FADING

Fading is the distortion that a carrier-modulated telecommunication signal experiences over certain propagation media. A fading channel
is a communication channel that experiences fading. In wireless systems, fading is due to multipath propagation and is sometimes referred
to as multi path induced fading.

Key concepts
In wireless communications, the presence of reflectors in the environment surrounding a transmitter and receiver create multiple paths that
a transmitted signal can traverse. As a result, the receiver sees the superposition of multiple copies of the transmitted signal, each
traversing a different path. Each signal copy will experience differences in attenuation, delay and phase shift while traveling from the
source to the receiver. This can result in either constructive or destructive interference, amplifying or attenuating the signal power seen at
the receiver. Strong destructive interference is frequently referred to as a deep fade and may result in temporary failure of communication
due to a severe drop in the channel signal-to-noise ratio.

A common example of multipath fading is the experience of stopping at a traffic light and hearing an FM broadcast degenerate into static,
while the signal is re-acquired if the vehicle moves only a fraction of a meter. The loss of the broadcast is caused by the vehicle stopping at
a point where the signal experienced severe destructive interference. Cellular phones can also exhibit similar momentary fades. Fading
channel models are often used to model the effects of electromagnetic transmission of information over the air in cellular networks and
broadcast communication. Fading channel models are also used in underwater acoustic communications to model the distortion caused by
the water. Mathematically, fading is usually modeled as a time-varying random change in the amplitude and phase of the transmitted
signal.

Types of Fading
Fast Fading Slow Fading Flat fading
Selective Fading Rayleigh Fading Rician Fading

Slow versus fast fading ------- The terms slow and fast fading refer to the rate at which the magnitude and phase change
imposed by the channel on the signal changes. The coherence time is a measure of the minimum time required for the magnitude
change of the channel to become decorrelated from its previous value.

 Slow fading arises when the coherence time of the channel is large relative to the delay constraint of the channel. In this regime,
the amplitude and phase change imposed by the channel can be considered roughly constant over the period of use. Slow fading
can be caused by events such as shadowing, where a large obstruction such as a hill or large building obscures the main signal
path between the transmitter and the receiver. The amplitude change caused by shadowing is often modeled using a log-normal
distribution with a standard deviation according to the log-distance path loss model.

 Fast fading occurs when the coherence time of the channel is small relative to the delay constraint of the channel. In this regime,
the amplitude and phase change imposed by the channel varies considerably over the period of use.

In a fast-fading channel, the transmitter may take advantage of the variations in the channel conditions using time diversity to help
increase robustness of the communication to a temporary deep fade. Although a deep fade may temporarily erase some of the information
transmitted, use of an error-correcting code coupled with successfully transmitted bits during other time instances (interleaving) can
allow for the erased bits to be recovered. In a slow-fading channel, it is not possible to use time diversity because the transmitter sees only
a single realization of the channel within its delay constraint. A deep fade therefore lasts the entire duration of transmission and cannot be
mitigated using coding.

The coherence time of the channel is related to a quantity known as the Doppler spread of the channel. When a user (or reflectors in its
environment) is moving, the user's velocity causes a shift in the frequency of the signal transmitted along each signal path. This
phenomenon is known as the Doppler shift. Signals travelling along different paths can have different Doppler shifts, corresponding to
different rates of change in phase. The difference in Doppler shifts between different signal components contributing to a single fading
channel tap is known as the Doppler spread. Channels with a large Doppler spread have signal components that are each changing
independently in phase over time. Since fading depends on whether signal components add constructively or destructively, such channels
have a very short coherence time.In general, coherence time is inversely related to Doppler spread, typically expressed aswhere Tc is the
coherence time, Ds is the Doppler spread, and k is a constant taking on values in the range of 0.25 to 0.5.
Flat versus frequency-selective fading
As the carrier frequency of a signal is varied, the magnitude of the change in amplitude will vary. The coherence bandwidth measures the
separation in frequency after which two signals will experience uncorrelated fading.

 In flat fading, the coherence bandwidth of the channel is larger than the bandwidth of the signal. Therefore, all frequency
components of the signal will experience the same magnitude of fading.
 In frequency-selective fading, the coherence bandwidth of the channel is smaller than the bandwidth of the signal. Different
frequency components of the signal therefore experience decorrelated fading.

Since different frequency components of the signal are affected independently, it is highly unlikely that all parts of the signal will be
simultaneously affected by a deep fade. Certain modulation schemes such as OFDM and CDMA are well-suited to employing frequency
diversity to provide robustness to fading. OFDM divides the wideband signal into many slowly modulated narrowband subcarriers, each
exposed to flat fading rather than frequency selective fading. This can be combated by means of error coding, simple equalization or
adaptive bit loading. Inter-symbol interference is avoided by introducing a guard interval between the symbols. CDMA uses the Rake
receiver to deal with each echo separately. Frequency-selective fading channels are also dispersive, in that the signal energy associated
with each symbol is spread out in time. This causes transmitted symbols that are adjacent in time to interfere with each other. Equalizers
are often deployed in such channels to compensate for the effects of the intersymbol interference.

Fading models Examples of fading models for the distribution of the attenuation are:

 Nakagami fading Weibull fading Rayleigh fading Rician fading

 Dispersive fading models, with several echoes, each exposed to different delay, gain and phase shift, often
constant. This results in frequency selective fading and inter-symbol interference. The gains may be
Rayleigh or Rician distributed. The echoes may also be exposed to Doppler shift, resulting in a time varying
channel model.
 Log-normal shadow fading

Diversity scheme
Terrestrial microwave radio system with two antenna arrays configured for space-diversity. In telecommunications, a diversity scheme
refers to a method for improving the reliability of a message signal by utilizing two or more communication channels with different
characteristics. Diversity plays an important role in combating fading and co-channel interference and avoiding error bursts. It is based on
the fact that individual channels experience different levels of fading and interference. Multiple versions of the same signal may be
transmitted and/or received and combined in the receiver. Alternatively, a redundant forward error correction code may be added and
different parts of the message transmitted over different channels. Diversity techniques may exploit the multipath propagation, resulting in
a diversity gain, often measured in decibels.

The following classes of diversity schemes can be identified:

 Time diversity: Multiple versions of the same signal are transmitted at different time instants. Alternatively, a redundant forward
error correction code is added and the message is spread in time by means of bit-interleaving before it is transmitted. Thus, error
bursts are avoided, which simplifies the error correction.

 Frequency diversity: The signal is transferred using several frequency channels or spread over a wide spectrum that is affected
by frequency-selective fading. Middle-late 20th century microwave radio relay lines often used several regular wideband radio
channels, and one protection channel for automatic use by any faded channel. Later examples include:
o OFDM modulation in combination with subcarrier interleaving and forward error correction
o Spread spectrum, for example frequency hopping or DS-CDMA.

 Space diversity: The signal is transferred over several different propagation paths. In the case of wired transmission, this can be
achieved by transmitting via multiple wires. In the case of wireless transmission, it can be achieved by antenna diversity using
multiple transmitter antennas (transmit diversity) and/or multiple receiving antennas (reception diversity). In the latter case, a
diversity combining technique is applied before further signal processing takes place. If the antennas are far apart, for example at
different cellular base station sites or WLAN access points, this is called macrodiversity. If the antennas are at a distance in the
order of one wavelength, this is called microdiversity. A special case is phased antenna arrays, which also can be utilized for
beamforming, MIMO channels and Space–time coding (STC).

 Polarisation diversity: Multiple versions of a signal are transmitted and received via antennas with different polarization. A
diversity combining technique is applied on the receiver side.
  Multiuser diversity: Multiuser diversity is obtained by opportunistic user scheduling at either the transmitter or the receiver.
Opportunistic user scheduling is as follows: the transmit selects the best user among candidate receivers according to the qualities
of each channel between the transmitter and each receiver. In FDD systems, a receiver must feed back the channel quality
information to the transmitter with the limited level of resolution.

 Cooperative diversity: Achieves antenna diversity gain by utilizing the cooperation of distributed antennas belonging to each
node.

Multipath Fading:- MULTIPATH is simply a term used to describe the multiple paths a radio wave may
follow between transmitter and receiver. Such propagation paths include the ground wave, ionospheric refraction,
reradiation by the ionospheric layers, reflection from the earth’s surface or from more than one ionospheric layer, and so on. Figure 1-
11 shows a few of the paths that a signal can travel between two sites in a typical circuit. One path, XYZ, is the basic ground
wave. Another path, XFZ, refracts the wave at the F layer and passes it on to the receiver at point Z. At point Z, the received signal
is a combination of the ground wave and the sky wave. These two signals, having traveled different paths, arrive at point Z at
different times. Thus, the arriving waves may or may not be in phase with each other. A similar situation may result at point A.
Another path, XFZFA, results from a greater angle of incidence and two refractions from the F layer. A wave traveling that
path and one traveling the XEA path may or may not arrive at point A in phase. Radio waves that are received in phase
reinforce each other and produce a stronger signal at the receiving site, while those that are received out of phase
produce a weak or fading signal. Small alterations in the transmission path may change the phase relationship of the two
signals, causing periodic fading.

Figure 1-11.—Multipath transmission

Multipath fading may be minimized by practices called SPACE DIVERSITY and FREQUENCY DIVERSITY In space diversity,
two or more receiving antennas are spaced some distance apart. Fading does not occur simultaneously at both antennas. Therefore,
enough output is almost always available from one of the antennas to provide a useful signal. In frequency diversity, two transmitters
and two receivers are used, each pair tuned to a different frequency, with the same information being transmitted
simultaneously over both frequencies. One of the two receivers will almost always produce a useful signal. Selective
Fading resulting from multipath propagation varies with frequency since each frequency arrives at the receiving point via a
different radio path. When a wide band of frequencies is transmitted simultaneously, each frequency will vary in the amount of
fading. This variation is called SELECTIVE FADING. When selective fading occurs, all frequencies of the transmitted signal
do not retain their original phases and relative amplitudes. This fading causes severe distortion of the signal and limits the total
signal transmitted. Frequency shifts and distance changes because of daily variations of the different ionospheric layers are summarized
in table 1-1. 1-9

2-44 MULTIPATH FADING occurs when a transmitted signal divides and takes more than one path to a receiver and some of the signals
arrive out of phase, resulting in a weak or fading signal.

Some TRANSMISSION LOSSES that affect radio-wave propagation are ionospheric absorption, ground reflection, and free-space
losses.
ELECTROMAGNETIC INTERFERENCE (emi), both natural and man-made, interfere with radio communications.
The MAXIMUM USABLE FREQUENCY (muf) is the highest frequency that can be used for communications between two locations at
a given angle of incidence and time of day.
The LOWEST USABLE FREQUENCY (luf) is the lowest frequency that can be used for communications between two locations.
Multi path fading telecom definition
Also known as multipath interference (MPI). Signal attenuation and distortion due to multipath propagation. Wireless radio or optical
signals bounce off of physical obstructions they encounter between a transmitter and a receiver. Those signal elements that travel the most
direct routes not only arrive soonest, but also suffer less absorption and diffusion attenuate the least and, therefore, are the strongest. Those
that travel the least direct routes arrive last and are weakest. In broadcast television and poorly installed cable television, ghosting is the
result of multipath fading. In broadcast television and poorly installed cable television, MPI specter, or ghosting, is the result of multipath
fading. Signals that travel different paths but arrive at approximately the same time can cancel each other.All of these factors contribute to
multipath fading. See also attenuation, diffusion, distortion, ghosting, MPI specter, multipath absorption, and propagation.

Multipath Reception
Experiments with mobile communication were done at VHF frequencies, near 50 MHz, already in the 1920s.
Results of these tests revealed a very hostile propagation environment, particularly in urban centers. The signal
quality varied from "excellent" to "no signal". Moving the vehicle over a few meters resulted in dramatic
changes of the received field strength.

The mobile or indoor radio channel is characterized by 'multipath reception': The signal offered to the receiver contains not only a direct
line-of-sight radio wave, but also a large number of reflected radio waves. Even worse in urban centers, the line-of-sight is often blocked
by obstacles, and a collected of differently delayed waves is all what is received by a mobile antenna. These reflected waves interfere with
the direct wave, which causes significant degradation of the performance of the link. If the antenna moves the channel varies with location
and time, because the relative phases of the reflected waves change. This leads to fading: time variations of the received amplitude and
phase. In a non-fading (thus fixed) radio channel the BER decreases rapidly when the signal-to-noise (or signal-to-interference) ratio is
increased. In a fading channel, every now and then the received signal is very weak and many bit errors occur. This phenomenon remains
present, even if the (average) signal-to-noise ratio is large. So the BER only improves very slowly, and with a fixed slope, if plotted on a
log-log scale. (Diversity or error correction can help to make the slope steeper, hence improve performance.)

A wireless system has to be designed in such way that the adverse effect of multipath fading is minimized. In the past, multipath has
notoriously hindered the development of reliable and inexpensive mass-product systems. A better understanding of these phenomena, and
the advent of powerful signal processing techniques contributed to the explosion of digital wireless communication since the 1980s.

The basic model of Rayleigh fading assumes a received multipath signal to consist of a
(theoretically infinitely) large number of reflected waves with independent and Lord Rayleigh, "On the resultant of a large
identically distributed inphase and quadrature amplitudes. This model has played a number of vibrations of the same pitch and of
major role in our understanding of mobile propagation. The model was first proposed in arbitrary phase", Phil. Mag., Vol. 10, August
a comment paper written by Lord Rayleigh in 1889, describing the resulting signal if 1880, pp. 73-78 and Vol. 27, June 1889, pp. 460-
many violinists in an orchestra play in unison, long before its application to mobile radio 469.
reception was recognized.

More recently, this model of many randomly phased sinusoids appeared to appropriately describe the wireless radio channel, and to allow
calculation of outage probabilities, fade durations and many other critical parameters of wireless links. It greatly facilitated the
development systems that can reliably communicate despite the anomalies and unpredictability of the mobile communication channel.

As the demand for mobile communication increases, systems have to be more efficient and cell sizes are chosen smaller and smaller. To
describe microcellular propagation, the Rayleigh model lacked the effect of a dominant line-of-sight component, and Rician model
appeared to be more appropriate. Most conventional digital modulation techniques are sensitive to intersymbol interference unless the
channel symbol rate is small compared to the delay spread of the channel. On the other hand a narrowband signal with bit durations much
longer than the delay spread may vanish completely in fade. A signal received at a frequency and location where reflected waves cancel
each other, is heavily attenuated and may thus suffer large bit error rates.

Models for multipath reception Narrowband Rayleigh, or Rician models mostly address the channel behavior at one frequency
only. Time dispersion, or the Doppler spread is the critical phenomenon. Frequency dispersion and intersymbol interference, on
the other hand, are modeled by the delay spread. A model that combines these aspects is the
See also:

Fast Fading
• Fast fading occurs if the channel impulse response changes rapidly within the symbol duration.
• In other works, fast fading occurs when the coherence time of the channel TD is smaller than the symbol period of the the transmitted
signal T ⇒ TD _ T.
• This causes frequency dispersion or time selective fading due to Doppler spreading.
• Fast Fading is due to reflections of local objects and the motion of the objects relative to those objects.
 Fast Fading
• The receive signal is the sum of a number of signals reflected from local surfaces, and these signals sum in a constructive or destructive
manner = relative phase shift.
• Phase relationships depend on the speed of motion, frequency of transmission and relative path lengths.

SMALL SCALE FADING

Types of Small-Scale Fading

Section 5.3 demonstrated that the type of fading experienced by a signal propagating through a mobile radio channel depends on the nature
of the transmitted signal with respect to the characteristics of the channel. Depending on the relation between the signal parameters (such
as bandwidth, symbol period, etc.) and the channel parameters(such as rms delay spread and Doppler spread), different transmitted signals
will undergo different types of fading. The time dispersion and frequency dispersion mechanisms in a mobile radio channel lead to four
possible distinct effects, which are manifested depending on the nature of the transmitted signal, the channel, and the velocity. While multi
path delay spread leads to time dispersion and frequency selective fading, Doppler spread leads to frequency dispersion and time selective
fading. The two propagation mechanisms are independent of one another. Figure 5.11 shows a tree of the four different types of fading.

Fading Effects Due to Multi path Time Delay Spread Time dispersion due to multipath causes the
transmitted signal to undergo either flat or frequency selective fading.

Flat fading If the mobile radio channel has a constant gain and linear phase response over a bandwidth which is greater than
the bandwidth of the transmitted signal, then the received signal will undergo flat fading. This type of fading is historically the
most common type of fading described in the technical literature. In flat fading, the multipath structure of the channel is such that
the spectral characteristics of the transmitted signal are preserved at the receiver. However the strength of the received signal
changes with time, due to fluctuations in the gain of the channel caused by multipath. The characteristics of a flat fading channel are
illustrated in Figure 5.12. It can be seen from Figure 5.12 that if the channel gain changes over time, a change of amplitude occurs
in the received signal.

Flat fading channels are also known as amplitude varying channels and are sometimes referred to as narrowband channels, since the
bandwidth of the applied signal is narrow as compared to the channel flat fading bandwidth. Typical flat fading channels cause deep fades,
and thus may require 20 or 30 dB more transmitter power to achieve low bit error rates during times of deep fades as compared to systems
operating over non-fading channels. The distribution of the instantaneous gain of flat fading channels is important for designing radio
links, and the most common amplitude distribution is the Rayleigh distribution. The Rayleigh flat fading channel model assumes that the
channel induces an amplitude which varies in time according to the Rayleigh distribution.

Frequency Selective Fading

If the channel possesses a constant-gain and linear phase response over a bandwidth that is smaller than the bandwidth of transmitted
signal, then the channel creates frequency selective fading on the received signal. Under such conditions, the channel impulse response has
a multi path delay spread which is greater than the reciprocal bandwidth of the transmitted message waveform. When this occurs, the
received signal includes multiple versions of the transmitted waveform which are attenuated (faded) and delayed in time, and hence the
received signal is distorted.

Frequency selective fading is due to time dispersion of the transmitted symbols within the channel. Thus the channel induces
intersymbol interference (ISI). Viewed in the frequency domain, certain frequency components in the received signal spectrum
have greater gains than others. Frequency selective fading channels are much more difficult to model than flat fading channels
since each multipath signal must be modeled and the channel must be considered to be a linear filter. It is for this reason that
wideband multipath measurements are made, and models are developed from these measurements. When analyzing mobile
communication systems, statistical impulse response models such as the two-ray Rayleigh fading model (which considers the
impulse response to be made up of two delta functions which independently fade and have sufficient time delay between them
to induce frequency selective fading upon the applied signal), or computer generated or measured impulse responses, are
generally used for analyzing frequency selective small-scale fading. Figure 5.13 illustrates the characteristics of a frequency
selective fading channel.

Fading Effects Due to Doppler Spread Fast Fading

Depending on how rapidly the transmitted baseband signal changes as compared to the rate of change of the channel, a channel may be
classified either as a fast fading or slow fading channel. In a fast fading channel, the channel impulse response changes rapidly within the
symbol duration. That is, the coherence time of the channel is smaller than the symbol period of the transmitted signal. This causes
frequency dispersion (also called time selective fading) due to Doppler spreading, which leads to signal distortion. Viewed in the frequency
domain, signal distortion due to fast fading increases with increasing Doppler spread relative to the bandwidth of the transmitted signal.

It should be noted that when a channel is specified as a fast or slow fading channel, it does not specify whether the channel is flat fading or
frequency selective in nature. Fast fading only deals with the rate of change of the channel due to motion. In the case of the flat fading
channel, we can approximate the impulse response to be simply a delta function (no time delay). Hence, a flat fading, fast fading channel
is a channel in which the amplitude of the delta function varies faster than the rate of change of the transmitted baseband signal. In the case
of a frequency selective, fast fading channel, the amplitudes, phases, and time delays of any one of the multi path components vary faster
than the rate of change of the transmitted signal. In practice, fast fading only occurs for very low data rates.

Slow Fading

In a slow fading channel, the channel impulse response changes at a rate much slower than the transmitted base band signal s(t). In this
case, the channel may be assumed to be static over one or several reciprocal bandwidth intervals. In the frequency domain, this implies that
the Doppler spread of the channel is much less than the bandwidth of the baseband signal. It should be clear that the velocity of the mobile
(or velocity of objects in the channel) and the baseband signaling determines whether a signal undergoes fast fading or slow fading. The
relation between the various multipath parameters and the type of fading experienced by the signal are summarized in Figure 5.14. Over
the years, some authors have confused the terms fast and slow fading with the terms large-scale and small-scale fading. It should be
emphasized that fast and slow fading deal with the relationship between the time rate of change in the channel and the transmitted signal,
and not with propagation path loss models.

Matrix illustrating type of fading experienced by a signal as a function of: (a) symbol period; and (b) base band signal bandwidth.
Frequency Reuse
 Extensive frequency reuse allows for many users to be supported at the same time.

 Total spectrum allocated to the service provider is broken up into smaller bands.

 A cell is assigned one of these bands. This means all communications (transmissions to and from users) in this cell occur over these
frequencies only.

 Neighboring cells are assigned a different frequency band.

 This ensures that nearby transmissions do not interfere with each other.

 The same frequency band is reused in another cell that is far away. This large distance limits the interference caused by this co-
frequency cell.

 More on frequency reuse a bit later.

Speech coding
Speech coding is the application of data compression of digital audio signals containing speech. Speech coding uses speech-specific
parameter estimation using audio signal processing techniques to model the speech signal, combined with generic data compression
algorithms to represent the resulting modeled parameters in a compact bit stream.The two most important applications of speech coding
are mobile telephony and Voice over IP. The techniques used in speech coding are similar to that in audio data compression and audio
coding where knowledge in psychoacoustics is used to transmit only data that is relevant to the human auditory system.

For example, in narrowband speech coding, only information in the frequency band 400 Hz to 3500 Hz is transmitted but the reconstructed
signal is still adequate for intelligibility.Speech coding differs from other forms of audio coding in that speech is a much simpler signal
than most other audio signals, and that there is a lot more statistical information available about the properties of speech. As a result, some
auditory information which is relevant in audio coding can be unnecessary in the speech coding context. In speech coding, the most
important criterion is preservation of intelligibility and "pleasantness" of speech, with a constrained amount of transmitted data.

It should be emphasised that the intelligibility of speech includes, besides the actual literal content, also speaker identity, emotions,
intonation, timbre etc. that are all important for perfect intelligibility. The more abstract concept of pleasantness of degraded speech is a
different property than intelligibility, since it is possible that degraded speech is completely intelligible, but subjectively annoying to the
listener.In addition, most speech applications require low coding delay, as long coding delays interfere with speech interaction.

Sample commanding viewed as a form of speech coding

From this viewpoint, the A-law and μ-law algorithms used in traditional PCM digital telephony can be seen as a very early precursor of
speech encoding, requiring only 8 bits per sample but giving effectively 12 bits of resolution. Although this would generate unacceptable
distortion in a music signal, the peaky nature of speech waveforms, combined with the simple frequency structure of speech as a periodic
waveform with a single fundamental frequency with occasional added noise bursts, make these very simple instantaneous compression
algorithms acceptable for speech.A wide variety of other algorithms were tried at the time, mostly variants on delta modulation, but after
careful consideration, the A-law/μ-law algorithms were chosen by the designers of the early digital telephony systems. At the time of their
design, their 33% bandwidth reduction for a very low complexity made them an excellent engineering compromise. Their audio
performance remains acceptable, and there has been no need to replace them in the stationary phone network.

Modern speech compression

Much of the later work in speech compression was motivated by military research into digital communications for secure military radios,
where very low data rates were required to allow effective operation in a hostile radio environment. At the same time, far more processing
power was available, in the form of VLSI integrated circuits, than was available for earlier compression techniques. As a result, modern
speech compression algorithms could use far more complex techniques than were available in the 1960s to achieve far higher compression
ratios.

These techniques were available through the open research literature to be used for civilian applications, allowing the creation of digital
mobile phone networks with substantially higher channel capacities than the analog systems that preceded them. The most common speech
coding scheme is Code Excited Linear Prediction (CELP) coding, which is used for example in the GSM standard. In CELP, the modelling
is divided in two stages, a linear predictive stage that models the spectral envelope and code-book based model of the residual of the linear
predictive model. In addition to the actual speech coding of the signal, it is often necessary to use channel coding for transmission, to avoid
losses due to transmission errors. Usually, speech coding and channel coding methods have to be chosen in pairs, with the more important
bits in the speech data stream protected by more robust channel coding, in order to get the best overall coding results. The Speex project is
an attempt to create a free software speech coder, unencumbered by patent restrictions

Frequency reuse Example of frequency reuse factor or pattern 1/4

The increased capacity in a cellular network, compared with a network with a single transmitter, comes from the fact that the
same radio frequency can be reused in a different area for a completely different transmission. If there is a single plain
transmitter, only one transmission can be used on any given frequency. Unfortunately, there is inevitably some level of
interference from the signal from the other cells which use the same frequency. This means that, in a standard FDMA system,
there must be at least a one cell gap between cells which reuse the same frequency.

The frequency reuse factor is the rate at which the same frequency can be used in the network. It is 1/K (or K according to
some books) where K is the number of cells which cannot use the same frequencies for transmission. Common values for the
frequency reuse factor are 1/3, 1/4, 1/7, 1/9 and 1/12 (or 3, 4, 7, 9 and 12 depending on notation).

In case of N sector antennas on the same base station site, each with different direction, the base station site can serve N
different sectors. N is typically 3. A reuse pattern of N/K denotes a further division in frequency among N sector antennas
per site. Some current and historical reuse patterns are 3/7 (North American AMPS), 6/4 (Motorola NAMPS), and 3/4 (GSM).

If the total available bandwidth is B, each cell can only utilize a number of frequency channels corresponding to a bandwidth
of B/K, and each sector can use a bandwidth of B/NK.

Code division multiple access-based systems use a wider frequency band to achieve the same rate of transmission as FDMA,
but this is compensated for by the ability to use a frequency reuse factor of 1, for example using a reuse pattern of 1/1. In other
words, adjacent base station sites use the same frequencies, and the different base stations and users are separated by codes
rather than frequencies. While N is shown as 1 in this example, that does not mean the CDMA cell has only one sector, but
rather that the entire cell bandwidth is also available to each sector individually.

Depending on the size of the city, a taxi system may not have any frequency-reuse in its own city, but certainly in other nearby
cities, the same frequency can be used. In a big city, on the other hand, frequency-reuse could certainly be in use.