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February 11, 2012March 31, 2012Antennas

Some Common Antenna Radiation Patterns

A Radiation Pattern is a 3 dimensional description of how an antenna radiates power in the surrounding space. This pattern is usually measured at a sufficient distance from the antenna known as the far-field. In simple words it is the power radiated in a certain direction with reference to an omni-directional antenna (a theoretical antenna that radiates equally in all the directions). Given below are the radiation patterns for some common antenna types. Dipole Antenna 3D Radiation Pattern Although the Radiation Pattern is a 3 dimensional quantity it is usually sufficient to describe it in two orthogonal planes (one […]

February 8, 2012February 8, 2012Antennas

Antenna Gain and Directivity

Antenna Gain and Directivity are two terms that are sometimes not that well understood. The Antenna Gain and Directivity are related through the following equation. G(θ,φ)=E*D(θ,φ) That is, the Antenna Gain in a particular direction is equal to the Directivity in that direction multiplied by the Antenna Efficiency. Antenna Directivity is the ratio of energy transmitted (or received) by the antenna in a particular direction to the energy transmitted (or received) in that direction by an isotropic source. This is also known as the Directive Gain. The Antenna Gain (also known as the Power Gain) seems to be a better […]

February 1, 2012February 1, 2012Antennas

E-field of a Dipole Antenna

In the previous post we plotted the E-field of a half wave dipole. We now turn our attention to higher antenna lengths such 1,1.5 and 2.0 times the wavelength. The E-field pattern is a three dimensional pattern, however, we only plot the E-field in a 2D plane along the axis of the dipole. It is observed that as the antenna length is increased from 0.5*wavelength to 1.0*wavelength the antenna becomes more directional. However, as the length is further increased from 1.0*wavelength to 1.5*wavelength and 2.0*wavelength sidelobes begun to appear. These sidelobes are an unwanted phenomenon in a typical telecommunications application. […]

January 26, 2012February 1, 2012Antennas, Random Thoughts

Half Wave Dipole Antenna

A dipole antenna is a simple antenna that can be built out of electrical wire. The most common dipole antenna is a half wave dipole which is constructed from a piece of wire half wavelength long. The wire is split in the center to connect the feeding wires. The E-field of the antenna has a circular pattern along a plane which cuts the axis of the antenna perpendicularly and is similar to a figure of 8 in a plane along the axis of the antenna [3D pattern]. The exact E-field can be calculated as: The MATLAB code for generating the […]

January 10, 2012February 2, 2012Channel Modeling, LTE

Implementing a Non-Uniformly Spaced Tapped Delay Line Channel Model

Question: Since you are good on fundamentals I would like to ask you a question that puzzles me. LTE channels models are defined at irregular time intervals as shown in [1]. The EPA, EVA and ETU channel taps can best be described as being sampled at multiples of 10 nsec. However, LTE signal is sampled at multiples of 3.84 MHz (Ts=260.416667 nsec). So how does one perform convolution operation. Answer: Empirical multipath channel is usually characterized as a τ-spaced tapped delay line (TDL), whose power delay profile (PDP) is either uniformly spaced, or more frequently, spaced with arbitrary time delay(s). […]

January 6, 2012June 7, 2012Channel Modeling, LTE

WINNER-II Path Loss Model

In simple terms the path loss is the difference between the transmitted power and the received power of a wireless communication system. This may range from tens of dB to more than a 100 dB e.g. if the transmitted power of a wireless communication system is 30 dBm and the received power is -90 dBm then the path loss is calculated as 30-(-90)=120 dB. Path loss is sometimes categorized as a large scale effect (in contrast to fading which is a small scale effect). According to the WINNER-II model the path loss can be calculated as: Here d is the […]

December 15, 2011December 27, 2011Capacity, LTE

Soft Frequency Reuse in LTE

Frequency Reuse is a well known concept that has been applied to wireless systems over the past two decades e.g. in GSM systems. As the name suggests Frequency Reuse implies using the same frequencies over different geographical areas. If we have a 25MHz band then we can have 125 GSM channels and 125*8=1000 time multiplexed users in a given geographical area. Now if we want to increase the number of users we would have to reuse the same frequency band in a geographically separated area. The technique usually adopted is to use a fraction of the total frequency band in […]

December 8, 2011June 4, 2014BER Performance, LTE, WiMAX

QAM Theoretical BER in AWGN

Quadrature Amplitude Modulation (QAM) is an important modulation scheme as it allows for higher data rates and spectral efficiencies. The bit error rate (BER) of QAM can be calculated through Monte Carlo simulations. However this becomes quite complex as the constellation size of the modulation schemes increases. Therefore a theoretical approach is sometimes preferred. The BER for Gray coded QAM, for even number of bits per symbol, is shown below. Gray coding ensures that a symbol error results in a single bit error. The code for calculating the theoretical QAM BER for k even (even number of bits per symbol) […]

November 25, 2011April 27, 2012Capacity, LTE, WiMAX

MIMO Capacity in a Fading Environment

The Shannon Capacity of a channel is the data rate that can be achieved over a given bandwidth (BW) and at a particular signal to noise ratio (SNR) with diminishing bit error rate (BER). This has been discussed in an earlier post for the case of SISO channel and additive white Gaussian noise (AWGN). For a MIMO fading channel the capacity with channel not known to the transmitter is given as (both sides have been normalized by the bandwidth [1]): Shannon Capacity of a MIMO Channel where NT is the number of transmit antennas, NR is the number of receive […]