Delay Spread
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Delay Spread
In system evaluations, we typically prefer to address a class of channels
with properties that are likely to be encountered, rather than one specific
impulse response. Therefor we define the (local-mean) average power which is
received with an excess delay that falls within the interval ( T , T
+ dt ). Such characterization for all T gives the "delay profile"
of the channel.
The delay profile determines the frequency dispersion, that is, the extent
to which the channel fading at two different frequencies f 1
and f 2 is correlated .
MP2 audio : Measured channel
data in Edinburgh.
Source: Research group of Prof. Peter
Grant , U. of Edinbourough. See also: discussion of channel
modeling to study CDMA
array processing . Playlist
leading you through the topic of array processing and adaptive antennas
for CDMA. It includes a discussion of the channel model.
In indoor and micro-cellular channels, the delay spread is usually smaller, and rarely exceed a few hundred nanoseconds. Seidel and Rappaport reported delay spreads in four European cities of less than 8 microsec in macro-cellular channels, less than 2 microsec in micro-cellular channels, and between 50 and 300 ns in pico-cellular channels.
Figure: Typical delay profile: Exponential
Figure: Typical indoor delay profile:
In an indoor environment, early reflections
often arrive with almost identical power. This gives a fairly flat profile up to some
point, and a tail of weaker reflections with larger excess delay.
Figure: Typical "bad urban" delay profile
Besides the normal reflections from nearby obstacles (which cause reflection with a short excess delay),
remote high-rise buildings cause strong reflections with large excess delay.
The combined effects often result in multiple clusters of reflections.
From the delay profile, one can compute the correlation of the fading
at different carrier frequencies.
Figure Auto-Covariance of the received amplitude of
two carriers transmitted with certain frequency offset.
The above expressions only represent the behavior of the profile curve.
A correction factor is needed to ensure that the integral over all t equals unity, or to represent the total local-mean power.
Often propagation parameters are measured in frequency domain. Klaus Witrisal
discusses how the delay spread can be estimated
directly from a frequency transfer function .
Figure: Example of impulse response and frequency transfer function
of a multipath channel.
Figure: Measured Delay profile in a German urban environment at 1800 MHz
Delay Spread = 1.2 m sec; coherence BW = 1.3 MHz
Source: Research group of Prof. Paul Walter Baier, U. of Kaiserslautern, Germany.
See also: corresponding scatter plot .
FIGURE: R.M.S. Delay Spread vs. propagation distance in the
U.C. Berkeley, Cory Hall Building.
Source: John Davis and Jean-Paul Linnartz
Figure: Illustration of reflections of various kinds.
Source: Peter Grant, U. of Edinbourough.
exp(- t /1 m s)
0.5 exp(5- t /1 m s)
for 0 < t < 5 m s
for 5 < t < 10 m s
exp(-3.5 t /1 m s)
0.1 exp(15- t /1 m s)
for 0 < t < 2 m s
for 15 < t < 20 m s
Adaptive channel equalization
Channel estimation training sequence
Use the handset only in small cells with small delay spreads
Diversity and channel selection can help a little bit (pick a channel where late reflections are in a fade)
Rake receiver separately recovers signals over paths with excessive delays.
CDMA array processing can further improve
performance, because it also exploits angle spreads .
OFDM multi-carrier modulation: The radio
channel is split into many narrowband (ISI-free) subchannels
RMS Delay Spread, Excess Delay Spread and Multi-path ...
In above equation Ac denotes multipath intensity profile. τ denotes time delay, μTm denotes average delay spread.
You can also think Ac as power profile which exponentially decreases over time as multipath delay in time
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Home / Wireless Communication / RMS Delay Spread, Excess Delay Spread ...
The fundamental distinction between wireless and wired connections is that in wireless connections signal reaches at receiver thru multipath signal propagation rather than directed transmission like co-axial cable. In wireless communication, there is no set communication path between the transmitter and the receiver. The line of sight path, also known as the LOS path, is the shortest and most direct communication link between TX and RX. The rest of the communication pathways are referred to as non-line of sight (NLOS) paths. Reflection and refraction of transmitted signals with building walls, foliage, and other objects create NLOS paths.
The linear nature of the multipath component signals is evident. This signifies that one multipath component signal is a scalar multiple of another.
Let me give you an example to help you understand. Let's assume we're sending an impulse signal from the transmitter. The single impulse response is then transmitted to the receiver via LOS and NLOS pathways. If a LOS path is not available, the signal is only transmitted via NLOS paths. The probability of LOS communication decreases as the density of the region increases. Because there are numerous obstacles between the transmitter and the receiver, such as buildings, etc.
The arrival time difference between the very first and final multipath components (MPCs) at the receiver side is simply referred to as excess delay spread. For example, suppose the first multipath component arrives at the receiver at time t1 and the last multipath component arrives at time t2. The Excess Delay Spread will then be (t2 -t1).
The Power Delay Profile shows how received power changes with time dispersion or time delay caused by multipath in a wireless communication channel.
The RMS Delay Spread is the power delay profile's second central momentum. As we all know, we get multi-path components at the receiver end of the wireless communication process. As a result, in order to obtain necessary data, we must use stronger multipath and then add them. Then we divide the total value by total weightages. In the case of power delay profile computation, we see that power decreases exponentially with time.
The signal traversal path is shorter at higher frequencies than it is at lower frequencies. As a result, cellular network coverage is limited in those situations. And there isn't much of a LOS component in a city or urban scenario. There are NLOS communication pathways available. When frequency is very high, however, only a few stronger NLOS components reach the receiver. In a congested metropolitan area, the rest of the NLOS components are lost due to repeated reflection and diffraction. Because path loss is directly proportional to the carrier frequency of the operational signal, higher frequencies experience more path loss.
In today's wireless communication, RMS delay spread is a critical characteristic. It totally depends on the physical constructions of a area, like, buildings, foliage, etc. There will be linear multipath components, or MPCs, whenever we transmit a signal in a wireless setting. Simply put, we will receive many copies of the same single sent impulse response. As a result, it takes some time for all MPCs of the transmitted impulse response to reach the receiver. If we broadcast the following signal immediately after the first, the MPCs of the first symbol cause interference on the receiving side. Because the receiver receives the next symbol as well as the MPCs of the first symbol. Inter-symbol interferences, or ISI, are the result of this. To eliminate interference, we broadcast signals at intervals ten times greater than the RMS delay spread.
The Power Delay Profile shows how received power varies with the time dispersion of MPCs. We can also see that only a few MPCs contain practically all abilities for high frequency. Only a few MPCs often carry nearly 80-85% of total energy for higher frequencies.
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Even though a same signal is transmitted from single transmission antenna, the signal may go through various different path. Each of the different path may cause different travel distance if the signal get reflected by one or more obstacles (like buildings) and in some case different path may has different physical property of propagation media, so it is higly likely that the signal traveling
through different path would arrive at the reciever antenna at different timing. So if you send a signal from a transmitter antenna and measure the arrival time at the reciever antenna which is a certain distance away from the transmitter antenna, you would get multiple different arrival timing.
If you plot those arrival timing on the axis of time, you would see a certain variation (spread) of those values. This spread is called 'Delay Spread'.
I think this is enough for the definition for layman. If you want to dig into further details and go through some mathematical model of these delay spread see the following. (I will put description later)
If I plot the signals detected by a reciever antenna in time vs amplitude plot, it can be represented as follows. As you see here, you will see multiple copies of the same signal coming in with different timing and different amplitue. Using these time variation and amplitude variation, we can defined several different criteria (metrics) to define the nature of the channel. To introduce these criteria (metric) is the main purpose of this page.
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