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…
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…
My friend Mr. Balaji volunteers for Vibha, a non-profit organization whose mission is to ensure that every underprivileged child attains his or her right to education, health and opportunity. Vibha, which was founded in 1991 has a volunteer network of 825 members spread across Atlanta, Austin, Bay Area, Boston, Chicago, Dallas, Houston, Jacksonville, Los Angeles,…
Understanding gradients is essential in machine learning, as they indicate the direction and rate of change in the loss function with respect to model parameters. This post covers the gradients for the vanilla Linear Regression case taking two loss functions Mean Square Error (MSE) and Mean Absolute Error (MAE) as examples. The gradients computed analytically…
Question 34 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q34. Consider the differential equation with and The numerical value of is (A) -2 (B) -1 (C) 0 (D) 1
In this post, let us derive the theoretical bit error probability for 16PSK modulation using Gray coded mapping. For deriving the equation, we will refer material from the following posts: (a) Symbol Error Rate for 16PSK (b) Gray code to Binary code conversion for PSK (c) Binary to Gray code conversion for PSK As discussed…
From the post on Closed Form Solution for Linear regression, we computed 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. In that model all the values in the training set is given equal importance. Let us consider the case where it is known…
Using the services of a new author ‘RV’, we are starting a new series of articles in the blog. Typically in India, many of the competitive examinations pertaining to Engineering (GATE, IES) and rectuitment by private and public sector companies (ISRO, BSNL, BEL, BHEL) uses examination with objective questions for the first level screening. We…
This post attempts to build further on the MIMO equalization schemes which we have discussed – (a) Minimum Mean Square Error (MMSE) equalization, (b) Zero Forcing equalization with Successive Interference Cancellation (ZF-SIC) and (c) ZF-SIC with optimal ordering. We have learned that successive interference cancellation with optimal ordering improves the performance with Zero Forcing equalization….
In two previous posts, we have discussed Convolutional Coding and the associated hard decision Viterbi decoding. In this post lets extent Viterbi decoding algorithm to soft input decision scheme. The modulation used is BPSK and the channel is assumed to be AWGN alone.
Let us try to understand simulation of a typical Orthogonal Frequency Division Multiplexing (OFDM) transmission defined per IEEE 802.11a specification. Orthogonal pulses In a previous post (here ), we have understood that the minimum frequency separation for two sinusoidals with arbitrary phases to be orthogonal is , where is the symbol period. In Orthogonal Frequency…
Its been a nice week for me, wherein I guest posted an article in DSPDesignLine.com. 🙂 The article derives the theoretical symbol error rate for M-QAM modulation. The theoretical results are further supplemented by Matlab/Octave simulation scripts. Those who are familiar with derivation of symbol error rate for 16-QAM modulation will find the equations easy…
I happened to visit ‘The Digital Signal Processing Blog’, maintained by Mr. Andres Kwasinski, Ph. D. In the blog one can find details about the upcoming IEEE conferences pertaining to communication and multimedia processing. Further, in some of the posts, author shares his thoughts on topics like fixed point arithmetic (here) and wavelets (here) etc….
Given that we have discussed Binary to Gray code conversion, let us discuss the Gray to BInary conversion. Conversion from Gray code to natural Binary Let be the equivalent Gray code for an bit binary number with representing the index of the bit. 1. For , i.e, the most significant bit (MSB) of the Gray…