Simulation – Page 3

December 17, 2018June 4, 2022Antennas, Fundamentals

Fundamentals of a Circular Array – Mathematical Model and Code

Array Factor and Element Factor In the previous post we discussed the case of a Square Array which is a special case of a Rectangular Array. The code we shared can handle both the cases as well as Uniform Linear Array. We did briefly talk about the response of an element vs the response of an array, but we did not put forward the mathematical relationship. So here it is: Response of an Array = Array Factor x Element Factor In this post as well as previous posts we have assumed the element response to be isotropic (or at least […]

November 2, 2018December 9, 2018Antennas, Fundamentals

Fundamentals of a Rectangular Array – Mathematical Model and Code

Background In the previous few posts we discussed the fundamentals of Uniform Linear Arrays (ULAs), Beamforming, Multiuser Detection and Massive MIMO ([1], [2], [3], [4]). Now we turn our attention to more complicated array structures such as rectangular, triangular and circular. We still assume each element of the array to have an isotropic or omni-directional (in the plane of the array) radiation pattern. The mathematical models for more complicated radiation patterns are an extension of the what is developed here. Square and Rectangular Arrays In this post we consider a square array which is a special case of rectangular array. […]

October 14, 2018December 22, 2018Antennas, BER Performance, Fundamentals, LTE

Massive MIMO Fundamentals and Code

Background Just like different frequency bands and time slots can be used to multiplex users, spatial domain can also be exploited to achieve the same result. It is well known that if there are 4 transmit antennas and 4 receive antennas then four simultaneous data streams can be transmitted over the air. This can be scaled up to 8 x 8 or in the extreme case to 128 x 128. When the number of transmit or receive antennas is greater than 100 we typically call it a Massive MIMO scenario and we need specialized signal processing techniques to handle this […]

February 9, 2018October 20, 2018Antennas, BER Performance, Channel Modeling, LTE

Fundamentals of Linear Array Processing – Receive Beamforming

In the previous two posts we discussed the fundamentals of array processing particularly the concept of beamforming (please check out array processing Part-1 and Part-2). Now we build upon these concepts to introduce some linear estimation techniques that are used in array processing. These are particularly suited to a situation where multiple users are spatially distributed in a cell and they need to be separated based upon their angles of arrival. But first let us introduce the linear model; I am sure you have seen this before. x=Hs+w Here, s is the vector of symbols transmitted by M users, H […]

January 27, 2018September 6, 2019Antennas, Fundamentals, LTE, WiFi

Basics of Beamforming in Wireless Communications

In the previous post we had discussed the fundamentals of a Uniform Linear Array (ULA). We had seen that as the number of array elements increases the Gain or Directivity of the array increases. We also discussed the Half Power Beam Width (HPBW) that can be approximated as 0.89×2/N radians. This is quite an accurate estimate provided that the number of array elements ‘N’ is sufficiently large. But the max Gain is always in a direction perpendicular to the array. What if we want the array to have a high Gain in another direction such as 45 degrees. How can […]

January 21, 2018June 26, 2022Antennas, Fundamentals

Fundamentals of a Uniform Linear Array (ULA)

A Uniform Linear Array (ULA) is a collection of sensor elements equally spaced along a straight line. The most common type of sensor is a dipole antenna that can transmit and receive Electromagnetic Waves over the air. Other types of sensors include acoustic sensors that may be used in air or under water. The requirements of a ULA are different for different applications but the most common requirement is to improve the Signal to Noise Ratio (SNR) and to improve its response (Gain) in a particular direction.

August 24, 2017August 28, 2017BER Performance, Channel Modeling, LTE, WiMAX

BER for BPSK-OFDM in Frequency Selective Channel

As the data rates supported by wireless networks continue to rise the bandwidth requirements also continue to increase (although spectral efficiency has also improved). Remember GSM technology which supported 125 channels of 200KHz each, which was further divided among eight users using TDMA. Move on to LTE where the channel bandwidth could be as high as 20MHz (1.4MHz, 3MHz, 5MHz, 10MHz, 15MHz and 20MHz are standardized). This advancement poses a unique challenge referred to as frequency selective fading. This means that different parts of the signal spectrum would see a different channel (different amplitude and different phase offset). Look at […]

August 22, 2017August 22, 2017Channel Modeling, Fundamentals, LTE

Rayleigh Fading Envelope Generation – Python

When wireless signals travel from a transmitter to a receiver they do so after reflection, refraction, diffraction and scattering from the environment. Very rarely is there a direct line of sight (LOS) between the transmitter and receiver. Thus multiple time delayed copies of the signal reach the receiver that combine constructively and destructively. In a sense the channel acts as an FIR (finite impulse response) filter. Furthermore since the transmitter or receiver may be in motion the amplitude and phase of these replicas varies with time. There are several methods to model the amplitude and phase of each of these […]

July 16, 2017July 17, 2017BER Performance, Fundamentals

Alamouti – Transmit Diversity Scheme – Implemented in Python

We have already seen in previous posts that the BER of BPSK increases significantly when the channel changes from a simple AWGN channel to a fading channel. One solution to this problem, that was proposed by Alamouti, was to use Transmit Diversity i.e. multiple transmit antennas transmit the information over multiple time slots increasing the likelihood of receiving the information. We have considered the simplest case of two transmit antennas and BPSK modulation (QPSK modulation would give the same BER with twice the throughput). Given below is the Python code for this, feel free to modify it and run it […]