Contents• Multipath characterstics of radio waves• Fading• LCR fading statistics• Doppler spread• Diversity techniques
Radio Propagation• What is Radio?• Radio Xmitter induces E&M fields – Electrostatic field components ∝ 1/d3 – Induction field components ∝ 1/d2 – Radiation field components ∝ 1/d• Radiation field has E and B component – Field strength at distance d = E×B ∝ 1/d2 – Surface area of sphere centered at transmitter
General Intuition• Two main factors affecting signal at receiver – Distance (or delay) ⇒ Path attenuation – Multipath ⇒ Phase differences Green signal travels 1/2λ farther than Yellow to reach receiver, who sees blue. For 2.4 GHz, λ (wavelength) =12.5cm.
Objective• Invent models to predict what the field looks like at the receiver. – Attenuation, absorption, reflection, diffraction... – Motion of receiver and environment… – Natural and man-made radio interference... – What does the field look like at the receiver?
Models are Specialized• Different scales – Large scale (averaged over meters) – Small scale (order of wavelength)• Different environmental characteristics – Outdoor, indoor, land, sea, space, etc.• Different application areas – macrocell (2km), microcell(500m), picocell
Fading• Fading refers to 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 multipath induced fading.
• 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 experienced differences in attenuation, delay and phase shift while travelling 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
• 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• Slow Fading• 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• 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• 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 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.
Flat vs. Frequency-selective 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.
• In a frequency-selective fading channel, 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.• Frequency-selective fading channels are also dispersive, in that the signal energy associated with each symbol is spread out in time.
Mitigation• Fundamentally, fading causes poor performance in traditional communication systems because the quality of the communications link depends on a single path or channel, and due to fading there is a significant probability that the channel will experience a deep fade.• The probability of experiencing a fade (and associated bit errors as the signal-to-noise ratio drops) on the channel becomes the limiting factor in the links performance.
• The effects of fading can be combated by using diversity to transmit the signal over multiple channels that experience independent fading and coherently combining them at the receiver.• The probability of experiencing a fade in this composite channel is then proportional to the probability that all the component channels simultaneously experience a fade, a much more unlikely event.
How to overcome fading?• Common techniques used to overcome signal fading include:• Diversity reception and transmission• OFDM• Rake receivers• Space–time codes• MIMO
• 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.
Classes of Diversity Schemes• 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. Examples are: – OFDM modulation in combination with subcarrier interleaving and forward error correction – 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 (diversity reception). In the latter case, a diversity combining technique is applied before further signal processing takes place. If the antennas are at far distance, 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 that the transmit selects the best user among candidate receivers according to qualities of each channel between the transmit and each receiver. In FDD systems, a receiver must feed back the channel quality information to the transmitter with the limited level of resolution.• Antenna diversity: transmitted along different propagation paths.• Cooperative diversity: enables to achieve the Antenna diversity gain by the use of the cooperation of distributed antennas belonging to each node.
LCR fading Statistics:• Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.• It assumes that the magnitude of a signal that has passed through such a transmission medium (also called a communications channel) will vary randomly, or fade, according to a Rayleigh distribution — the radial component of the sum of two uncorrelated Gaussian random variables.• It is a reasonable model for tropospheric and ionospheric signal propagation as well as the effect of heavily built-up urban environments on radio signals.• Rayleigh fading is most applicable when there is no dominant propagation along a line of sight between the transmitter and receiver.• If there is a dominant line of sight, Rician fading may be more applicable.
The model• Rayleigh fading is a reasonable model when there are many objects in the environment that scatter the radio signal before it arrives at the receiver. The central limit theorem holds that, if there is sufficiently much scatter, the channel impulse response will be well-modelled as a Gaussian process irrespective of the distribution of the individual components.• If there is no dominant component to the scatter, then such a process will have zero mean and phase evenly distributed between 0 and 2π radians.• The envelope of the channel response will therefore be Rayleigh distributed. Calling this random variable R, it will have a probability density function where Ω = E(R2).• Often, the gain and phase elements of a channels distortion are conveniently represented as a complex number. In this case, Rayleigh fading is exhibited by the assumption that the real and imaginary parts of the response are modelled by independent and identically distributed zero- mean Gaussian processes so that the amplitude of the response is the sum of two such processes.
ApplicabilityDensely-built Manhattan has been shown to approach a Rayleigh fading environment.
• One second of Rayleigh fading with a maximum Doppler shift of 10Hz.• The requirement that there be many scatterers present means that Rayleigh fading can be a useful model in heavily built-up city centres where there is no line of sight between the transmitter and receiver and many buildings and other objects attenuate, reflect, refract and diffract the signal.• Rayleigh fading is a small-scale effect. There will be bulk properties of the environment such as path loss and shadowing upon which the fading is superimposed.
Doppler power spectral density• The normalized Doppler power spectrum of Rayleigh fading with a maximum Doppler shift of 10Hz.• The Doppler power spectral density of a fading channel describes how much spectral broadening it causes. This shows how a pure frequency e.g. a pure sinusoid, which is an impulse in the frequency domain is spread out across frequency when it passes through the channel. It is the Fourier transform of the time-autocorrelation function. For Rayleigh fading with a vertical receive antenna with equal sensitivity in all directions, this has been shown to be where is the frequency shift relative to the carrier frequency. This equation is only valid for values of between ; the spectrum is zero outside this range.• This spectrum is shown in the figure for a maximum Doppler shift of 10 Hz. The bowl shape or bathtub shape is the classic form of this doppler spectrum.
Fading Models• Nakagami 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