Wireless Communications For Transmitted Signal

Isotropic Antennas and Radiation Patterns

An Isotropic Antenna is basically a point source of radiation. A point source emits the radiation in all the direction with equal magnitude. There is no loss during this transmission. Unlike the practical antennas, this ideal antenna has no directivity in one particular direction. This antenna is used as a reference antenna and the radiation pattern of other antennas is directly compared with an isotropic antenna. It is also called an Omni-directional radiating antenna [1]. The radiation pattern offered by this antenna looks like a doughnut in 3D. It has a gain of 1. Sun is an example of isotropic antenna. 

The nature of radiation is stated by radiation pattern. Through radiation pattern the amount of radiation from the source and its reception can be easily understood [2]. Radiation pattern is the field magnitude variation in all the direction from the radiator. 

A signal may deteriorate and lose its strength by the time it reaches the receiver due to many factors. This attenuation of the signal is called as fading [3]. There are many factors that are responsible for this phenomena practically, one of the most important is multiple path distraction. When a signal transmitted, may get reflected by the reflecting edges of the objects that are present in the channel. This causes single transmitted signal to divide into various signals that differ by phases as well as amplitude. They do not reach the receiver at the same time and thus interference occurs which can be either constructive or destructive. Fading is undesirable and it has to be mitigated. 

1. Diffraction is the ending of the light waves around the corners of the obstacles when the dimension is of the order of the wavelength [4]. Whereas scattering is a phenomena when a particle goes in a random fashion after colliding with a surface.
2. Diffraction is a wave phenomenon while scattering is a particle phenomenon.
3. Diffraction happens due to the property of the waves whereas scattering happens due to surface and only or any other external reason. 

1. The channel’s impulse response varies very fast within the duration in case of fast fading whereas it is very less as compared to the transmitted signal in the case of slow fading.
2. In fast fading the coherent time is less than the symbol period while in slow fading it is

Greater.

1. Wherever low data rate is involved, fast fading occurs whereas in the case of slow fading, the environment along with the user plays an important role. If the motion is low, slow fading occurs. 

1. When the bandwidth of the signal that is transmitted is less than the bandwidth of the linear phase response of the channel along with a constant gain, it is said to be flat fading. While if the vice versa happens, it is said to be selective fading.
2. In flat fading the signal bandwidth is less than the channel bandwidth whereas it is greater than the channel bandwidth in the case of frequency selective fading.
3. The symbol period is much higher as compared to the delay spread in the case of flat fading whereas it is less than the delay spread in frequency selective fading [5].
4. Signal to Noise (SNR) decreases in flat fading which is not in the case of frequency selective fading. 

1. Samplers that samples the analog signals produce a new signal entirely keeping the SNR same. Thus, the data signals can be over a greater distance as compared to the analog signals.
2. The errors that are introduced during the transmission can be easily identified and eliminated, which otherwise would have been a tedious job in the case of analog signals.
3. The digital signals adds more security as compared to the analog signals [6, 7]. 

In the case of Amplitude Shift Key technique (ASK), Logical low of the data signal does not allow the transmission of the high frequency carrier wave whereas the logical high permits [8]. 

QAM (Quadrature Amplitude Modulation) is a dual modulation technique involving both the analog modulation as well as the digital modulation [9]. The biggest advantage of this technique is that it can modulate to data signals simultaneously, thus reducing the bandwidth and hence cost. Each data signal is first amplitude modulated or amplitude shift key modulated in the case of analog and digital data signal respectively and then each of these signal is phase modulated or phase shift key modulated in the case of analog and digital data signal respectively such that the carrier wave the first by a phase of 19°. Due to this difference in the phase angle it is called as quadrature and since amplitude modulation is involved, it is called as Amplitude Modulation. The resultant signal is then multiplexed and transmitted which is then resected by the QAM receiver, demodulated, passed through low pass filter to get the original data signal.   

Fading in Wireless Communications

Given, the length of the desired antenna is equal to half of its wavelength, which means that L =λ/ 2

The frequency of the waves from this antenna (f) =30Hz

Since, c =3×10⁸ ms^-1, which is the speed of the wave.

Therefore, λ =c/ f

         =3×10⁸/ 30;

                     =10⁷ m

                     = 10000 km

Since, the length of the given antenna= λ /2;

Therefore, =10000/ 2

      = 5000 km 

1. Given, the length of the desired antenna is equal to half of its wavelength to send the radio, which means that L =λ/ 2

The frequency of the waves that has to be sent from the antenna (f) =300Hz

Since, c =3×10⁸ ms^-1, which is the speed of the wave.

Therefore, λ =c/ f

         =3×10⁸/ 300;

                     =1000 km

Since, L = λ/ 2

                = 1000/ 2

     = 500 km

Since, the required length of the given antenna= 500 km 

1. Given, the length of the antenna is equal to half of its wavelength to send the radio, which means that L =λ/ 2

But it is already given as 1 m. So, 1 = λ/ 2

Therefore, λ =2m

Since carrier frequency (f) =c / λ

Where, c is the speed of wave (3×10⁸ ms^-1) and λ is the wavelength just calculated (2m).

So, f =3×10⁸ ms^-1 /2m

        =150 MHz 

Given, the length of the filling is equal to half of its wavelength to send the radio, which means that L = λ/ 2

But it is already given as 0.0025 m. So, 0.0025 = λ/ 2

Therefore, λ =0.005m

Since frequency that will be received by our filling (f) =c / λ

Where, c is the speed of wave (3×10⁸ ms^-1) and λ is the wavelength just calculated (0.005m).

So, f =3×10⁸ ms^-1 /0.005m

=60 GHz 

We need to convert the unit of length from ‘m’ to ‘km’ and the unit of frequency from ‘Hz’ to ‘MHz’ in the equation, P_t/ P_r = (4?fd)² /c²;

Where, ‘f’ denotes frequency, ‘d’ denotes length, ‘c’ denotes Signal speed, ‘P_t’ denotes power that is radiated and ‘P_r’ denotes power received.

Writing the SI units,

= (4? Hz m)² / (ms^-1)² 

=16?² Hz² m² s²/m²

= 16?² (10^-6)² Hz² (10^-3)² m² s² / (10^-6)² (10^-3)² m²

= 16?² MHz² km² s² / (10^-6)² km² (Here, 1Hz = 10^-6 MHz and 1m =10^-3km)

= (4?fd)² / (10^-6 c)²;

The directed radiation pattern consists of a big main loop which signifies the direction of maximum power transmission or reception by the directional antenna. The axis passing through this main loop through its centre is called as the beam axis or boresight axis. Ideally there should be only one main loop but practically side groups may be present. This structure increases the performance of the antenna and decreases its interference with its surrounding environment. Among all the lobes apart from the main lobe, the side lobes are the largest and proper measures has to be taken to eliminate them [10]. The unwanted lobes are called back lobes.

The nature of radiation is stated by radiation pattern. Through radiation pattern the amount of radiation from the source and its reception can be easily understood [2]. Radiation pattern is the field magnitude variation in all the direction from the radiator.

References

[1] Everything RF. (2017, Jan. 5). What is an Isotropic Antenna [online].Available: https://www.google.co.in/search?q=isotropic+antenna&rlz=1C1CHBF_enIN813IN813&oq=isotropic+antenna&aqs=chrome.0.69i59j69i60l3j0l2.4170j1j9&sourceid=chrome&ie=UTF-8

[2] M. Hughes. (2016). Antenna Basics: Radiation Patterns, Permittivity, Directivity, and Gain [online]. Available: https://www.allaboutcircuits.com/technical-articles/antenna-basics-field-radiation-patterns-permittivity-directivity-gain/

[3] Teletopix (2013, Jan. 3). What is fading, its type and effect in RF design [online]. Available: https://www.teletopix.org/gsm/what-is-fading-its-type-and-effect-in-rf-design/

[4] Difference Between. (2011, Nov. 3). Diffraction vs scattering [online]. Available: https://www.differencebetween.com/difference-between-diffraction-and-vs-scattering/

[5] National Instruments. (2018, Sept. 12). Understanding RF signal fading types [online].Available: https://www.ni.com/white-paper/14916/en/

[6] ECE Dunia. (2016, Mar. 7). Advantages of Digital Transmission [online].Available: https://ecedunia.blogspot.com/2016/03/advantages-of-digital-transmission.html

[7] Tech Study Electronics. (2012, Sept. 25). Digital Communication’s Advantages over Analog Communication [online]. Available: https://www.wikiforu.com/2012/09/digital-communication-advantages-over-analog.html

[8] M. N. U. S. Chapal (2011). Amplitude-Shift Keying (ASK) Modulation [online]. Available: https://technoeverywhere.blogspot.com/2011/05/amplitude-shift-key-ask modulation.html

[9] K. Vanitha. (2013). Quadrature Amplitude Modulation and Demodulation in detail [online]. Available: https://www.indiastudychannel.com/resources/160761-Quadrature-Amplitude-Modulation-demodulation-detail.aspx

[10] M. Rouse. (2012). Directional Antenna [online]. Available: https://whatis.techtarget.com/definition/directional-antenna