While trying to derive the theoretical bit error rate (BER) for BPSK modulation in a Rayleigh fading channel, I realized that I need to discuss chi square random variable prior. What is chi-square random variable? Let there be independent and identically distributed Gaussian random variables with mean and variance and we form a new random…
In this post, let us discuss a simple implementation friendly scheme for computing the absolute value of a complex number . The technique called (alpha Max + beta Min) algorithm is discussed in Chapter 13.2 of Understanding Digital Signal Processing, Richard Lyons and is also available online at Digital Signal Processing Tricks – High-speed vector…
Minimum shift keying (MSK) is an important concept to learn in digital communications. It is a form of continuous phase frequency shift keying . In minimum phase shift keying, two key concepts are used. (a) The frequency separation of the sinusoidals used for representing bits 1’s and 0’s are , where is the symbol period….
Question 39 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q39. The signal as shown is applied both to a phase modulator (with as the phase constant) and a frequency modulator (with as the frequency constant) having the same carrier frequency. The ratio for the same maximum phase deviation is,…
Question 24 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q24. Two independent random variables X and Y are uniformly distributed in the interval [-1, 1]. The probability that max[X,Y] is less than 1/2 is (A) 3/4 (B) 9/16 (C) 1/4 (D) 2/3
Coding is a technique where redundancy is added to original bit sequence to increase the reliability of the communication. In this article, lets discuss a simple binary convolutional coding scheme at the transmitter and the associated Viterbi (maximum likelihood) decoding scheme at the receiver. Update: For some reason, the blog is unable to display the…
We have installed Google FriendConnect on dspLog.com. With Google Friend Connect, you can: (a) You can interact with other members who have similiar interests. You will come to know the list of other sites (apart from dspLog.com) where the members have joined. You can add a member as a friend and so on. (b) You…
This is the third 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 previous posts, we had discussed equalization of a 2×2 MIMO channel with Zero Forcing (ZF) equalization and later, Zero Forcing equalization with successive interference cancellation (ZF-SIC). In this post, we will explore a variant of ZF-SIC called Zero Forcing Successive Interference Cancellation with optimal ordering. We will assume that the channel is a flat…
Question 52 on electromagnetics from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. An infinitely long uniform solid wire of radius carries a uniform dc current of density . Q52. The magnetic field at a distance from the center of the wire is proportional to (A) for and for (B) for and for (C) for and for (D) for and for Solution…
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…
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 25 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q25. If , then the value of is, (a) (b) (c) (d) 1
In this post, let us evaluate the impact of frequency offset resulting in Inter Carrier Interference (ICI) while receiving an OFDM modulated symbol. We will first discuss the OFDM transmission and reception, the effect of frequency offset and later we will define the loss of orthogonality and resulting signal to noise ratio (SNR) loss due…