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…
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….
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…
In the previous post on Batch Gradient Descent and Stochastic Gradient Descent, we looked at two iterative methods for finding 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. A closed form solution for finding the parameter vector is possible, and in this post…
In a classification problem, the output (also called the label or class) takes a small number of discrete values rather than continuous values. For a simple binary classification problem, where output takes only two discrete values : 0 or 1, the sigmoid function can be used to transform the output of a linear regression model…
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…
Those who are regular visitors to dsplog.com might have noticed the small FeedBurner chicklet on the side showing subscriber count showing 1000+ subscribers. Its a nice milestone to reach, one that looked so distant when I wrote the first post stating the objective of this blog on 26th February 2007. We now have around 86…
Let us try to understand simulation of a typical Orthogonal Frequency Division Multiplexing (OFDM) transmission defined per IEEE 802.11a specification. Orthogonal pulses In a previous post (here ), we have understood that the minimum frequency separation for two sinusoidals with arbitrary phases to be orthogonal is , where is the symbol period. In Orthogonal Frequency…
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…
Following a brief discussion with my friend Mr. Rethnakaran Pulikkoonattu on phase noise profiles, he pointed me to his write up on Oscillator Phase Noise and Sampling Clock Jitter . In this post, we will discuss the math behind integrating the phase noise power spectral density (in dBc/Hz) to find the root mean square jitter value.
Advanced Computing and Communication Society (ACS) of India is organizing ICCBN 2008 conference (International Conference on Communication, Convergence, and Broadband Networking) from July 17th to 20th 2008 at National Science Seminar Complex at Indian Institute of Science (IISc), Bangalore. ICCBN Conference aims to provide a premier forum for researchers, industry practitioners and educators to present…
In a previous post, we discussed about a probable first order digital PLL for tracking constant phase offset. The assumption was that as the phase offset is small and the bits gets decoded correctly, the phase difference between the ideal and actual constellation gives the initial value of phase. However, in typical scenarios it may…
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…
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…