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.
While trying to derive the theoretical bit error rate (BER) for BPSK modulation in a Rayleigh fading channel, I realized that I need to discuss chi square random variable prior. What is chi-square random variable? Let there be independent and identically distributed Gaussian random variables with mean and variance and we form a new random…
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)…
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…
In typical digital signal processing applications, there arises need to increase the sampling frequency of a signal sequence, where the higher sampling frequency is an integer multiple of the original sampling frequency i.e for a signal sequence with a sampling frequency , change the sampling frequency to , where is an integer.
Question 12 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q12. With initial condition the solution of the differential equation, is (A) (B) (C) (D) Solution From the product rule used to find the derivative of product of two or more functions, Applying this to the above equation, we…
IEEE 802.11ac Very High Throughput (for <6GHz band) is an upcoming standard which is development by IEEE standardization committee. The mandate of Task Group AC is supposed to enhance the High Throughput rates achieved by 802.11n. As described in the document VHT below 6GHz PAR plus 5C’s (802.11-08/0807r4) the group has the following objectives :
Question 46 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q46. The maximum value of in the interval [1, 6] is (A) 21 (B) 25 (C) 41 (D) 46 Solution Let us start by finding the critical points of the function . The first derivative is, . Solving by…
In the past, we had discussed two transmit, one receive antenna Alamouti Space Time Block Coding (STBC) scheme. In this post, lets us discuss the impact of having two antennas at the receiver. For the discussion, we will assume that the channel is a flat fading Rayleigh multipath channel and the modulation is BPSK.
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)))…
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
In the post on Soft Input Viterbi decoder, we had discussed BPSK modulation with convolutional coding and soft input Viterbi decoding in AWGN channel. Let us know discuss the derivation of soft bits for 16QAM modulation scheme with Gray coded bit mapping. The channel is assumed to be AWGN alone.
This is the second 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…