Unit - 5
Introduction to Wireless Channels and Diversity
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
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 1 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) = 
Rician Fading Channel
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 2 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.
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
Key takeaway
If antenna is kept still or its speed is zero than there is no fading due to no fluctuations in signals.
Rayleigh fading is for C=0
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
The reception of a signal in a channel transmitted through any type of fading channel degrades in quality if the signal level attenuation is below the expected operation region of the receiver. In this situation, the received signal power is not expectedly enough comparing with signal noise and interference power for reliable reception. The solution to overcome the channel attenuation because of fading problem in channel is to increase the transmitted power adjusted to the attenuation which is called power control (PC). On the other hand, there are two primary problems with this power control (PC) system.
One of these problems is that the dynamic range of the transmitter and the required transmitting power is extremely high if it’s intended to fully compensate the fading. This is impossible because of the radiation power limitations, the cost and the size of the amplifiers, and the limited battery power in the portable unit. Moreover, excess transmitted power increases the interference level at the other channels and users in the system unit. Another problem in power control (PC) approach that a feedback link is needed for the channel unless the operation of the radio channel is in time division duplex (TDD) mode. In a TDD system, the same frequency band is used for the downlink transmission from the base station to mobile unit and for the uplink transmission from the mobile unit to the base station. As a result, the transmitted signal undergoes the fading channel as the received signal due to its reciprocal characteristic of the channel, the transmitted power of transmitter is adjusted according to the received signal power. The feedback information usage decreases throughout the channel and increases the complexity in the system. Even an appropriate feedback link may not available in some application.
Using PC the fading can’t be overcome completely but the attenuation may compensate considerably. It can mention that large-scale fading can be compensated as well in the uplink of a system, for example CDMA. But stringent power control is required in prevention near far problem in the system. The rate of large-scale fading is simply slow, as a result it can be tracked well and the delay in the feedback of the power control commands can be neglected comparing with the rapid fading. On the other hand, small-scale fading can result in such rapid variations in the signal power that even the power control can’t follow them.
Diversity Techniques:
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. Some of them are following:
- Multipath/frequency diversity
- Spatial/space diversity
- Temporal/time diversity
- Polarization diversity
- Angle diversity
- Antenna diversity
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 3 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.
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.
Receive Diversity: Multiple antennas are use at the receiver to obtain diversity and employ switching and combining or selection intending to improve the quality of received signal. Since it is easier and cost effective to use multiple antennas at the base station than the terminal which is a positive manner of receive diversity. This technique may utilize channel state information (CSI) at receiver and it’s fully fit for uplink which is remote to base. But the main problems of receive diversity are cost, size and necessary power at the remote units. This technique is larger in size and expensive in cost because of multiple antennas, radio frequency chains or selections and its switching circuits.
Transmit Diversity: Unlike receive diversity, transmit diversity needs multiple transmitting antennas. Moreover, unlike receive diversity, transmit diversity does not utilize CSI in its single information signal. Effective signal processing technique should be used to extract the noisy and distorted received signal in transmit diversity.
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 4 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.
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.
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.
Key takeaway
- Using PC the fading can’t be overcome completely but the attenuation may compensate considerably.
- It can mention that large-scale fading can be compensated as well in the uplink of a system, for example CDMA. But stringent power control is required in prevention near far problem in the system.
- The rate of large-scale fading is simply slow, as a result it can be tracked well and the delay in the feedback of the power control commands can be neglected comparing with the rapid fading.
- On the other hand, small-scale fading can result in such rapid variations in the signal power that even the power control can’t follow them.
References:
1. Wireless Communications- Principles and Practice, T S Rappaport, Pearson Education India, Second Edition.
2. Wireless Communication and Networks, Upen Dalal, Oxford university Press, First Edition, 2015.
3. Wireless Communication and Networks 3G and Beyond, Iti Saha Misra, Tata McGraw Hill Education Pvt. Ltd, Second Edition, 2009.
4. Mobile Communication Engineering – Theory and Applications W C Y Lee, TMH Publication, Second Edition, 2008.
5. Wireless Communication, Andrea Goldsmith, Cambridge University Press, 2005
6. Fundamentals of Wireless Communication, David Tse and Pramod Viswanath, Cambridge University Press, 2005
