Analog Carrier Signal Is Modulated Computer Science Essay


Modulation is the process of changing one or more properties of a carrier wave with a modulating signal which contains the information to be transmitted. Modulation techniques can be categorized into two classes namely the analog and digital modulation technique. Analog modulation is further divided into amplitude modulation and angle modulation. The angle modulation is further classified into phase modulation and frequency modulation. Digital modulation techniques are more important for modern wireless systems. Digital modulation offers a number of advantages over analog modulation like higher spectral efficiency, powerful error correction techniques, resistance to channel impairments, more efficient multiple access strategies and better security and privacy.

2 Digital Modulation

In digital modulation, an analog carrier signal is modulated by a digital bit stream. There are three major classes of digital modulation techniques used for transmission of digitally represented data:

Phase-shift keying(PSK)

Frequency-shift keying(FSK)

Amplitude-shift keying(ASK)

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Phase-shift keying(PSK) is a digital modulation scheme that transmits data by modulating the phase of the carrier wave. PSK uses a finite number of phases, each allocated a unique pattern of binary bits. Each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase.

Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave. The simplest FSK is binary FSK (BFSK). BFSK literally implies using a couple of discrete frequencies to transmit binary (0s and 1s) information. With this scheme, the "1" is called the mark frequency and the "0" is called the space frequency.

Amplitude-shift keying (ASK) is a form of modulation that represents digital data as variations in the amplitude of a carrier wave. The amplitude of an analog carrier signal varies in accordance with the bit stream (modulating signal), keeping frequency and phase constant. The amplitude level can be used to represent binary logic 0s and 1s. [1]

Differential Phase Shift Keying (DPSK)

DPSK is a common form of phase modulation that transmits data by modulating the phase of the carrier wave. DPSK can be considered as the non-coherent version of PSK. Phase synchronization is removed using differential encoding that is the encoding of bits 1 and 0 is done via the phase difference between two successive bits. To send bit "0", the current signal waveform is phase advanced by 1800 and to send bit "1", the phase remains unchanged. DPSK signals can be generated by combining two basic operations

Differential encoding of the information binary bits

Phase shift keying

The differential encoding process starts with an arbitrary first bit, serving as a reference. Let {mi} be the input information binary sequence and let {di} be the differentially binary encoded bit sequence.

If the incoming bit mi is "1", the symbol di remain unchanged with respect to the previous bit di-1

If the incoming bit mi is "0", the symbol di changes with respect to the previous bit di-1

The reference bit is taken here as "1".

The DSK transmitter diagram is as shown below.


QAM is a modulation technique that employs both phase modulation and amplitude modulation. The word "quadrature" comes from the fact that the phase modulation states are 900 apart from each other. 64-QAM is 64 possible signal combinations with each symbol represent 6 bits (26=64). 64-QAM is a complex modulation scheme but gives rise to high spectral efficiency. This digital frequency modulation technique is used in the transmission digital signals such as digital cable TV and cable Internet service. 64-QAM is very efficient since it supports up to 28-Mbps transfer rates over a single 6-MHz channel. However, 64-QAM is prone to interference making it less suitable to noisy upstream transmissions.

Multipath Fading

Fading refers to the distortion that a carrier-modulated telecommunication signal experiences over certain propagation media. In wireless systems fading is due to multipath propagation and is sometimes referred to as multipath induced fading. In wireless telecommunications, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Atmospheric ducting, ionosphere reflection and refraction, and reflection from terrestrial objects, such as mountains and buildings are causes of multipath. Due to multipath signal propagation paths, multiple signals will arrive at the receiver and the actual signal levels is the vector sum of all the signals. The effects of multipath include constructive and destructive interference, and phase shifting of the signal [2]. The rapid signal-level fluctuation in time that a signal experiences due to multipath distortion is called fading.

Causes of Fading

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Fading is caused by different physical phenomenon:

Doppler Shift

There is always a relative motion between the cell-site transmitter and the mobile receiver. As a result, Doppler effect occurs in the received carrier frequency. Doppler spectrum is the spectrum of the received signal strength. Multipath fading provides the distributions of the amplitude of a radio signal. It is important to know for what time signal strength will be below a pre-defined threshold value, that is, the duration of fade, and how often it crosses the threshold value, that is, frequency of transitions or fading rate. Doppler effect results in the inaccurate operation of the system.

Multipath propagation, speed of mobile unit, speed of reflecting objects, and Doppler shift are the main causes of fading. Multipath propagation can result in a positive or negative Doppler shift. As a mobile unit moves around, the resulting reception of waves reflected from different objects can also result in a positive or negative Doppler shift.

, where v is the constant velocity a mobile is moving, vs is the velocity of the source, f' is the observed frequency and f is the emitted frequency.

From the above equation, it can be observed that the detected frequency increases for objects moving towards the observer and decreases when the source moves away. This phenomena is known as the Doppler effect.


Refection occurs when a signal encounters a surface that is large relative to the wavelength of the signal. Radio waves may be reflected from various substances or objects they meet when travelling between the transmitting and receiving sites. The amount of reflection depends on the reflecting material. Smooth metal surfaces of good electrical conductivity are efficient reflectors of radio waves. The surface of the Earth itself is a fairly good reflector. The radio wave is not reflected from a single point on the reflector but rather from an area on its surface. The size of the area required for reflection to take place depends on the wavelength of the radio wave and the angle at which the wave strikes the reflecting substance. When radio waves are reflected from flat surfaces, a phase shift in the alternations of the wave occurs. The shifting in phase relationship of reflected radio waves is one of the major reasons for fading. [3]


Diffraction is the name given to the mechanism by which waves enter into the shadow of an obstacle. Diffraction occurs at the edge of an impenetrable body that is large compare to wavelength of radio wave. A radio wave that meets an obstacle has a natural tendency to bend around the obstacle. The bending, called diffraction, results in a change of direction of part of the wave energy from the normal line-of-sight path. This change makes it possible to change the receive energy around the edges of an obstacle. The ratio of the signal strengths without and with the obstacle is referred to as the diffraction loss. The diffraction loss is affected by the pass geometry and the frequency of operation. The signal strength will fall by 6 dB as the receiver approaches the shadow boundary, but before it enters into the shadow region. Deep in the shadow of an obstacle, the diffraction loss increases with 10*log(frequency). If the frequency is doubled, the loss will increase by 3 dB. This establishes a general truth, namely that radio waves of longer wavelength will penetrate more deeply into the shadow of an obstacle.



When an electromagnetic wave is incident on a rough surface, the wave is not so much reflected as "scattered". Scattering is the process by high small particles suspended in a medium of a different index of refraction diffuses a portion of the incident radiation in all directions. Scattering occurs when incoming signal hits an object whose size is in the order of the wavelength of the signal or less.


Types of fading

According to the effect of multipath, there are two types of fading

1. Large scale/ Long term fading/ Slow fading

2. Small scale/ Short term fading/ Fast fading

Large scale fading

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When fading duration is very long and signal attenuation is large, it is called as large scale fading. The large scale fading is due to several factors such as atmosphere, large pathloss, shadowing, trees and foliage. Such kind of fading is usually low observed I rural areas. This slow changing fading is referred as slow fading. Large scale fading can be compensated by increasing transmitter power so that received signal can be within certain limits. [3]

Small scale fading

When fading duration is very small that is signal strength varies very fast for short distance, it is called small scale fading. Small scale fading occurs mainly because of multipath propagation, speed of surrounding obstacles, transmission bandwidth of signal and Doppler shift. The change in amplitude is about 20 or 30 dB over short distance. This rapidly changing fading phenomenon is referred to as fast fading. [3]

Selective fading

When different spectral components of received radio signal fluctuates unequally, it is called as selective fading. Selective fading is relative to the bandwidth of the entire communication channel. Non-selective fading implies that the signal bandwidth of interest is narrower than the entire spectrum affected by fading. [3]

Fading channels

A fading channel is a communication channel comprising different fading phenomenon during the transmission of a signal. The multipath fading channel can be divided on the basis of distribution function of the instantaneous power of the channel on the radio environment. Different types of fading multipath channels are as follows:

1. Additive White Gaussian Noise (AWGN) channel

2. Log Normal Fading Channel

3. Rayleigh Fading Channel

4. Rician Fading Channel

Additive White Gaussian Noise (AWGN) channel

Noise exists in all communications systems operating over an analog physical channel, such as radio. The main sources are thermal background noise, electrical noise in the receiver amplifiers and inter-cellular interference. This noise can also be generated inside the communication system itself due to inter-symbol interference, inter-carrier interference and inter-modulation distortion. The sources of noise reduce the signal to noise ratio, thus limiting the spectral efficiency of the system. Noise is the main detrimental effect in most radio communication systems.

Most types of noise present in radio communication system can be modeled accurately using Additive White Gaussian Noise (AWGN). In an AWGN channel, the modulated signal s(t) has noise n(t) added to it prior to reception. The noise n(t) is a white random Gaussian process with mean 0 and power spectral density N0/2. Thus the received signal is r(t) = s(t) + n(t).

Block Diagram of AWGN channel model

Bit Error Rate (BER) for DPSK and QAM64 over an AWGN channel

The quantities γs = Es/N0 and γb = Eb/N0 are called the average signal to noise ratio (SNR) per symbol and average SNR per bit respectively where Es is the energy of a symbol and Eb is the energy of a bit. For performance specification, it is important to find the bit error probability Pb as function of γb. However, for M-array signaling, the bit error probability Pb depends on both the symbol error probability and the mapping of bits to symbols. The bit error probability for DPSK modulation on AWGN channel is given by the equation below.

Pb =

If the unit of γb is in dB, we can convert it to a unitless parameter and replace Pb and γb with BER and Eb/N0 respectively. It yields


The bit error rate for QAM64 modulation over an AWGN channel is given by the equation below.

BER= ) -

Log Normal Fading Channel

The propagation models that are developed to determine path loss are known as large scale fading models as they all characterizes the receiving power by averaging it over large distance. But due to tree, foliage, rainfall and atmospheric condition, there is gradual change in local mean power and such type of fading channel is characterized by the log normal distribution function. The probability distribution function (pdf) and cumulative distribution function (cdf) are given by


, where m and σ are the mean and deviation, Pr(.) is the probability function , and erf(x) is the error function. [4]

Rayleigh fading channel

Rayleigh fading exists when there are multiple indirect paths between transmitter and receiver that is there is no distinct line of sight (LOS) path. Wireless channels with relatively small bandwidth are typically characterized as a Rayleigh fading channel. Rayleigh fading leads to significant degradation in bit error probability (BEP) performance compared to Gaussian channel since Rayleigh fading decrease the signal to noise ratio (SNR). In a Gaussian channel, the BEP decreases exponentially with the SNR, while in a Rayleigh fading channel, it decreases linearly with the average SNR.

Bit Error Rate (BER) for DPSK and QAM64 over a Rayleigh fading channel

The average probability of error over a fading channel is computed by integrating the error probability in AWGN over the fading distribution as shown by the equation below.


, where is the probability of error in AWGN with SNR . For a given distribution of fading amplitude r, is computed by making the change of variable


In Rayleigh fading, the received signal amplitude r has the Rayleigh distribution


and the signal power is exponentially distributed with mean 2. The SNR per symbol for a given amplitude r is


, where is the PSD of the noise in the in-phase and quadrature branches. Differentiating both sides of this expression yields


Substituting 4 and 5 into 3 and then 2 yields

Since the average SNR per symbol is just , the above equation can be rewritten as

, which is exponential. For binary signaling this reduces to

For noncoherent modulation, if we assume the channel phase is relatively constant over a symbol time, then the probability of error is obtained by integrating the error probability in AWGN over the fading distribution. For DPSK, this yields

The approximation for symbol error probability (SEP) for QAM64 with Rayleigh fading is

, where is the average SNR per symbol. and are two constants related to the type of approximation and modulation. Assuming that the symbol energy is separated equally among all bits and Gray coding is used, we have the following assumptions for MQAM

and are expressed by

The BEP with Rayleigh fading for MQAM is given by

If M=64, then =4 and =. Substituting them into the equation above and replacing and with and respectively, we obtain the average BER for QAM64 with Rayleigh fading

If , we set: [4]

Rician Fading Channel

Rician fading exists when there is direct line of sight (LOS) path along with a number of indirect paths. This model is mostly applicable indoor environment whereas Rayleigh fading model characterizes outdoor environment. Fading causes the signal to spread and become diffuse. The k-factor parameter which is part of the statistical description represents the direct-path (unspread) and diffuse power.

For Ricean channel, with reasonably strong signal K=4 to 16. The spectrum of the Rician process is determined by the Jakes PSD.[5]

Free-space propagation model

Free-space propagation model is the fundamental for all propagation path-loss models for any wireless communication application. A free-space propagation model is used to predict the received signal strength when the transmitter and receiver have an unobstructed line of sight.

In most operating environments, it is observed that the radio signal strength decays as some power of the distance called the path loss exponent. That is, if the power is Pt, the signal strength at a distance 'r' in meters will be proportional to. In free space propagation, there is no loss of energy as a radio wave propagates in free space, but there is attenuation due to spreading of the waves. For a free-space propagation model, is set to 2.

The received power Pr in free space is given by

, where is the transmitted power, is the received power, is the transmitter antenna gain, is the receiver antenna gain, d is the transmitter-receiver distance in meters and is the wavelength in meters.

The equation above is known as the Friis free space equation and is used to estimate the signal power received by a receiver antenna separated from a transmitting antenna by a distance r in free space, neglecting the system losses.

Free-space propagation path loss , is defined as

When (unity gain), then free space path loss is given by


Two-ray ground reflection model

In free space communication, where there is a single path from the transmitter and the receiver, the path loss is given by the Friis equation. In cellular communication, the transmitted signal arrives at the receiver via multiple paths due to reflection, diffraction, scattering by the terrain. These multipath components are time-delayed and amplitude attenuated versions of the transmitted signal. They add vectorially at the receiver to produce a composite signal whose power is attenuated far more than is predicted by the Friis equation. A simple two-ray radio path model is used to estimate the propagation path loss and received signal strength at the receiver, which takes into consideration the transmitter and receiver antenna heights.

The received power at the receiver antenna output is given as follows:

The path loss of the two-ray model is

The two equations above show that the received power is inversely proportional to the fourth power of distance for a two-ray model. The resulting path loss is much greater than the free space loss. Furthermore, it becomes independent of the signal frequency. The two-ray model is applicable to an open area with flat ground.[7]

Simplified path loss model

The complexity of signal propagation makes it difficult to obtain a single model that characterizes path loss accurately across a range of different environments. Accurate path-loss models can be obtained from complex analytical models or empirical measurements when tight system specifications must be met or the best locations for base stations or access-point layout must be determined. However for general trade-off analysis of various systems designs, it is sometimes best to use a simple model that captures the essence of signal propagation without resorting to complex path loss models, which are only approximations to the real channel anyway. Thus, the following simplified model for path loss as a function of distance is commonly used for system design:

In this approximation, K is a unitless constant that depends on the antenna characteristics and the average channel attenuation and is the reference distance for the antenna far field. The values for K, and can be obtained to approximate an analytical or empirical model. In particular the free space path loss model and the two ray model are of the same form as the equation above. Because of scattering phenomena in the antenna near field, the model is generally valid at transmission distances , where is typically assumed to be 1-10m indoors and 10-100m outdoors. When the simplified model is used to approximate empirical measurements, the value of is sometimes set to the free space path gain at a distance assuming omnidirectional antennas.

Substituting this in the previous equation yields

For the approximation of a free-space model or a two-ray model is set to 2 or 4.[8]

IEEE 802.11 Wireless LAN

IEEE 802.11 is the IEEE standards for wireless local area network(WLAN) computer communication developed by the IEEE LAN/MAN Standards Committee (IEEE 802) in the 5 GHz and 2.4 GHz public spectrum bands.

The 802.11 family includes over-the-air modulation techniques that use the same basic protocol. Defined standards include 802.11a, the first wireless networking standard, 802.11b, 802.11b. 802.11g and 802.11n.[12]

WLAN network architecture

A simple 802.11 WLAN comprises a number of stations which may operate in one of the two following configurations:

Independent configuration (basic service set- BSS)-in this mode, stations communicate directly with one other. There is no formal network structure and such networks are sometimes called as ad hoc networks. Ad hoc networks are relatively easy to operate but their coverage area is limited. Such configuration is termed a basic service set (BSS). When the BSS is not connected to an external network, it is termed as an independent BSS (IBSS).

Infra-structure configuration (extended service set-ESS)-in this configuration, station select a nearby access point (AP) and associate with it. The access point (AP) provides access to an external data network, which in IEEE 802.11-terminology is a distribution system. Typically most traffic within a given BSS will thus flow via the access point (AP). A number of BSSs can be grouped together to create an extended service set (ESS). An ESS in intended to provide connection for wider WLAN coverage area by allowing stations to roam from one BSS or AP area to another. This is achieved by bridging the separate BSSs across the distribution system.[13]

Direct Sequence Spread Spectrum

Direct sequence spread spectrum(DSSS) encodes redundant information into the RF signal to be transmitted. This provides the 802.11 radio with greater chance of understanding the reception of a packet, given background noise or interference on the channel. Every data bit is expanded into a string of bits, or chips, called a chipping sequence of barker sequence. The chipping rate mandated by IEEE 802.11 is 11 chips per bit. It uses phase-shift keying at the 1 and 2 Mbps rates and 8 chips(complementary code keying-CCK) at the 11 and 5.5 Mbps rate. The chipping sequence is transmitted across the spread spectrum frequency range.[14]

802.11b Direct Sequence channels

14 channels are defined in the IEEE 802.11b direct sequence (DS) channel set. Each DS channel transmitted is 22MHz wide, but the channel separation is only 5 Mhz. This leads to channel overlap such that signals from neighboring channel s can interfere with each other. In a 14-channel DS system, only three non-overlapping channels 25MHz apart are possible (channels 1,6 and 11)

The channel spacing governs the use and allocation of channels in a multi-AP environment, such as an office or campus. APS usually deployed in a cellular fashion within an enterprise, where adjacent office APs are allocated non-overlapping channels. Alternatively, APs can be co-located using channels 1,6 and 11 to deliver 33 Mbps bandwidth to a single area (but only 11 Mbps to a single client). The channel allocation scheme is illustrated in the figure below.[14]

Figure IEEE802.11 DSS Channel Allocations

IEEE 802.11g

802.11g provides for a high data rate (up to 54Mbps) in the 2.4-GHz band, the same spectrum as 802.11b. 802.11g is backward-compatible with 802.11b and provides additional data rates of 6, 9, 12, 18, 24, 36, 48, 54Mbps. At higher data rates, 802.11g uses the orthogonal frequency division multiplexing (OFDM) modulation technique.

The table below lists 802.11g modulation and transmission types for the various data rates.


Transmission Type

Bits per Subchannel

Data rate (Mbps)

















































OFDM Physical Layer

IEEE 802.11a defines requirements for the physical layer of the OSI model, operating in the 5.0 GHz UNII frequency, with data rates ranging from 6Mbps to 54Mbps. It uses Orthogonal Frequency Division Multiplexing (OFDM), which is a multi-carrier system. OFDM allows sub-channels to overlap, providing a high spectral efficiency. The modulation technique allowed in OFDM is more efficient than spread spectrum techniques used with 802.11b.[14]

IEEE 802.11a channels

The 802.11a channel shows the center frequency of the channels. the frequency of the channel is 10MHz on either side of the dotted line. There is 5 Mhz of separation between channel as shown in the figure below.[14]

Figure Channel Set Example

Factors influencing the


[2] pg23-24


[4]Theory and Design of Digital Communication Systems pg196-199

[5]Wireless Communication by V.S Bagad pg 1-2 to 1-3

[6]Wireless Communication Systems: From RF subsystems to 4G Enabling Technologies by Ke-Lin Du, M. N. S. Swami pg48


[8] Wireless Communications by Singal pg66 to71

[9]Theory and Design of Digital Communication Systems pg196-199

[9]Wireless Communications by Andrea Goldsmith pg 46-47