An important milestone for the dspLog happened on Oct 21st 2008. On this day last year, the blog migrated from the Blogger platform to the independently hosted platform at www.dsplog.com ! Belated birthday wishes for the blog!!! 🙂 Looking back, the first year was satisfying – both in terms of contents and traffic. We started…
Thanks to Mr. Raghava G D’s comments on the post discussing Question 38 on Communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper, realized that I had made an error in the solution. Have the updated the post with the right answer and additional explanations.
In the past, we had discussed BER for BPSK in flat fading Rayleigh channel. In this post, lets discuss a frequency selective channel with the use of Zero Forcing (ZF) equalization to compensate for the inter symbol interference (ISI). For simplifying the discussion, we will assume that there is no pulse shaping at the transmitter….
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.
Question 46 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q46. The maximum value of in the interval [1, 6] is (A) 21 (B) 25 (C) 41 (D) 46 Solution Let us start by finding the critical points of the function . The first derivative is, . Solving by…
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)…
In a previous post, we had discussed a 2×2 MIMO transmission using BPSK modulation in Rayleigh channel with a Zero Forcing equalizer. The simulated results with the 2×2 MIMO system with zero forcing equalizer showed matching results as obtained in for a 1×1 system for BPSK modulation in Rayleigh channel. In this post, we will…
Some of us would have used Newton’s method (also known as Newton-Raphson method) in some form or other. The method has quite a bit of history, starting with the Babylonian way of finding the square root and later over centuries reaching the present recursive way of finding the solution. In this post, we will describe…
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,…
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 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…
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….
Post describes about the need for I-Q modulation by comparing the spectral efficiency of passband PAM and passband QAM.
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…