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…
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Question 15 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q15. A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount and decreases that of the…
In two previous posts, we have derived theoretical symbol error rate for 16-QAM and 16-PSK modulation schemes. The links are: (a) Symbol error rate for 16-PSK (b) Symbol error rate for 16-QAM Given that we are transmitting the same number of constellation points in both 16-PSK and 16-QAM, let us try to understand the better…
Let us derive the theoretical 16QAM bit error rate (BER) with Gray coded constellation mapping in additive white Gaussian noise conditions. Further, the Matlab/Octave simulation script can be used to confirm that the simulation is in good agreement with theory.
From the previous posts on Linear Regression (using Batch Gradient descent, Stochastic Gradient Descent, Closed form solution), we discussed couple of different ways to estimate the parameter vector in the least square error sense for the given training set. However, how does the least square error criterion work when the training set is corrupted by…
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….
Wishing all the readers of dsplog.com a great year 2010 ! Its been a mixed year for dsplog. Some key milestones a) Crossing 1000 subscribers with 1100+ comments in March 2009 b) Crossing 100 posts with 2200 subscribers and 2600+ comments in October 2009 c) As I write this, we have 102 posts with 2603…
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 38 on Communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q38. A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0)=9/10, then the probability of error for an optimum receiver will be (A) 7/80 (B) 63/80 (C)…
Long back in time we discussed the BER (bit error rate) for BPSK modulation in a simple AWGN channel (time stamps states August 2007). Almost an year back! It high time we discuss the BER for BPSK in a Rayleigh multipath channel. In a brief discussion on Rayleigh channel, wherein we stated that a circularly…
Coding is a technique where redundancy is added to original bit sequence to increase the reliability of the communication. 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 article which discuss…
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,…