A friend called me up couple of days back with the question – How white is AWGN? I gave him an answer over phone, which he was not too happy about. That got me thinking bit more on the topic and the result is this post – brief write up on thermal noise and it’s…
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…
In the previous post on Binary to Gray code conversion for PSK, I had claimed that “for a general M-QAM modulation the binary to Gray code conversion is bit more complicated“. However following a closer look, I realize that this is not so complicated. 🙂 The QAM scenario can be treated as independent PAM modulation…
When QAM (Quadrature Amplitude Modulation) is used, typically one may find a scaling factor associated with the constellation mapping operation. It may be reasonably obvious that this scaling factor is for normalizing the average energy to one. This post attempts to compute the average energy of the 16-QAM, 64-QAM and M-QAM constellation (where is a…
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,
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…
Typical communication systems use I-Q modulation and we had discussed the need for I-Q modulation in the past. In this post, let us understand I-Q imbalance and its effect on transmit signal.
The article gives a quick overview of a simple statistical multipath channel model called Rayleigh fading channel model. Multipath environment In a multipath environment, it is reasonably intuitive to visualize that an impulse transmitted from transmitter will reach the receiver as a train of impulses.
In this post, let us try to derive the symbol error rate for 16-PSK (16-Phase Shift Keying) modulation. Consider a general M-PSK modulation, where the alphabets, are used. (Refer example 5-38 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]) Figure: 16-PSK constellation plot
Question 13 on analog electronics from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q13. The diodes and the capacitors in the circuit shown are ideal. The voltage across the diode is (A) (B) (C) (D) Solution The first half of the circuit is a negative clamper circuit and the second half…
Last week, I received an email from Mr. Kishore. He was wondering about the physical significance of negative frequency. Does negative frequency really exist? Though I have seen conflicting views on the net (thread in complextoreal.com, thread in comp.dsp), my perspective is that negative frequency exist. The concept of negative frequency helps me a lot…
We have quite a few articles discussing bit and symbol error rates for popular digital modulation schemes in Additive White Gaussian Noise (AWGN) channel. This post summarizes the articles discussing the theoretical and simulated error rates for the digital modulation schemes like BPSK, QPSK, 4–PAM, 16PSK and 16QAM. Further, Bit Error Rate with Gray coded…
In a previous post (here), we looked at using CORDIC (Co-ordinate Rotation by DIgital Computer) for understanding how a complex number can be rotated by an angle without using actual multipliers. Let us know try to understand how we can use CORDIC for finding the phase and magnitude of a complex number. Basics The CORDIC…
The earlier posts on phase noise discussed about phase noise in oscillators, conversion of phase noise profile to jitter and the impact of phase noise on the error vector magnitude (evm). This post discuss the impact of phase noise on the spectrum of the transmit waveform. A simple random QPSK modulated symbols, oversampled and passed…