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…
Question 38 on Communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q38. A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0)=9/10, then the probability of error for an optimum receiver will be (A) 7/80 (B) 63/80 (C)…
TETRA (TErrestrial Trunked RAdio) is a wireless specification intended to be used by government agencies, public health services, rail transport, military etc. TETRA specification comes from ETSI (European Telecommunication Standards Institute). We plan to start a post series on the building blocks of TETRA physical layer and radio specifications and this is the first post…
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…
Its been a nice week for me, wherein I guest posted an article in DSPDesignLine.com. 🙂 The article derives the theoretical symbol error rate for M-QAM modulation. The theoretical results are further supplemented by Matlab/Octave simulation scripts. Those who are familiar with derivation of symbol error rate for 16-QAM modulation will find the equations easy…
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
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)))…
Question 11 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q11. The unilateral Laplace transform of is . The unilateral Laplace transform ofis (A) (B) (C) (D) Solution From the definition of Laplace transform for a function defined for all real numbers is, , where with real numbers and . To find the Laplace…
In problem 4.37 of DSP-Proakis [1], the task is to analyze the total harmonic distortion in quantized sinusoidal, where .
The post covers various neural network based word embedding models. Starting from the Neural Probabilistic Language Model from Bengio et al 2003, then reduction of complexity using Hierarchical softmax and Noise Contrastive Estimation. Further works like CBoW, GlOVe, Skip Gram and Negative Sampling which helped to train on much higher data.
We have discussed quite a few receiver structures for a 2×2 MIMO channel namely, (a) Zero Forcing (ZF) equalization (b) Minimum Mean Square Error (MMSE) equalization (c) Zero Forcing equalization with Successive Interference Cancellation (ZF-SIC) (d) ZF-SIC with optimal ordering and (e) MIMO with MMSE SIC and optimal ordering From the above receiver structures, we…
An earlier post we discussed hard decision decoding for a Hamming (7,4) code and simulated the the bit error rate. In this post, let us focus on the soft decision decoding for the Hamming (7,4) code, and quantify the bounds in the performance gain.
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]).
Oscillators are used in typical radio circuits to drive the mixer used for the up-conversion or down-conversion of the passband transmission. Ideally, the spectrum of the oscillator is expected to have an impulse at the frequency of oscillation with no frequency components else where. However the spectrum of practical oscillators do have spectrum skirts around…