Simulation – Page 5

June 26, 2012June 29, 2012Channel Modeling, Fundamentals

Uniform, Gaussian and Rayleigh Distribution

It is sometimes important to know the relationship between various distributions. This can be useful if there is a function available for one distribution and it can be used to derive other distributions. In the context of Wireless Communications it is important to know the relationship between the Uniform, Gaussian and Rayleigh distribution. According to Central Limit Theorem the sum of a large number of independent and identically distributed random variables has a Gaussian distribution. This is used to model the amplitude of the in-phase and quadrature components of a wireless signal. Shown below is the model for the received […]

May 22, 2012May 31, 2022BER Performance, Fundamentals, LTE, Modulation, WiMAX

M-QAM Bit Error Rate in Rayleigh Fading

We have previously discussed the bit error rate (BER) performance of M-QAM in AWGN. We now discuss the BER performance of M-QAM in Rayleigh fading. The one-tap Rayleigh fading channel is generated from two orthogonal Gaussian random variables with variance of 0.5 each. The complex random channel coefficient so generated has an amplitude which is Rayleigh distributed and a phase which is uniformly distributed. As usual the fading channel introduces a multiplicative effect whereas the AWGN is additive. The function “QAM_fading” has three inputs, ‘n_bits’, ‘M’, ‘EbNodB’ and one output ‘ber’. The inputs are the number of bits to be passed […]

May 21, 2012May 31, 2022BER Performance, Fundamentals, LTE, Modulation, WiMAX

M-QAM Bit Error Rate in AWGN

Quadrature Amplitude Modulation has been adopted by most wireless communication standards such as WiMAX and LTE. It provides higher bit rates and consequently higher spectral efficiencies. It is usually used in conjunction with Orthogonal Frequency Division Multiplexing (OFDM) which provides a simple technique to overcome the time varying frequency selective channel. We have previously discussed the formula for calculating the bit error rate (BER) of QAM in AWGN. We now calculate the same using a simple Monte Carlo Simulation. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % FUNCTION THAT CALCULATES THE BER OF M-QAM IN AWGN % n_bits: Input, number of bits % M: Input, constellation […]

April 6, 2012April 6, 2012Antennas, LTE, WiMAX

Antennas on Samsung Galaxy S

We have previously discussed the theory of Planar Inverted F Antennas (PIFA), now let us look at a practical example. Shown below is the rear view of a Samsung Galaxy S phone with six antennas. The description of these antennas is given below. 1. 2.6 GHz WiMAX Tx/Rx Antenna 2. 2.6 GHz WiMAX Antenna Rx Only (as a diversity antenna) 3. WiFi/Bluetooth Tx/Rx Antenna 4. Cell/PCS CDMA/EVDO Tx/Rx Antenna 5. Cell/PCS CDMA/EVDO Rx Only (as a diversity antenna) 6. GPS Antenna Rx Only The figure above shows the top conducting plane of the PIFAs. The bottom conducting plane (ground plane) is […]

March 27, 2012April 6, 2012Antennas, LTE, WiMAX

Planar Inverted F Antenna (PIFA)

A Planar Inverted F Antenna or PIFA is a very common antenna type being used in cell phones. In fact a cell phone would have multiple PIFAs for LTE, WiMAX, WiFi, GPS etc. Furthermore, there would be multiple PIFAs for diversity reception and transmission. A PIFA is composed of 5 basic elements. 1. A large metallic ground plane 2. A resonating metallic plane 3. A substrate separating the two planes 4. A shorting pin (or plane) 5. A feeding mechanism The resonant frequency of the PIFA can be calculated from the relationship between the wavelength of the antenna and the […]

March 6, 2012March 6, 2012Antennas

E and H Field of a Patch

The Electric and Magnetic Field variations within a patch are sometimes a bit confusing and difficult to visualize. The figure below shows the E and H Field variations within a rectangular patch of length L and width W. E and H Field of a Patch As can be seen the E-field varies along the length of the patch with minimum at the centre and maximum at the edges (maximum positive and maximum negative). The H-field also varies along the length is in a direction perpendicular to the E-field. The H-field is maximum at the center and minimum at the edges. […]

February 23, 2012February 23, 2012Antennas

Patch Antenna Design using Transmission Line Model

A microstrip antenna can be designed using either the transmission line model or the cavity model (more complex models also exist that suit a particular design). We here demonstrate the transmission line model since it is fairly simple to implement and results in antenna designs with reasonably good performance in terms of return loss and efficiency. The design starts with selecting the operating frequency, selecting a substrate with the required permittivity, and defining the width of the substrate. Thick substrates with low permittivity result in antenna designs with high efficiency and large bandwidths. Thin substrates with high permittivity lead to a smaller […]

February 17, 2012March 16, 2012Antennas

E-field of a Patch Antenna

A Microstrip Patch Antenna or simply a Patch Antenna is a very common antenna type used in cell phones and many other electronic devices. It basically consists of two metallic plates separated by a dielectric layer. The metallic plates are usually made of copper or some other highly conductive material. Another important feature of this antenna is the feeding mechanism, which is also made of a highly conductive material. A Microstrip Patch Antenna fed by a 50 ohm transmission line and a quarterwave transformer is shown below. The E-field and H-field generated by the Patch Antenna can be calculated by using […]

February 15, 2012August 9, 2013Antennas

Some Commonly Used Antenna Terminology

Antenna Pattern Antenna Pattern or Radiation Pattern is a three dimensional description of how the antenna radiates energy in to the space around it. All practical antennas are directional i.e. they radiate more energy in certain directions and lesser energy in other directions. Although the Radiation Pattern is a three dimensional quantity it can be described in two perpendicular planes known as the principal planes. Usually one of these planes is horizontal (azimuth plane) and the other is vertical (elevation plane). Gain As discussed previously antennas do not radiate uniformly in all directions. Antenna Gain is the ratio of the […]