Modulation – RAYmaps

Wireless Book

About this book This textbook covers fundamental topics in Telecommunication including Channel Modeling, Modulation/Demodulation, Channel Coding/Decoding, Multicarrier, Capacity, Antenna Arrays, Diversity, and 4G/5G. It will also cover advanced topics such as High-Resolution Spectral Estimation, Reconfigurable Intelligent Surfaces, Index Modulation, Full-Duplex, and Millimeter Wave. This book will mainly target engineering students (both graduate and advanced undergraduate) who are new to the fields of Communication and Signal Processing and are struggling to understand the fundamental concepts. This book will help the students step by step by introducing the concepts first in their most basic form and then providing the code that the students can […]

May 5, 2020June 3, 2022Modulation

Index Modulation Explained

A relatively new technique to improve the spectral efficiency and the energy efficiency of wireless communication system is called Index Modulation (IM). There are two main types of IM, one that uses multiple transmit antennas (Spatial Modulation) and one that uses multiple carriers (OFDM-IM). We will focus here on Spatial Modulation also known as SM.

June 4, 2014November 17, 2019BER Performance, Fundamentals, LTE

Theoretical BER of M-QAM in Rayleigh Fading

We have previously discussed the Bit Error Rate of M-QAM in Rayleigh Fading using Monte Carlo Simulation. We now turn our attention to calculation of Bit Error Rate (BER) of M-QAM in Rayleigh fading using analytical techniques. In particular we look at the method used in MATLAB function berfading.m. In this function the BER of 4-QAM, 16-QAM and 64-QAM is calculated from series expressions having 1, 3 and 5 terms respectively. These are given below (M is the constellation size and must be a power of 2). if (M == 4) ber = 1/2 * ( 1 – sqrt(gamma_c/k./(1+gamma_c/k)) ); elseif […]

May 22, 2012May 31, 2022BER Performance, Fundamentals, LTE, Modulation, WiMAX

M-QAM Bit Error Rate in Rayleigh Fading

We have previously discussed the bit error rate (BER) performance of M-QAM in AWGN. We now discuss the BER performance of M-QAM in Rayleigh fading. The one-tap Rayleigh fading channel is generated from two orthogonal Gaussian random variables with variance of 0.5 each. The complex random channel coefficient so generated has an amplitude which is Rayleigh distributed and a phase which is uniformly distributed. As usual the fading channel introduces a multiplicative effect whereas the AWGN is additive. The function “QAM_fading” has three inputs, ‘n_bits’, ‘M’, ‘EbNodB’ and one output ‘ber’. The inputs are the number of bits to be passed […]

June 2, 2011June 3, 2014BER Performance

Bit Error Rate of QPSK

Simulating a QPSK system is equivalent to simulating two BPSK systems in parallel. So there is no difference in bit error rate(BER). Since the simulation is at baseband we multiply the in-phase and quadrature streams by 1 and j respectively (instead of cos and sin carriers). At the receiver we just use the real and imag functions to separate the two symbol streams. The BER is the average BER of the two parallel streams. As in the case of BPSK we can show that the baseband representation (using 1 and j) is equivalent to using the passband representation (using cosine […]

June 1, 2011May 21, 2020BER Performance

Bit Error Rate of BPSK

Modulation is the process by which a binary stream (zeros and ones) is converted to a format that is suitable for transmission over a wired or wireless channel that is prone to noise and interference as well as distortion. The most basic modulation scheme is BPSK or Binary Phase Shift Keying. It transmits the information in the phase of the signal which could be one of two values (0 degrees or 180 degrees). BPSK signal can be represented as (called the passband representation) s(t)=a(t)*cos(2*pi*f*t) where a(t) is a time varying parameter which can have one of two values (+1 or […]