Multicarrier Beamforming at mmWave
Discussion of Multicarrier Beamforming particularly in the context of Massive MIMO and Millimeterwave
Read moreCategory: Fundamentals
The basic building blocks.
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 […]
Read moreFundamentals 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. […]
Read moreMassive 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 […]
Read moreBasics 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 […]
Read moreFundamentals 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.
Read moreIbn al-Haytham to Maxwell: A Long Road
The journey that started with Ibn al-Haytham experimenting with his Camera Obscura in the eleventh century was completed eight hundred years later by James Clerk Maxwell and Heinrich Hertz. While Maxwell laid down the mathematical framework that described the behavior of Electromagnetic waves, Hertz conclusively proved the existing of these invisible waves through his experiments.
Read moreOmar Khayyam’s Solution to Cubic Equations
Omar Khayyam was a Muslim mathematician and poet of the 11th and 12th centuries (1048-1131). His poetic works known as Rubaiyat of Omar Khayyam were translated from Persian to English and made popular by Edward Fitzgerald in the late nineteenth century.
Read moreOn the Origins of Snell’s Law (Ibn Sahl’s Law)
Most of Physics courses present Snell’s law of refraction in one form or another. But a little known mathematician with the name Ibn Sahl (c. 940–1000) found this law about 650 years before Snell (Willebrord Snellius c. 1580–1626). This mathematical expression was lost for centuries until some scholars recently were able to dig it up from historical records.
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