Modulation

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Binary to Gray code conversion for PSK and PAM

by Krishna Sankar on May 11, 2008

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 [...]

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Comparing 16PSK vs 16QAM for symbol error rate

by Krishna Sankar on March 29, 2008

Comparing 16PSK and 16QAM symbol error rate

In two previous posts, we have derived theoretical symbol error rate for 16-QAM and 16-PSK modulation schemes. The links are: (a) Symbol error rate for 16-PSK (b) Symbol error rate for 16-QAM Given that we [...]

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Symbol Error Rate for 16PSK

by Krishna Sankar on March 18, 2008

angle between constellation points 16psk

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 [...]

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Simulating Minimum Shift Keying Transmitter

by Krishna Sankar on January 19, 2008

phase transition diagram in binary MSK

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) [...]

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Symbol Error Rate (SER) for 16-QAM

by Krishna Sankar on December 9, 2007

16QAM constellation plot

Given that we have went over the symbol error probability for 4-PAM and symbol error rate for 4-QAM , let us extend the understanding to find the symbol error probability for 16-QAM (16 Quadrature Amplitude [...]

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Symbol Error Rate (SER) for QPSK (4-QAM) modulation

by Krishna Sankar on November 6, 2007

probability density function of 4QAM

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 [...]

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Symbol Error Rate (SER) for 4-PAM

by Krishna Sankar on October 7, 2007

Probability Distribuition Function 4PAM alphabet1

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 [...]

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Coherent demodulation of DBPSK

by Krishna Sankar on September 30, 2007

tx_rx_coherent_demod_dbpsk

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 [...]

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Scaling factor in QAM

by Krishna Sankar on September 23, 2007

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 [...]

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Bit Error Rate (BER) for frequency shift keying with coherent demodulation

by Krishna Sankar on August 30, 2007

FSK Orthogonal Signals vs BPSK antipodal signals

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 [...]

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Bit Error Rate (BER) for BPSK modulation

by Krishna Sankar on August 5, 2007

Probability Density Function (PDF) for BPSK in AWGN

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 [...]

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