly simple question has become a separate branch of communications theory (often calledqueuing theory), with several textbooks dedicated to it (see, e.g., Gross and Harris [1998]).
In this subsection, we describe in a very simplified way how to compute the required number of communications channels so that a given number of users can be served with “sufficient quality.” We assume, for present purposes, a pure FDMA system that does not need any channels for signaling.
Furthermore, we assume a system that is designed purely for speech communications. For the following, we define the offered traffic, as the product of the call arrival rate and the average call holding time (duration); the offered traffic is usually said to have the unit “Erlang,” though this is really a dimensionless quantity (call arrival rate is in units of 1/s; call holding time has units of s).
There are two extreme cases in the planning of a cellular network:
1. Worst case design: it is assumed that all users want to call simultaneously. If the network operator wants to serve 700 users per cell, it has to provide 700 speech channels. Of course such a network should never be built in practice – this would be like designing a hospital that can treat all inhabitants of a city at the same time.
2. Best case design: we know that a typical user uses a phone only 20 min per day; if there are 700 potential users per cell, then 14,000 minutes of call time are actually used. A system with 10 speech channels per cell offers 24∗60∗10=14,400 minutes of talk time, and could thus supply the required number of users. However, this computation assumes that all users call sequentially–i.e., new users dial in as soon as old ones have finished their calls – and they do so evenly distributed over a 24-hour period.
Obviously, neither of the two extreme cases is realistic. The art of network design is, to a considerable degree, to predict the call behavior of users, and derive the physical infrastructure (available number of speech channels) that guarantees an acceptablegrade of service.
Several factors influence this planning process:
1. The number and duration of calls depend on the time of day. We therefore define abusy hour (usually around 10h00 and 16h00), which is defined as the hour when most calls are made. The traffic during that busy hour determines the required network capacity.
2. The spatial distribution of users is time variant. While business districts (city centers) usually see a lot of activity during the daytime, suburbs and entertainment districts experience more traffic during the nighttime.
3. Telephoning habits change over the years. While in the late 1980s, calls from cellular phones were usually limited to a few minutes, now hour-long calls have become quite common.
4. Changing user habits are also related to the offering of new services (e.g., data connections) and new pricing structures (e.g., free calls in the evening hours). The strategy of selling “minute accounts” that have to be used up each month also leads to longer talk times than a pricing strategy of charging per minute.
Based on statistical knowledge of user habits, we can now design a system thatwith a certain probability allows a given number of users per cell to make calls. If, through a statistical fluke, more users want to telephone simultaneously, some of the calls will be blocked. Note that the carried traffic is the offered traffic, multiplied by 1−Prblock.
For the computation of the blocking probability of a simplified system, we make the following assumptions: (i) the times when the calls are placed are statistically independent, (ii) the duration of calls is an exponentially distributed random variable, (iii) if a user is rejected, his/her next call attempt is made statistically independent of the previous attempt (i.e., behaves like a new user).1 Such a system is called anErlang-B system; theprobability of call blocking can be shown to be
Prblock= TtrNc/NC!
NC
k=0
Ttrk/ k!
(17.1)
where NC is the number of speech channels (per cell), and Ttr is the average offered traffic.
Figure 17.2 shows the relationship graphically. We see that the ratio of required channels to offered
1This obviously does not agree with reality. Typically, a blocked user retries immediately. After being blocked several times within a short time interval, she or he usually gives up and places the next call after a much longer wait-time.
Multiple Access and the Cellular Principle 369
10 × trunking gain
Blocking probability
Offered traffic/Erlang 1
NC = 1
NC = 2
NC = 3 NC = 5
NC = 8 NC = 10
NC = 20 NC = 30
NC = 50 NC = 80
NC = 100
NC = 15 0.1
0.01
0.001
0.1 1 10 100
Figure 17.2 Blocking probability in an Erlang-B system.NCis the number of available speech channels. As an example, the admissible traffic going fromNC=2 toNC=20 increases from 0.15 to approx. 12 Erlang at 0.01 blockage probability; since the available number of speech channels increases only by a factor 10, the trunking gain is a factor 8.
traffic is very high ifNCis small, especially for low required blocking probabilities. For example, for a required blocking probability of 1%, the ratio of possible offered traffic to available channels is less than 0.1 if NC=2. If NC is very large, then the ratio is only slightly less than unity, and becomes almost independent of the required blocking probability. Assuming again a required blocking probability of 1%, the ratio of admissible offered traffic to available channels is about 0.9 forNC=50.
An alternative model, called Erlang-C, assumes that any user that is not immediately assigned a channel is transferred to a waiting loop, and assigned a channel as soon as it becomes available.
Theprobability that a user is put on hold is
Prwait= TtrNC TtrNC+NC!
1−NTtrCNC−1 k=0 Ttrk/ k!
(17.2)
and the average wait-time is
twait=Prwait Tcall
NC−Ttr (17.3)
whereTcall is the average duration of the call.
Example 17.1 Consider an Erlang-C system where users are active 50% of the time, and the average call duration is 5 minutes. It is required that no more than 5% of all calls are put into a waiting loop. How many channels are required fornuser=1, 8, 30 users? What is the average wait-time in each of these cases?
SinceTtr=0.5ãnuseris the average offered traffic, we need to findNCthat fulfills:
0.05≥ (0.5ãnuser)NC (0.5ãnuser)NC+NC!
1−0.5ãnNCuserNC−1 k=0
(0.5ãnuser)k k!
(17.4)
This equation needs to be solved numerically; the results are given in Table 17.1 below.
WithTcall=5 min, the average wait-time is twait=Prwait 5
NC−0.5ãnuser (17.5)
The required number of channels to fulfill inequality and the resulting average wait-time is Table 17.1 Parameters of the considered Erlang-C system
nuser 1 8 30
NC 3 9 23
Prwait 0.0152 0.0238 0.0380
twait 0.0304 0.0238 0.0238
The probability that a call can be placed, and is not blocked, is an important part of service quality: remember that quality of service is defined as 100% minus the percentage of blocked calls, minus ten times the percentage of lost calls (Section 1.3.7). In an FDMA system, a large system load can lead only to blocked calls, but not lost calls, as long as each user stays in the coverage area of his/her BS (note that in this section, we are neglecting call blocking or dropping due to too-high BER). However, calls can be dropped when a user with an ongoing call tries to move to a different cell whose BS is already fully occupied. And as we will see in Section 17.6, a fully loaded system also increases interference with neighboring cells, making the links in that cell more sensitive to fluctuations in signal strength, and possibly increasing the number of dropped calls due to insufficient Signal-to-Noise Ratio (SNR) and Signal-to-Interference Ratio (SIR).
Summarizing, we find that the number of users that can be accommodated with a given quality of service increases faster than linearly with the number of available speech channels. The difference between actual increase and linear increase is called the trunking gain. From a purely technical point of view, it is thus preferable to have a large pool of speech channels that serves all users.
This situation could be fulfilled, e.g., were there only a single operator for cellular systems, owning the complete spectrum assigned to cellular services. The reasons fornot choosing this approach are political (pricing, monopoly), not technical.2
Example 17.2 In an Erlang-B system, 30 channels are available. A blocking probability of less than 2% is required. What is the traffic that can be served if there is one operator or three operators?
2An approach envisioned in the U.S.A. in the early days of cellular telephony was to assign the available spectrum to exactly two providers, thus striking a compromise between political requirement (avoiding a monopoly) and technical expediency.
Multiple Access and the Cellular Principle 371
1. By inserting the required blocking probability Pblock=0.02 and the number of channels NC=30 into Eq. (17.1), we get:
0.02= Ttr30/30!
30 k=0
Ttrk/ k!
(17.6)
Solving this equation forTtr, we get:
Ttr=21.9 (17.7)
2. Similarly, sharing the 30 speech channels among the three operators, each havingNC=10 speech channels, results in an average trafficTtr of each operator of:
Ttr=5.1 (17.8)
Hence, the total average traffic that can be handled by all three operators together is
Ttr,tot=3ã5.1=15.3 (17.9)