In this post, let us try to understand Gray codes and their usage in digital communication. Quoting from Wiki entry on Gray code [Gray-Wiki], The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one digit. In a digital communication system,…
Let us try to understand the formula for Channel Capacity with an Average Power Limitation, described in Section 25 of the landmark paper A Mathematical Theory for Communication, by Mr. Claude Shannon. Further, the following writeup is based on Section 12.5.1 from Fundamentals of Communication Systems by John G. Proakis, Masoud Salehi
Thanks to the nice article from Xilinx TechXclusives [XLNX-TECH], let us try to understand the probable digital implementation of resistor-capacitor based low pass filter. Consider a simple RC filter shown in the figure below. Assuming that there is no load across the capacitor, the capacitor charges and discharges through the resistor path. Figure: RC low…
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,
The post on IQ imbalance in transmitter, briefly discussed the effect of amplitude and phase imbalance and also showed that IQ imbalance results in spectrum at the image frequency. In this article, we will quantify the power of the image with respect to the desired tone (also known as IMage Rejection Ratio IMRR) for different…
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 Problem 4.36 of DSP-Proakis [1], the task is to provide insights into harmonic distortion which may be present in practical sinusoidal generators. Consider the signal , where . My take: The discrete time signal of fundamental period can consist of frequency components separated by radians or cycles (Refer Section4.2 in [1]). The Fourier series…
Two points suffice for drawing a straight line. However we may be presented with a set of data points (more than two?) presumably forming a straight line. How can one use the available set of data points to draw a straight line? A probable approach is to draw a straight line which hopefully minimizes the…
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.
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.
In a post on Minimum Shift Keying (MSK), we had discussed that MSK uses two frequencies which are separated by and phase discontinuity is avoided in symbol boundaries. In that post, we had discussed MSK as a continuous phase transmit signal and showed that phase changes through 0, 90, 180 and 270 degrees. In this…
In the past, we had discussed several posts on two transmit two receive MIMO communication, where the transmission was based on V-BLAST. The details about V-BLAST can be read from the landmark paper V-BLAST: An architeture for realizing very high data rates over the rich scattering wireless channel – P. W. Wolniansky, G. J. Foschini,…
Following the request by Siti Naimah, this post discuss the bit error probability for coherent demodulation of binary Frequency Shift Keying (BFSK) along with a small Matlab code snippet. Using the definition provided in Sec 4.4.4 of [DIG-COMM-SKLAR]), in binary Frequency shift keying (BFSK), the bits 0’s and 1’s are represented by signals and having…
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…