Given that we have went over the symbol error probability for 4-PAM and symbol error rate for 4-QAM , let us extend the understanding to find the symbol error probability for 16-QAM (16 Quadrature Amplitude Modulation). Consider a typical 16-QAM modulation scheme where the alphabets (Refer example 5-37 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]). are used.
In the past, we had discussed BER for BPSK in flat fading Rayleigh channel and BER for BPSK in a frequency selective channel using Zero Forcing Equalization. In this post, lets discuss a frequency selective channel with the use of Minimum Mean Square Error (MMSE) equalization to compensate for the inter symbol interference (ISI). For…
Considering a typical scenario where there might exist a small phase offset between local oscillator between the transmitter and receiver. Figure 1 : Transmitter receiver with constant phase offset In such cases, it might be desirable to estimate and track the phase offset such that the performance of the receiver does not degrade.
After a gap of around 7 months, we decided to migrate to a new template (recall, last time we changed was in May 2008). The template which we decided to use is designed by Elegant Themes. They have a wide array of themes and I chose to use the Who’s Who theme.
Let us try to understand the formula for Channel Capacity with an Average Power Limitation, described in Section 25 of the landmark paper A Mathematical Theory for Communication, by Mr. Claude Shannon. Further, the following writeup is based on Section 12.5.1 from Fundamentals of Communication Systems by John G. Proakis, Masoud Salehi
Question 11 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q11. The unilateral Laplace transform of is . The unilateral Laplace transform ofis (A) (B) (C) (D) Solution From the definition of Laplace transform for a function defined for all real numbers is, , where with real numbers and . To find the Laplace…
Question 6 on digital circuit from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q6. Consider the given circuit In this circuit, the race around (A) does not occur (B) occurs when CLK=0 (C) occurs when CLK=1 and A=B=1 (D) occurs when CLK=1 and A=B=0
I happened to stumble on Prof. Andrew Ng’s Machine Learning classes which are available online as part of Stanford Center for Professional Development. The first lecture in the series discuss the topic of fitting parameters for a given data set using linear regression. For understanding this concept, I chose to take data from the top…
Two points suffice for drawing a straight line. However we may be presented with a set of data points (more than two?) presumably forming a straight line. How can one use the available set of data points to draw a straight line? A probable approach is to draw a straight line which hopefully minimizes the…
Given that we have discussed symbol error rate probability for a 4-PAM modulation, let us know focus on finding the symbol error probability for a QPSK (4-QAM) modulation scheme. Background Consider that the alphabets used for a QPSK (4-QAM) is (Refer example 5-35 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]). Download free e-Book discussing theoretical and simulated error rates for…
When QAM (Quadrature Amplitude Modulation) is used, typically one may find a scaling factor associated with the constellation mapping operation. It may be reasonably obvious that this scaling factor is for normalizing the average energy to one. This post attempts to compute the average energy of the 16-QAM, 64-QAM and M-QAM constellation (where is a…
In a previous post, the variance of the in-band quantization noise for a first order sigma delta modulator was derived. Taking it one step furhter, let us find the variance of the quantization noise filtered by a second order filter. With a first order filter, the quantization noise passes through a system with transfer function…
In the previous post on Batch Gradient Descent and Stochastic Gradient Descent, we looked at two iterative methods for finding the parameter vector which minimizes the square of the error between the predicted value and the actual output for all values in the training set. A closed form solution for finding the parameter vector is possible, and in this post…
The definition of Toeplitz matrix from [1] is: A matrix is said to be Toeplitz if the elements are determined completely by the difference .