Question 7 on digital from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q7. The output Y of a 2-bit comparator is logic 1 whenever the 2 bit input A is greater than 2 bit input B. The number of combinations for which output is logic 1 is (A) 4 (B)…
The post covers various neural network based word embedding models. Starting from the Neural Probabilistic Language Model from Bengio et al 2003, then reduction of complexity using Hierarchical softmax and Noise Contrastive Estimation. Further works like CBoW, GlOVe, Skip Gram and Negative Sampling which helped to train on much higher data.
This is the first post in the series discussing receiver diversity in a wireless link. Receiver diversity is a form of space diversity, where there are multiple antennas at the receiver. The presence of receiver diversity poses an interesting problem – how do we use ‘effectively‘ the information from all the antennas to demodulate the…
In this post, we will derive the theoretical equation for bit error rate (BER) with Binary Phase Shift Keying (BPSK) modulation scheme in Additive White Gaussian Noise (AWGN) channel. The BER results obtained using Matlab/Octave & Python simulation scripts show good agreement with the derived theoretical results. System Model Transmitter With Binary Phase Shift Keying…
We have discussed quite a few receiver structures for a 2×2 MIMO channel namely, (a) Zero Forcing (ZF) equalization (b) Minimum Mean Square Error (MMSE) equalization (c) Zero Forcing equalization with Successive Interference Cancellation (ZF-SIC) (d) ZF-SIC with optimal ordering and (e) MIMO with MMSE SIC and optimal ordering From the above receiver structures, we…
In the past, I have wondered about discussing personal thoughts in this blog. The answer in my mind was NO and I ve been focusing only on technical topics till date. However, there is a change of mind, thanks to my friend Manoj. Thanks to him, I happened to see Prof. Randy Pausch’s brief 10…
Following the request by Siti Naimah, this post discuss the bit error probability for coherent demodulation of binary Frequency Shift Keying (BFSK) along with a small Matlab code snippet. Using the definition provided in Sec 4.4.4 of [DIG-COMM-SKLAR]), in binary Frequency shift keying (BFSK), the bits 0’s and 1’s are represented by signals and having…
For curve fitting using linear regression, there exists a minor variant of Batch Gradient Descent algorithm, called Stochastic Gradient Descent. In the Batch Gradient Descent, the parameter vector is updated as, . (loop over all elements of training set in one iteration) For Stochastic Gradient Descent, the vector gets updated as, at each iteration the…
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…
In this post, the objective is to figure out the minimum separation between two sinusoidals having frequencies , of duration each to be orthogonal. Let the phase difference between the sinusoidals is where can take any value from to (Refer Example 4.3 [DIG-COMM-SKLAR]). For the two sinuosidals to be orthogonal,
Question 52 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q2. The power spectral density of a real process for positive frequencies is shown below. The values of and , respectively are (A) (B) (C) (D) Solution For a wide sense stationary function, the auto-correlation with delay is defined as,…
The definition of Toeplitz matrix from [1] is: A matrix is said to be Toeplitz if the elements are determined completely by the difference .
Following the discussion on thermal noise and it’s modeling and noise figure computation for a simple resistor network, in this article let us discuss the Noise Figure of cascaded stages.
Oflate, I am getting frequent requests for bit error rate simulations using OFDM (Orthogonal Frequency Division Multiplexing) modulation. In this post, we will discuss a simple OFDM transmitter and receiver, find the relation between Eb/No (Bit to Noise ratio) and Es/No (Signal to Noise ratio) and compute the bit error rate with BPSK.