GATE-2012 ECE Q25 (math)
Question 25 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q25. If , then the value of is, (a) (b) (c) (d) 1
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GATE-2012 ECE Q15 (communication)
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…
Interpreting the output of fft() operation in Matlab
It might be interesting to interpret the output of the fft() function in Matlab. Consider the following simple examples. fsMHz = 20; % sampling frequency fcMHz = 1.5625; % signal frequency N = 128; % fft size % generating the time domain signal x1T = exp(j*2*pi*fcMHz*[0:N-1]/fsMHz); x1F = fft(x1T,N); % 128 pt FFT figure; plot([-N/2:N/2-1]*fsMHz/N,fftshift(abs(x1F)))…
MIMO with MMSE equalizer
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…
Scaling factor in QAM
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…
Maximal Ratio Combining (MRC)
This is the third post in the series discussing receiver diversity in a wireless link. Receiver diversity is a form of space diversity, where there are multiple antennas at the receiver. The presence of receiver diversity poses an interesting problem – how do we use ‘effectively‘ the information from all the antennas to demodulate the…
Bit Error Rate (BER) for BPSK modulation
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…
Newton’s method to find square root, inverse
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…
Derivation of BPSK BER in Rayleigh channel
This is a guest post by Jose Antonio Urigüen who is an Electrical and Electronic Engineer currently studying an MSc in Communications and Signal Processing at Imperial College in London. This guest post has been created due to his own curiosity when reviewing some concepts of BER for BPSK in Rayleigh channnel published in the…
Batch Gradient Descent
I happened to stumble on Prof. Andrew Ng’s Machine Learning classes which are available online as part of Stanford Center for Professional Development. The first lecture in the series discuss the topic of fitting parameters for a given data set using linear regression. For understanding this concept, I chose to take data from the top…
Symbol Error Rate (SER) for 4-PAM
Following discussion of bit error rate (BER) for BPSK and bit error rate for FSK, it may be interesting to move on to discuss a higher order constellation such as Pulse Amplitude Modulation (PAM). Consider that the alphabets used for a 4-PAM is (Refer example 5-34 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]).
Hamming (7,4) code with hard decision decoding
In previous posts, we have discussed convolutional codes with Viterbi decoding (hard decision, soft decision and with finite traceback). Let us know discuss a block coding scheme where a group of information bits is mapped into coded bits. Such codes are referred to as codes. We will restrict the discussion to Hamming codes, where 4…
Non coherent demodulation of pi/4 DQPSK (TETRA)
In TETRA specifications, one of the modulation technique used is Differential Quaternary Phase Shift Keying (DQPSK). We will discuss the bit error rate with non-coherent demodulation of DQPSK in Additive White Gaussian Noise (AWGN) channel.
Simulating Minimum Shift Keying Transmitter
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….