Gram-Schmidt procedure and constellations
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The Gram-Schmidt procedure is used to generate an orthonormal basis from a set of signals. It works by taking the first signal as the first basis function, and then generating subsequent basis functions as the components of the remaining signals that are orthogonal to the previous basis functions. Any signal can then be represented as a linear combination of the orthonormal basis in an N-dimensional signal space. A constellation diagram visually represents signals modulated with a digital scheme by mapping them to points in a signal space based on their amplitude.
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QAM Stands for Quadrature Amplitude Modulation. QAM is both an analog and a digital modulation method. But here, we are only talking about QAM as a digital modulation.
Quadrature means that two carrier waves are being used, one sine wave and one cosine wave. These two waves are out of phase with each other by 90°, this is called quadrature.
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As shown in this picture, the I and I' bits are sent to the sine wave modulation path, and the Q and Q' bits are sent to the cosine wave path. Since the bits are split and sent in parallel, so the symbol rate has been reduced to a quarter of the input binary bit rate. If the input binary data rate is 100 Gbps, then the symbol rate is reduced to only 25 Gbaud/second. This is the reason why 16QAM is under hot research for 100Gbps fiber optic communication.
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So each pair of bits has 4 different outputs. Then they are added up at the linear summer. 4X4 is 16, so there is a total of 16 different combinations at the output, that is why this is called 16QAM.
This illustration shows an example of how the QUADBIT 0000 is modulated onto the carrier waves.
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This document summarizes a research paper that proposes a novel technique to double the data rate of spectrally efficient frequency division multiplexing (SEFDM) systems using Hilbert pulse pairs. The technique transmits two symbol streams simultaneously within the same bandwidth using a Hilbert pair as pulse-shaping filters. At the transmitter, the symbol stream is split and modulated onto two sets of subcarriers before being combined using the Hilbert pair. At the receiver, the Hilbert pair separates the streams which can then be independently demodulated without interference. Simulations show the proposed technique achieves the same bit error rate as conventional SEFDM but with double the spectral efficiency through transmitting two data streams simultaneously. The use of turbo coding also provides significant bit error
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This document discusses various types of pulse modulation techniques used in analog and digital communication systems. It begins by defining pulse amplitude modulation (PAM) and describing how the amplitude of pulses varies proportionally to the message signal. It then discusses different types of PAM based on the sampling technique used - ideal, natural, and flat-top sampling. Flat-top sampling uses sample-and-hold circuits and can introduce amplitude distortion known as the aperture effect. The document also covers pulse width modulation (PWM), pulse position modulation (PPM), pulse code modulation (PCM), delta modulation (DM), and their advantages. It explains the sampling theorem and proves it through Fourier analysis. Finally, it discusses bandwidth requirements, transmission, drawbacks
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Masters Report 1
1. The document proposes a scheme called Superimposed Spatial Modulation (SSM) that allows for doubling of information conveyed in the spatial position of transmitting antennas.
2. SSM superimposes two independent spatial modulation systems on the same antenna array. Each system transmits different components of orthogonal symbols.
3. This approach increases spectral efficiency over conventional spatial modulation by doubling the size of the possible antenna constellations.
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Ch7 noise variation of different modulation scheme pg 63
This document summarizes the noise performance of various modulation schemes. It begins by introducing a receiver model and defining figures of merit used to evaluate performance. It then analyzes the noise performance of coherent demodulation for DSB-SC and SSB modulation. The following key points are made:
1) Coherent detection of DSB-SC signals results in signal and noise being additive at both the input and output of the detector. The detector completely rejects the quadrature noise component.
2) For DSB-SC, the output SNR and reference SNR are equal, resulting in a figure of merit of 1.
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Introduction to communication system part 2Unit-I Part 2.pptx
This document contains information about a course on communication systems including:
1) The course contains 5 units covering topics like introduction to communication systems, amplitude modulation, angle modulation, transmitters and receivers, and noise in analog communication.
2) Textbook references are provided for each unit from authors like Taub and Schilling, George F Kennedy, Simon Haykin, and R P Singh.
3) Additional reference books are also listed including works by Proakis and B.P. Lathi.
4) Unit 1 is further described covering topics like classification of signals, Fourier transforms, signal bandwidth, distortionless transmission, Parseval's theorem, and introduction to convolution and correlation of signals.
5
Introduction of communication system_Unit-I Part 2.pptx
This document discusses various types of signals that are commonly used in communication systems. It covers topics such as:
1) Signals can be classified based on properties like continuity, amplitude quantization, periodicity, causality, symmetry, and length. Common types include continuous-time/discrete-time, analog/digital, periodic/aperiodic, causal/non-causal, even/odd, and finite/infinite length signals.
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Final ppt
The document discusses channel modeling and Kalman filter-based estimation for OFDM wireless communication systems. It provides an introduction to OFDM systems and outlines the channel modeling process, including modeling the channel as a multipath frequency selective fading channel using a tapped delay line. It also discusses implementing channel estimation using a Kalman filter and presenting results on simulating OFDM signal transmission through a Rayleigh fading channel. The goal is to accurately estimate the channel fading parameters using a joint time-frequency domain estimation model.
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Signal Constellation, Geometric Interpretation of Signals
Signal Constellation, Geometric Interpretation of Signals
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pulse modulation technique (Pulse code modulation).pptx
Review on Doubling the Rate of SEFDM Systems using Hilbert Pairs
Review on Doubling the Rate of SEFDM Systems using Hilbert Pairs
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Ch7 noise variation of different modulation scheme pg 63
DSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time Signals
DSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time Signals
Introduction to communication system part 2Unit-I Part 2.pptx
Introduction to communication system part 2Unit-I Part 2.pptx
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- 2. INTRODUCTION ❑ The Gram-Schmidt orthogonalization procedure is a straightforward way by which an appropriate set of orthonormal functions can be obtained from any given signal set. ❑ PASSBAND SYSTEM Passband transmission shifts the signal to be transmitted in frequency to a higher frequency and then transmits it
- 3. Gram-Schmidt procedure First orthonomal waveform:- Second orthonomal waveform:- Substiution:-
- 4. Gram-Schmidt procedure with constant k: Expressing as linear combination:- ; N <= M
- 5. Gram-Schmidt procedure By, sk (t) expression we can say that, (or) N-dimensional signal space with coordinates {sk i, i=1,2,,…N}. Any signal can be represented geometrically as a point in the signal space spanned by the orthonormal functions {fn (t)}.
- 6. EXAMPLE signals {si(t), i=1,2,3,4} and its corresponding signals
- 7. EXAMPLE We see that C12 =0 s2 (t) and f2 (t) are orthogonal Consequently, s4 (t) is a linear combination of f1 (t) and f3 (t) and and, hence, f4 (t) = 0 .
- 8. CONSTELLATIONS A constellation diagram is a representation of a signal modulated by a digital modulation scheme such as quadrature amplitude modulation or phase-shift keying. The distance of a point from the origin represents a measure of the amplitude or power of the signal.
- 9. PROPERTIES MODULATION SCHEME: ► Bandwidth occupied by the modulation , dimension of the modulated signal ► Bandwidth occupied by the modulation , signal_points per dimension ► Probability of bit error is proportional to the distance between the closest points in the constellations
- 10. THANK YOU