Unit - 5

Introduction to Wireless Channels and Diversity

Q1) Explain AWGN channel modelling?

A1) The uplink model for discrete time is shown below. The equation for output can be given as

y[m] = x1[m]+x2[m]+w]m]

The performance of the channel can be achieved by knowing the capacity of the channel. The communication can be achieved by R<C and for R>C communication is not possible.

For multiuser case this range needs to be increased say for range (R1, R2). Which means that both the users can communicate at rates R1 and R2. There is trade-off between the communication rates as the users share same bandwidth.

Fig 1 Uplink two-user

The symmetric capacity

Csym = R

The sum capacity is Csum = R1+R2

The capacity region for AWGN channel is shown below

Fig 2 Capacity region of two-user uplink AWGN

The power of the received signal is the sum of the powers of individual received signals. The receiver will decode the information from both users. While decoding the first user signal it takes user 2 signal as gaussian noise and vice versa. This is called as successive interface cancellation. The point B can be found if we reverse the order of cancellation.

The above figure 2

R2= log (1+) – log(1+)

User 1 can achieve its single-user bound while at the same time user 2 can get a non-zero rate, in fact as high as its rate at point A above equation. By time sharing between multiple access the other points between AB can be found. We can increase both user rates by moving near to point on AB.

Q2) What do you mean by Rayleigh channel in fading?

A2) The Rayleigh fading occurs due to multipath reception. When there are N number of scattered waves which are received at the mobile antenna than the power received by the moving antenna is a random variable. The phasor representation is shown below.

Fig 3 Phasor for Rayleigh Fading

Let Cn be the amplitude of nth reflected wave. Then the transmitted signal is

V(t) = cos(wct+)

The signal received will be given as

r(t) =

The quadrature phase component can be given as

Q(t) =

Q3) Explain Nakagami fading?

A3) This model matches the empirical results for short wave ionospheric propagation. When Rayleigh fading signal combines with k branch maximum ratio combination the Nakagami fading is found. When there is large delay time spread for multipath scattering Nakagami fading occurs.

This fading occurs with cluster of reflected waves. The phase of individual reflected waves is different for one cluster. The envelop of each cluster is Rayleigh distributed. There can be interference when the bit time of signal is more than delay time.

The Nakagami model is equivalent to the Rician model. But it is not exactly same in all cases. This approximation holds good for the body of probability density function but not for its tail.

Q4) Explain Reflection and diffraction in channel?

A4) Reflection

• Reflections Occurs when a wave impinges upon a smooth surface.
• Dimensions of the surface are large relative to l.
• Reflections occur from the surface of the earth and from buildings and walls.

Diffraction

• Diffraction Occurs when the path is blocked by an object with large dimensions relative to l and sharp irregularities (edges).
• Secondary “wavelets” propagate into the shadowed region.
• Diffraction gives rise to bending of waves around the obstacle.

Q5) Explain briefly flat fading and Explain Ocumura and Hata Path loss??

A5) It is non-frequency selective fading. The channel has constant gain and its phase response is also linear but has BW greater than the transmitted signal.  The received signal frequency components fluctuate simultaneously in same proportion. The major flat fading can cause fade up to 30dB

This model has the information which is graphical based on the Okumara model. This model is used to predict the path loss in urban areas. This mode mainly has the waves which are reflected, diffracted and scattered from the obstacles. The parameters for this model are

• Frequency Range: 150 MHz to 1500 MHz
• Transmitter Height: 30 m to 200 m
• Link distance: 1 km to 20 km
• Mobile Station (MS) height: 1 m to 10 m

For urban area the model is as below

LU = 69.55+26.16 logf – 13.28loghB- CH + (44.9-6.55loghB) logd

The area for which antenna height is >10m

CH = 0.8 + (1.1 logf – 0.7) hM – 1.56logf

For Large Cities

CH = 8.29(log(1.54hM))2 – 1.1                      for 150MHz<f<200MHz

= 3.2(log(11.75hM))2 – 4.97                     for 200MHz<f<1500MHz

LU= Path loss in Urban Areas

hB= Height of base station antenna in meters (m)

hM= Height of mobile station antenna in meters (m)

f= Frequency of Transmission in megahertz (MHz).

CH= Antenna height correction factor

The Hata model equation for suburban areas is given by

LSU = LU – 2(log)2 – 5.4

LSU = Path loss in suburban areas in decibels (dB)

LU = Average Path loss in urban areas in decibels (dB)

f = Frequency of Transmission in megahertz (MHz).

The Hata model for areas with less obstruction is

Lo = LU – 4.78(logf)2 + 18.33logf – 40.94

LO = Path loss in open area. Unit: (dB)

LU = Path loss in urban area. Unit: decibel (dB)

f = Frequency of transmission. Unit: (MHz)

Q6) explain scattering in channel transmission and What do mean by Stochastic?

A6) Scattering

• Scattering Occurs when a wave impinges upon an object with dimensions on the order of l or less, causing the reflected energy to spread out or “scatter” in many directions.
• Small objects such as street lights, signs, & leaves cause scattering

The main purpose of a stochastic model for large-scale variations is to aid the design of the power and rate control algorithms, feedback schemes, admission control, and other functions in the upper layers of the standard network stack. A stochastic description of small-scale fading is an approach well suited to model many types of fading channels in the sense that it correctly predicts the significant difference between the rates achievable over a fading channel in comparison with the capacity of a channel that is only affected by AWGN.

Q7) Explain Rician fading model?

A7) There is a dominant component present in this model. The component which is dominant can be a LoS (line of sight). The antenna also receives many reflected and scattered waves. The phasor sum of two or more dominant signals can also be LoS.  The phasor for this is shown below.

Fig 4 Phasor for Rician Fading Signal

A sinusoidal transmitted carrier is taken with narrowband propagation channel

S(t) = cos wct

The received signal from Rician path is given by

V(t) = C cos wct+

Where C= amplitude of LoS

= amplitude of nth reflected wave

= phase of nth reflected wave

The ratio of signal power in dominant component to the scattered power is called as Rician factor denoted by k.

Q8) Compare Rician Fading and Rayleigh Fading?

A8) Rician Fading vs. Rayleigh Fading:

There is a variation of fading loss during sampling a radio wave in various spatial locations. If there are enough scatters in a dense multipath environment, the complex amplitude is well modeled by a Gaussian distribution. If there is a line-of-sight (LOS) propagation path in between transmitter and receiver, then the mean Gaussian distribution is non-zero [2]. It leads to attenuation with absolute value of complex amplitude which is Ricean distribution and it terms as Rician fading. The signal variation follows Rice probability density function (PDF) in channel here.

If there is a line-of-sight (LOS) propagation path in a dense urban environment, then there is a zero mean Gaussian distribution which is leading to a Rayleigh distributed attenuation and the channels is called Rayleigh fading channel. The envelope fluctuations of the signal follow the Rayleigh PDF in Rayleigh fading channel and the signal comes from almost the directions with the same average power. The Rayleigh fading is predominant and worst case in typical land mobile communication systems. Multipath fading phenomena occurs in three situations. If the mobile unit and the nearby scattering objects all moving, If the mobile unit is standing but the nearby scattering objects are moving and if the mobile unit and the nearby scattering objects all standing

Q9) What is bit error rate? Explain its effect on the fading channels?

A9) Bit error rate is a key parameter that is used in assessing systems that transmit digital data from one location to another. BER is applicable to radio data links, Ethernet, as well as fibre optic data systems. When data is transmitted over a data link, there is a possibility of errors being introduced into the system. If this is so, the integrity of the system may be compromised. As a result, it is necessary to assess the performance of the system, and BER provides an ideal way in which this can be achieved. BER assesses the full end to end performance of a system including the transmitter, receiver and the medium between the two.

BER is defined as the rate at which errors occur in a transmission system. In simple form,

BER expression is given by Rappaport (2002) as

Where Pb(E/r) = the conditional error probability P(r) = the pdf of the SNR

Q10) What is fast fading in wireless channel modelling explain in detail?

A10) Fading in a channel is the propagation losses by radio signal on both forward and reverse links. This impairment is a major problem of wireless communication channel. Fading introduce for the combined effect of multiple propagation paths, high speed of mobile units and reflectors. Multiple paths fading has a small-scale effect. In a multi-path propagation, received signal by a mobile terminal comes from a large number of propagation paths. Reflection, diffraction, scattering in radio wave in natural structure and human made structure like building, bridge is responsible for the creation of multi-path propagation.

Received signal suffers variation in magnitude and phase due to the multiple propagation paths and it interfere each other in both constructively and destructively which depends on the spatial position of the receiver. This variation in the received signal is called multipath fading and this fading is depends on the rate of speed of the receiver motion and the objects around the receiver. The performance of a wireless communication system in term of probability error can be severely degraded by fading. In mobile communication, there is not only multipath propagation exists but also its time varying. The phenomena results, a time-varying fading channel.

It’s very difficult to communicate through this kind of fading channel in communication systems. But there is some special technique may be taken to achieve satisfactory performance. In wireless communication, the received signal comes from both direct part and the path of scattering, reflections and diffractions. Because of the propagation loss, the effect of the terrain configuration implements small-scale long term fading which is also called shadowing fading and it changes with the atmosphere and electrical constants. Natural and man-made structures such as buildings, traffic, motion, trees, hills and the other nearby environment would cause the multi-path fading on the received signal called short-term fading.

If there is a long term shadowing effect of buildings or natural objects in terrain then slow fading occur in a channel. The local mean is influenced by the environment types. Therefore, it is really difficult to make a prediction. However, if it is plotted the signal fluctuation in a logarithmic scale, the fluctuation approaches a normal distribution. This kind of distribution is called log-normal. The typical value of the standard deviation of shadowing distribution is 8 in Decibel. When the symbol duration is (c) small comparing to coherent time, then the channel is called slow fading channel.

This type of channel often modeled as time invariant channels over a number of symbol intervals. Moreover, slow varying channel parameters can be estimated by different types of estimation techniques. Multipath propagation characteristics of a radio signal results path signals to add up to random phases in both ways constructively or destructively at the receiver end. These phases can vary extremely rapid way along with the receiver end and can be determined by the path length, and the carrier frequencies.

If we consider a large number of scattered wave fronts which has random amplitude and angles and if we consider that it arrives at the receiver end with uniformly distributed phases [0, 2], then in-phase and quadrature-phases components of the vertical electrical field Ez can described Gaussian process. The presence of a direct path in space, it will no longer be a Rayleigh distribution. Then it becomes a Ricean distribution. When there is a close or smaller coherent time to/than symbol duration, the channels are fast fading or time-selective fading. It is still a difficult phenomenon to estimate the parameters of the channel in a fast-fading channel

Q11) Compare slow and fast fading of wireless systems?

A11)

Fast Fading                   The time duration at which the channel behaves is a correlated manner is short compared with the time duration of the symbol.         The fading character of the channel will change several time during the time span of a symbol.         Fast fading can cause the baseband pulse to be distorted ISI.

Slow fading                   The time duration at which the channel behaves is a correlated manner is long compared with the time duration of the symbol         The channel state virtually remain unchanged during the time in which a symbol is transmitted         The propagation symbols will likely not suffer from pulse distortion.

Q12) Explain multipath diversity techniques?

A12) Diversity technique is used to decreased the fading effect and improve system performance in fading channels. In this method, we obtain L copies of desired signal through M different channels instead of transmitting and receiving the desired signal through one channel. The main idea here is that some the signal may undergo fading channel but some other signal may not. While some signal might undergo deep fade, we may still be able to obtain enough energy to make right decision on the transmitted symbol from other signals. There is a number of different diversities, which is commonly employed in wireless communication systems.

Multipath or Frequency Diversity:

In a channel, Transmitted signals with different frequencies are affected different way in frequency domain. The fact is an advantage in frequency diversity technique. Multiple replicas of information signal are sent over several affected frequency band in this diversity. There should be a distance more than coherent bandwidth between the frequency bands and achieve small-scale fading according to following equation.

c= 1/fd

Frequency diversity can also be implied as in the case of multipath diversity. Transmission of a wideband signal is given by the following equation where the bandwidth is more than the coherence bandwidth of the previously used channel and this results a frequency selective fading

c= 1/tm

In a sufficient wide signal bandwidth, multipath components can resolve. In the result, it is possible to obtain different independently fading signal. The number of resolvable multipath given by the following equation is used to approximate the maximum achievable diversity order for multipath diversity:

L= [Tm + W] +1

Channel equalization is another approach to achieve multipath diversity. A filter is used at receiver to make channel equalization to compensate the channel impairments. This process combines the multipath of signals and reduces inter-symbol-interference (ISI) and produce diversity.

Fig 5 Frequency Diversity

In general, the information signals are modulated through different carriers M in frequency diversity scheme. It is important that different signals undergo independent fading. The carriers should be separated by at least coherent bandwidth from each other. L copies of signals are optimally combined at the receiver to make a statistic decision. The maximum ratio combiner is the optimal combiner.

Q13) Explain spatial diversity techniques used in wireless systems?

A13) Spatial/Space Diversity:

Multiple antennas are used to transmit signals with carrying information at the transmitter and/or receiver to provide multiple independent fading paths in space diversity. This technique is used to provide significant performance gain with not sacrificing any valuable bandwidth on the transmitted power resources. Spatial diversity is widely used because it is easy to implement and it’s cost effective and very simple. This technique has a single transmitting but multiple receiving antennas. The receiving antennas should be at enough distance for that the multiple fading in the diversity will be uncorrelated. There should be a balanced average power between channels and the correlation coefficient should be very low to achieve a good diversity gain.

While wide distance is required between antennas for obtaining low correlation between channels but close distance is also required to synthesize to make a narrow beam not generating grating lobes which prevent introducing interference. Only one or two co-channel interfering signals are used in time division multiple access (TDMA) systems. However, the number of signals is more in code division multiple access (CDMA) the maximal ratio combining (MRC) is better than the performance of optimum adapting processing. It is suggested that if we increase antenna element separation as much as feasible the then high space diversity gain can be achieved with maximal ratio combining in a CDMA system. Most of the cellular communication system has only one transmitting antenna at the base station and two receiving antennas those are widely separated per sector in a space diversity system. In general, if we want to receive M copies of transmitted signals then we need M number of antennas in a space diversity system.

It is very important to keep enough space between the antennas so that the received signals undergo independent fading. Space diversity is different than frequency and temporal diversity. Unlike those spaces diversity needs no additional work at the transmission end and no additional bandwidth is required on the transmission time.

On the other hand, physical complexity restricts its application widely. Like several receiving antennas use in space diversity, several transmission antennas also can be used to send several copies of transmitted signals. This kind of diversity can be employed combating frequency and time selective fading both. There are two types of spatial diversity techniques such as receive diversity and transmit diversity.

Q14) Explain how the time diversity technique utilises coding of channels and interleaving to mitigate channel fading?

A14)

Time / Temporal Diversity: Interleaving and coding, over symbols across different coherent time periods, is used to obtain time or temporal diversity. This technique utilizes coding of channel and interleaving to mitigate channel fading at a cost of added delay and loss of bandwidth efficiency. It is uses on slow fading channels and on the channels which is delay sensitive. Intentional redundancy is introduced into the transmitted signal to achieve time diversity in the temporal domain. Redundancy can be done by repetition of channel coding. To make repetition coding, information bearing signals are transmitted in several time slots. But the separation between time slots should be more or equal than the coherent time of the channel to obtain independent faded signals which helps to gain full diversity advantages. Moreover, it is possible to obtain repetition coding by spreading in direct-sequence code division multiple access (DS-CDMA).

Fig 6 Time Diversity

In general, a desired signal is transmitted in M different periods of time in time diversity. For example, every symbol is transmitted M times. As it is mentioned earlier that intervals between the transmitted symbols should be at least coherence time to make ensure that different copies of the same symbol undergo independent fading. Maximum ratio combiner can be used to obtain optimal combiner. If we send the same symbol M times then it applies the (M, I) repetition code. We can also use non-trivial coding. Error control coding and interleaving is an effective way to combat time selective or fast fading.

Polarization Diversity: In polarization diversity, transmitted signals have uncorrelated fading statistics in VHF and VHF land mobile radio system when signals should be transmitted through two orthogonally propagations path. Spatial diversity may achieve by using multiple antennas with independent polarizations in the same location instead of multiple antennas in use in different locations. This is the method of polarization diversity. If an implementation of spatial diversity with small dimensions is desired, this is very attractive process. Normally two orthogonally polarized antennas are used on horizontal and vertical planes or with a slope of 150 to employ polarization diversity. Experiments show that polarization diversity may obtain in dense scattering environments when there is line of sight (LOS) and non-line of sight (non-LOS) situations.

Q15) Explain the diversity technique used in dense urban areas and is very effective?

A15) Angle Diversity/ Pattern Diversity / Direction Diversity:

Equal data traffic is used on the both uplink (reverse link) and downlink (forward link) in digital cellular communication but the system requires better reverse link performance because of the limitation of mobile terminal transmit power. There is uplink capacity deployed in CDMA system due to synchronize operation on forward link and asynchronies operation on reverse link. If we need to achieve better uplink reliability then we can use space diversity or polarization diversity. On the other hand, there is a huge demand of data applications on downlink capacity comparing to the uplink capacity. Improvement of reliability or downlink capacity is a major issue in three generation mobile system and the other generation mobile communication systems in future. One promising solution to improve downlink capacity is forming beam on downlink. It can also be implemented by forming multiple fixed narrow beams or by steering a beam toward a user in the system.

Additional protection which the angle diversity provides is protection from deep multipath fading in multiple beam systems. It is experimentally proved that the angle diversity is equally effective as conventional space diversity in dense urban area and it provides approximately 8 dB diversity gain at reliability level with selection combining. A multiple fixed narrow-beam antenna or an array antenna, which is fully adaptive, transmits and receives much more energy between the mobile terminal and base station comparing to a wide beam antenna system. On the other hand, a beam forming system using multiple antennas may experiences multipath fading sometimes when the multipath components are applied from very close angles.

The base station antenna system in a dense urban environment experiences antenna gain reduction and the multipath components will spread in wider angles. In this case, it is wise to use angle diversity to avoid deep multipath fading by choosing the best beam to collect energy. The size of the angle diversity is very smaller comparing to the space diversity system where we need the wide separation between the receiving antennas.

Multipath components in a cluster those have individual arrival angles travel through different paths and employ different fading. Very basic procedure to obtain angle diversity is to fix antennas with narrow beam widths different sector in the system. Then the arriving multipaths from the different beam directions are resolved and combined advantageously. This procedure not only creates diversity but also increases the antenna gain and reduces interference by providing angular discrimination. It is mentioned earlier that one more method of achieving diversity is to use antenna array with adaptive beam forming which termed as path diversity sometimes.

Q16) How antenna diversity is used to improve the performance in wireless communication systems explain?

A16) Antenna Diversity:

Antenna diversity is a popular and extensively used technique to improve performance in wireless communication systems. The technique reduces fast fading and inter-channel interference effects in the wireless network system. In an antenna diversity system, two or more antennas are used and fixed in positions which will provide uncorrelated signals with the same power level. Then the signals are combined and created an improved signal. The basic method of antenna diversity is that the antennas experience different kind of signals because of individual channel conditions and the signals are correlated partially. Then we can expect that if one signal from one antenna is highly faded, other signals from other antennas are not faded such way and these signals are our expected quality signals. In a multipath propagation environment, each receiving signal experiences individual fading characteristic.