The document discusses Shannon's theory of channel capacity from 1948. It explains key information theory concepts like entropy, self-information, and mutual information. It then discusses the channel capacity of various channel models including frequency-flat and frequency-selective channels with additive white Gaussian noise. The maximum achievable transmission bit rate without error for a given channel is equal to the channel capacity, which depends on factors like bandwidth, signal-to-noise ratio, and optimal power allocation across frequencies for frequency-selective channels.
This document summarizes a lecture on optimal receiver design for digital communication systems. It discusses different types of optimal receivers, including minimum bit-error rate (BER), maximum a-posteriori probability (MAP), maximum likelihood (ML), and minimum distance (MD) receivers. It also examines the receiver structures for transmitting a single symbol and a sequence of symbols over a linear channel with additive white Gaussian noise (AWGN). For a single symbol, the optimal receiver is a matched filter frontend followed by sampling at the symbol rate and decision device. For a sequence, a matched filter frontend and maximum likelihood sequence estimation (MLSE) are used.
This document summarizes a lecture on transmitter design for digital communication systems. It discusses:
1) The basic components of a transmitter including constellations for linear modulation such as PAM, PSK, and QAM, and transmit filters.
2) Preliminaries on passband versus baseband transmission and how a baseband equivalent model can be obtained using complex envelope signals.
3) Details on common constellation designs including distance metrics for PAM, PSK, and QAM in an AWGN channel.
4) Analysis of bit error rate performance for the transmission of a single symbol over an AWGN channel for different constellations. The document also discusses designing transmit pulses to eliminate
This document outlines a postacademic course on telecommunications transmission techniques taught by Marc Moonen at KU Leuven University. The course consists of 10 lectures covering basic digital communication principles as well as advanced topics like multicarrier modulation, CDMA, and MIMO transmission. It introduces concepts like modulation, channel coding, equalization, and multiple access. The document provides an overview of the course schedule, prerequisites, literature references and acknowledges prior work from which content has been adapted.
This document summarizes a lecture on equalization techniques for digital communications.
1) The optimal receiver structure for transmission over a channel consists of a whitened matched filter frontend and a maximum likelihood sequence estimator (MLSE) such as the Viterbi algorithm. However, the MLSE has high complexity.
2) Equalization filters combined with a memoryless decision device can provide a lower complexity alternative to the MLSE. Linear equalizers like zero-forcing and minimum mean squared error (MMSE) are discussed, as well as decision feedback equalizers.
3) The lecture reviews transmission models and optimal receivers developed in previous lectures, and establishes an input-output model of the transmission system to serve as the basis
The document summarizes a lecture on equalization techniques for digital communications. It begins with the lecturer acknowledging feedback that previous lectures moved too quickly and were too technical. It then provides a high-level overview of equalization techniques, including:
- Zero-forcing equalization using linear filters and decision feedback equalizers
- MMSE equalization
- Fractionally spaced equalizers
It also summarizes the key concepts from previous lectures on digital transmission models and the optimal receiver structure involving a whitened matched filter front-end and maximum likelihood sequence estimation (MLSE). The goal of equalization techniques is to provide a lower complexity alternative to MLSE for the decision device while approaching similar performance with the use of channel coding
This document summarizes a lecture on multi-tone modulation techniques. It discusses ADSL and VDSL specifications including spectrum allocation and channel characteristics. It then covers topics like bit loading, peak-to-average power ratio problems, time-domain equalization using a TEQ to shorten the channel impulse response, and alternative frequency-domain equalization structures. The document provides examples and illustrations of these concepts.
Transferring quantum information through theijngnjournal
Transmission of information in the form of qubits much faster than the speed of light is the important
aspects of quantum information theory. Quantum information processing exploits the quantum nature of
information that needs to be stored, encoded, transmit, receive and decode the information in the form of
qubits. Bosonic channels appear to be very attractive for the physical implementation of quantum
communication. This paper does the study of quantum channels and how best it can be implemented with
the existing infrastructure that is the classical communication. Multiple access to the quantum network is
the requirement where multiple users want to transmit their quantum information simultaneously without
interfering with each others.
Transferring Quantum Information through the Quantum Channel using Synchronou...josephjonse
Transmission of information in the form of qubits much faster than the speed of light is the important aspects of quantum information theory. Quantum information processing exploits the quantum nature of information that needs to be stored, encoded, transmit, receive and decode the information in the form of qubits. Bosonic channels appear to be very attractive for the physical implementation of quantum communication. This paper does the study of quantum channels and how best it can be implemented with the existing infrastructure that is the classical communication. Multiple access to the quantum network is the requirement where multiple users want to transmit their quantum information simultaneously without interfering with each others.
This document summarizes a lecture on optimal receiver design for digital communication systems. It discusses different types of optimal receivers, including minimum bit-error rate (BER), maximum a-posteriori probability (MAP), maximum likelihood (ML), and minimum distance (MD) receivers. It also examines the receiver structures for transmitting a single symbol and a sequence of symbols over a linear channel with additive white Gaussian noise (AWGN). For a single symbol, the optimal receiver is a matched filter frontend followed by sampling at the symbol rate and decision device. For a sequence, a matched filter frontend and maximum likelihood sequence estimation (MLSE) are used.
This document summarizes a lecture on transmitter design for digital communication systems. It discusses:
1) The basic components of a transmitter including constellations for linear modulation such as PAM, PSK, and QAM, and transmit filters.
2) Preliminaries on passband versus baseband transmission and how a baseband equivalent model can be obtained using complex envelope signals.
3) Details on common constellation designs including distance metrics for PAM, PSK, and QAM in an AWGN channel.
4) Analysis of bit error rate performance for the transmission of a single symbol over an AWGN channel for different constellations. The document also discusses designing transmit pulses to eliminate
This document outlines a postacademic course on telecommunications transmission techniques taught by Marc Moonen at KU Leuven University. The course consists of 10 lectures covering basic digital communication principles as well as advanced topics like multicarrier modulation, CDMA, and MIMO transmission. It introduces concepts like modulation, channel coding, equalization, and multiple access. The document provides an overview of the course schedule, prerequisites, literature references and acknowledges prior work from which content has been adapted.
This document summarizes a lecture on equalization techniques for digital communications.
1) The optimal receiver structure for transmission over a channel consists of a whitened matched filter frontend and a maximum likelihood sequence estimator (MLSE) such as the Viterbi algorithm. However, the MLSE has high complexity.
2) Equalization filters combined with a memoryless decision device can provide a lower complexity alternative to the MLSE. Linear equalizers like zero-forcing and minimum mean squared error (MMSE) are discussed, as well as decision feedback equalizers.
3) The lecture reviews transmission models and optimal receivers developed in previous lectures, and establishes an input-output model of the transmission system to serve as the basis
The document summarizes a lecture on equalization techniques for digital communications. It begins with the lecturer acknowledging feedback that previous lectures moved too quickly and were too technical. It then provides a high-level overview of equalization techniques, including:
- Zero-forcing equalization using linear filters and decision feedback equalizers
- MMSE equalization
- Fractionally spaced equalizers
It also summarizes the key concepts from previous lectures on digital transmission models and the optimal receiver structure involving a whitened matched filter front-end and maximum likelihood sequence estimation (MLSE). The goal of equalization techniques is to provide a lower complexity alternative to MLSE for the decision device while approaching similar performance with the use of channel coding
This document summarizes a lecture on multi-tone modulation techniques. It discusses ADSL and VDSL specifications including spectrum allocation and channel characteristics. It then covers topics like bit loading, peak-to-average power ratio problems, time-domain equalization using a TEQ to shorten the channel impulse response, and alternative frequency-domain equalization structures. The document provides examples and illustrations of these concepts.
Transferring quantum information through theijngnjournal
Transmission of information in the form of qubits much faster than the speed of light is the important
aspects of quantum information theory. Quantum information processing exploits the quantum nature of
information that needs to be stored, encoded, transmit, receive and decode the information in the form of
qubits. Bosonic channels appear to be very attractive for the physical implementation of quantum
communication. This paper does the study of quantum channels and how best it can be implemented with
the existing infrastructure that is the classical communication. Multiple access to the quantum network is
the requirement where multiple users want to transmit their quantum information simultaneously without
interfering with each others.
Transferring Quantum Information through the Quantum Channel using Synchronou...josephjonse
Transmission of information in the form of qubits much faster than the speed of light is the important aspects of quantum information theory. Quantum information processing exploits the quantum nature of information that needs to be stored, encoded, transmit, receive and decode the information in the form of qubits. Bosonic channels appear to be very attractive for the physical implementation of quantum communication. This paper does the study of quantum channels and how best it can be implemented with the existing infrastructure that is the classical communication. Multiple access to the quantum network is the requirement where multiple users want to transmit their quantum information simultaneously without interfering with each others.
Multi Qubit Transmission in Quantum Channels Using Fibre Optics Synchronously...researchinventy
A quantum channel can be used to transmit classical information as well as to deliver quantum data from one location to another . Classical information theory is a subset of Quantum information theory which is fundamentally richer, because quantum mechanics includes so many more elementary classes of static and dynamic resources. Quantum information theory contains many more facts other than described here, including the study of quantum data processing, manipulation and Quantum data compression. Here we consider quantum channel as Bosonic channels, which are a quantum-mechanical model for free space or fibre optic communication. In this paper the overview of theoretical scenario of quantum networks in particular to multiple user access to the quantum communication channel is considered. Multiple qubits are generated in different system, the proper alignment of qubits is a must it can be first come first serve or round robin fashion. The received data are grouped into codewords each of n qubits and quantum error correction is performed. These codewords are agreed between the transmitter and the receiver before transmitting over the quantum channel known as valid codewords.
This document summarizes a lecture on smart antennas. It introduces the concept of spatial division multiple access (SDMA) which allows multiple users in the same cell to use the same frequency channel by using antenna arrays and signal processing. It describes early SDMA approaches that assumed line-of-sight propagation and used beamforming. More advanced approaches are needed to handle multipath propagation using techniques like MIMO channel modeling and source separation.
Popular Interview Wireless Question with AnswerVARUN KUMAR
Favourable propagation refers to the orthogonality among vector-valued wireless channels that can maximize total system throughput. It occurs when the interference terms in the channel capacity equation, which involve the product of different channel coefficients, approach zero. Time division duplexing (TDD) is more complex than frequency division duplexing (FDD) due to hardware mismatches across base stations and user equipment for uplink and downlink channels. Channel reciprocity can be achieved through FDD if the uplink and downlink carrier frequencies are nearly equal, but not if they are significantly different.
Introduction to Channel Capacity | DCNIT-LDTalks-1Arunabha Saha
DCNIT-LDTalks-1
Here I have discussed the channel capacity for noiseless and noisy channels. How Nyquist capacity and Shannon capacity play a key role in the noiseless and noisy channels are discussed in detail. We will see the several expressions of SNR_dB in terms of power and amplitude and try to understand how both the capacity are different from each other. For extreme values of SNR, we will deduce the Shannon capacity formula to understand the bandwidth-limited region and power-limited region. Here I have used a few numerical examples to understand the concept clearly. In the last section of the talk, I have deduced the Shannon capacity formula from scratch to get better exposure and will understand how these ideas contribute to its mathematical framework.
Course: CMS-A-CC-4-8
youtube: https://www.youtube.com/watch?v=1OjlMqHWq6o
This document summarizes a research paper on a multi-user MIMO cognitive radio system that allows for simultaneous spectrum sensing and data transmission. The secondary receiver performs MMSE detection to decode signals from multiple secondary transmitters while also sensing the spectrum to detect potential primary activity. The analysis presents novel expressions for important metrics like detection probability, false alarm probability, and secondary transmission power under assumptions of Rayleigh fading, time-varying channels, and channel estimation errors. Numerical results verify the accuracy of the analysis.
Multiuser MIMO Gaussian Channels: Capacity Region and DualityShristi Pradhan
In this paper, I present the MIMO channel for single user case, discuss the decomposition of MIMO into parallel independent channels, and estimate the MIMO channel capacity. Then, I discuss on computation of capacity region for multiuser MIMO broadcast and multiple access channel and plot capacity regions for two users case. I conclude by showing the duality relationship between the multiple access and broadcast channel and show its significance for numerical standpoint.
OFDM is a digital multi-carrier modulation technique that is used in 4G wireless standards like LTE and WiMAX to support high data transmission rates over 100 Mbps. OFDM divides the available spectrum into multiple orthogonal subcarriers, each transmitting a low data rate stream that experiences flat fading to avoid inter-symbol interference caused by frequency selective fading. In contrast, single carrier systems experience frequency selective fading if the bandwidth is greater than the coherence bandwidth, resulting in inter-symbol interference.
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.
This document summarizes a lecture on adaptive equalization. It discusses how equalizers can be designed when the channel is unknown or time-varying using training sequences. Specifically, it describes how training sequences can be used to identify the channel model and design an optimal linear equalizer using a least squares approach. This results in an equation to compute the optimal equalizer coefficients directly from the received training sequence samples. Similar approaches are described for fractionally spaced and decision feedback equalizers.
This document summarizes a study on modeling GPRS session time distribution. The study group was asked to construct a model for simultaneous transmission of voice and data on mobile networks and determine equipment needs to provide a required quality of service. The summary develops:
1) A Markov chain model where voice calls have priority over data calls. The model accounts for variable voice, data arrival rates and data call sizes.
2) An initial model where each data call uses one channel. Balance equations are developed to calculate the stationary distribution.
3) Future work is outlined to model variable data call channel usage and develop numerical solutions to understand performance metrics like mean wait times.
This document discusses frequency hop codes for use in multiple access communication systems and multiuser radar/sonar systems. It introduces a new family of frequency hop codes called hyperbolic frequency hop codes, which are constructed based on congruence equations over finite fields. Hyperbolic frequency hop codes have several ideal characteristics. In communication systems, they achieve minimum error probability by ensuring at most one frequency "hit" between any two codes. In radar/sonar systems, they have at most two hits in their auto- and cross-ambiguity functions, providing high range/Doppler resolution while minimizing crosstalk between users. Examples are provided to illustrate address assignment and ambiguity functions using hyperbolic frequency hop codes.
Synthesis of Band-Limited Orthogonal Signals for Multichannel Data TransmissionAhmed Alshomi
This paper presents a method for orthogonal multiplexing of data channels to transmit multiple messages simultaneously through a band-limited channel without interchannel or intersymbol interference. The key points are:
1) Band-limited orthogonal signals are synthesized that can be transmitted at maximum possible data rate through the channel without interference.
2) A general method is provided to synthesize an infinite number of classes of band-limited orthogonal time functions within a limited frequency band.
3) This allows the synthesis of practical transmitting filter characteristics for any given amplitude characteristic of the transmission medium, without requiring ideal rectangular filters.
4) The amplitude and phase characteristics of the transmitting filters can be designed independently, and the received signals remain orthogonal regardless
Bit Error Rate Performance of MIMO Spatial Multiplexing with MPSK Modulation ...ijsrd.com
Wireless communication is one of the most effective areas of technology development of our time. Wireless communications today covers a very wide array of applications. In this, we study the performance of general MIMO system, the general V-BLAST architecture with MPSK Modulation in Rayleigh fading channels. Based on bit error rate, we show the performance of the 2x2 schemes with MPSK Modulation in noisy environment. We also show the bit error rate performance of 2x2, 3x3, 4x4 systems with BPSK modulation. We see that the bit error rate performance of 2x2 systems with QPSK modulation gives us the best performance among other schemes analysed here.
Introduction to Modulation and Demodulation.pptxNiharranjanAdit
1) The document discusses various modulation techniques used in communication systems including amplitude modulation (AM), frequency modulation (FM), phase modulation (PM), pulse amplitude modulation (PAM), frequency-shift keying (FSK), phase-shift keying (PSK), and their derivatives.
2) It explains the basic concepts of modulation such as using a message signal to control parameters of a carrier signal to transmit information.
3) Key modulation types covered are AM, which varies the amplitude of a carrier signal; FSK and PSK, which are used for digital modulation by shifting the frequency or phase of a carrier.
Study and Analysis Capacity of MIMO Systems for AWGN Channel Model ScenariosIJERA Editor
Future wireless communication systems can utilize the spatial properties of the wireless channel to enhance the spectral efficiency and therefore increases its channel capacity. This can be designed by deploying multiple antennas at both the transmitter side and receiver side. The basic measure of performance is the capacity of a channel; the maximum rate of communication for which arbitrarily small error probability can be achieved. The AWGN (additive white Gaussian noise) channel introduces the notion of capacity through a heuristic argument. The AWGN channel is then used as a basic building block to check the capacity of wireless fading channels in contrast to the AWGN channel. There is no single definition of capacity for fading channels that is applicable in all situations. Several notions of capacity are developed, and together they form a systematic study of performance limits of fading channels. The various capacity measures allow us to observe clearly the various types of resources available in fading channels: degrees of freedom, power and diversity. The MIMO systems capacity can be enhanced linearly with large the number of antennas. This paper elaborates the study of MIMO system capacity using the AWGN Channel Model, Channel Capacity, Channel Fast Fading, Spatial Autocorrelation and Power delay profile for various channel environments.
Deterministic MIMO Channel Capacity
• CSI is Known to the Transmitter Side
• CSI is Not Available at the Transmitter Side
Channel Capacity of Random MIMO Channels
Iaetsd a novel scheduling algorithms for mimo based wireless networksIaetsd Iaetsd
This document proposes new scheduling algorithms for MIMO wireless networks to improve system performance. It discusses designing practical user scheduling algorithms to maximize capacity in MIMO systems. Various MAC scheduling policies are implemented and modified to provide distributed traffic control, robustness against interference, and increased efficiency of resource utilization. Simulations using MATLAB compare the different policies and draw important results and conclusions. The paper suggests new priority scheduling and partially fair scheduling algorithms incorporating awareness of interference to improve system-level performance in MIMO wireless networks.
This document provides a summary of a lecture on multipath fading channels for mobile communication systems. It discusses various topics related to multipath fading including shadowing (slow fading), fast fading channels, mathematical models, and probability models. Specific topics covered include the lognormal distribution of shadowing, the two ray model, modeling the wireless channel as a black box, an introduction to fast fading, and Doppler shift. References several papers on topics like fading channels, narrowband land mobile channels, and the WSSUS channel model.
PERFORMANCE ANALYSIS OF 2*2 MIMO CHANNEL USING ZF EQUALIZER VaishaliVaishali14
The following content are present related to performance analysis of 2*2 mimo channel equalization technique
OBJECTIVE
INTRODUCTION
MIMO
2X2 MIMO CHANNEL
2X2 MIMO CHANNEL WITH ZF EQUALIZER
BER OF 2x2 MIMO CHANNEL WITH ZF EQUALIZER
PROGRAM AND SIMULATION OUTPUTS
RESULTS AND DISCUSSION
CONCLUSION
REFERENCES
This document contains a syllabus for a Communication Electronics course. The syllabus covers 6 units:
1) Amplitude Modulation
2) Angle Modulation
3) Pulse Modulation
4) Noise
5) AM and FM Receivers
6) Broadband Communication Links and Multiplexing
The syllabus provides an overview of the key topics that will be covered in each unit, including the concepts, mathematical analysis, generation methods, and applications of various modulation techniques. It also lists recommended textbooks and reference books for the course.
Multi Qubit Transmission in Quantum Channels Using Fibre Optics Synchronously...researchinventy
A quantum channel can be used to transmit classical information as well as to deliver quantum data from one location to another . Classical information theory is a subset of Quantum information theory which is fundamentally richer, because quantum mechanics includes so many more elementary classes of static and dynamic resources. Quantum information theory contains many more facts other than described here, including the study of quantum data processing, manipulation and Quantum data compression. Here we consider quantum channel as Bosonic channels, which are a quantum-mechanical model for free space or fibre optic communication. In this paper the overview of theoretical scenario of quantum networks in particular to multiple user access to the quantum communication channel is considered. Multiple qubits are generated in different system, the proper alignment of qubits is a must it can be first come first serve or round robin fashion. The received data are grouped into codewords each of n qubits and quantum error correction is performed. These codewords are agreed between the transmitter and the receiver before transmitting over the quantum channel known as valid codewords.
This document summarizes a lecture on smart antennas. It introduces the concept of spatial division multiple access (SDMA) which allows multiple users in the same cell to use the same frequency channel by using antenna arrays and signal processing. It describes early SDMA approaches that assumed line-of-sight propagation and used beamforming. More advanced approaches are needed to handle multipath propagation using techniques like MIMO channel modeling and source separation.
Popular Interview Wireless Question with AnswerVARUN KUMAR
Favourable propagation refers to the orthogonality among vector-valued wireless channels that can maximize total system throughput. It occurs when the interference terms in the channel capacity equation, which involve the product of different channel coefficients, approach zero. Time division duplexing (TDD) is more complex than frequency division duplexing (FDD) due to hardware mismatches across base stations and user equipment for uplink and downlink channels. Channel reciprocity can be achieved through FDD if the uplink and downlink carrier frequencies are nearly equal, but not if they are significantly different.
Introduction to Channel Capacity | DCNIT-LDTalks-1Arunabha Saha
DCNIT-LDTalks-1
Here I have discussed the channel capacity for noiseless and noisy channels. How Nyquist capacity and Shannon capacity play a key role in the noiseless and noisy channels are discussed in detail. We will see the several expressions of SNR_dB in terms of power and amplitude and try to understand how both the capacity are different from each other. For extreme values of SNR, we will deduce the Shannon capacity formula to understand the bandwidth-limited region and power-limited region. Here I have used a few numerical examples to understand the concept clearly. In the last section of the talk, I have deduced the Shannon capacity formula from scratch to get better exposure and will understand how these ideas contribute to its mathematical framework.
Course: CMS-A-CC-4-8
youtube: https://www.youtube.com/watch?v=1OjlMqHWq6o
This document summarizes a research paper on a multi-user MIMO cognitive radio system that allows for simultaneous spectrum sensing and data transmission. The secondary receiver performs MMSE detection to decode signals from multiple secondary transmitters while also sensing the spectrum to detect potential primary activity. The analysis presents novel expressions for important metrics like detection probability, false alarm probability, and secondary transmission power under assumptions of Rayleigh fading, time-varying channels, and channel estimation errors. Numerical results verify the accuracy of the analysis.
Multiuser MIMO Gaussian Channels: Capacity Region and DualityShristi Pradhan
In this paper, I present the MIMO channel for single user case, discuss the decomposition of MIMO into parallel independent channels, and estimate the MIMO channel capacity. Then, I discuss on computation of capacity region for multiuser MIMO broadcast and multiple access channel and plot capacity regions for two users case. I conclude by showing the duality relationship between the multiple access and broadcast channel and show its significance for numerical standpoint.
OFDM is a digital multi-carrier modulation technique that is used in 4G wireless standards like LTE and WiMAX to support high data transmission rates over 100 Mbps. OFDM divides the available spectrum into multiple orthogonal subcarriers, each transmitting a low data rate stream that experiences flat fading to avoid inter-symbol interference caused by frequency selective fading. In contrast, single carrier systems experience frequency selective fading if the bandwidth is greater than the coherence bandwidth, resulting in inter-symbol interference.
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.
This document summarizes a lecture on adaptive equalization. It discusses how equalizers can be designed when the channel is unknown or time-varying using training sequences. Specifically, it describes how training sequences can be used to identify the channel model and design an optimal linear equalizer using a least squares approach. This results in an equation to compute the optimal equalizer coefficients directly from the received training sequence samples. Similar approaches are described for fractionally spaced and decision feedback equalizers.
This document summarizes a study on modeling GPRS session time distribution. The study group was asked to construct a model for simultaneous transmission of voice and data on mobile networks and determine equipment needs to provide a required quality of service. The summary develops:
1) A Markov chain model where voice calls have priority over data calls. The model accounts for variable voice, data arrival rates and data call sizes.
2) An initial model where each data call uses one channel. Balance equations are developed to calculate the stationary distribution.
3) Future work is outlined to model variable data call channel usage and develop numerical solutions to understand performance metrics like mean wait times.
This document discusses frequency hop codes for use in multiple access communication systems and multiuser radar/sonar systems. It introduces a new family of frequency hop codes called hyperbolic frequency hop codes, which are constructed based on congruence equations over finite fields. Hyperbolic frequency hop codes have several ideal characteristics. In communication systems, they achieve minimum error probability by ensuring at most one frequency "hit" between any two codes. In radar/sonar systems, they have at most two hits in their auto- and cross-ambiguity functions, providing high range/Doppler resolution while minimizing crosstalk between users. Examples are provided to illustrate address assignment and ambiguity functions using hyperbolic frequency hop codes.
Synthesis of Band-Limited Orthogonal Signals for Multichannel Data TransmissionAhmed Alshomi
This paper presents a method for orthogonal multiplexing of data channels to transmit multiple messages simultaneously through a band-limited channel without interchannel or intersymbol interference. The key points are:
1) Band-limited orthogonal signals are synthesized that can be transmitted at maximum possible data rate through the channel without interference.
2) A general method is provided to synthesize an infinite number of classes of band-limited orthogonal time functions within a limited frequency band.
3) This allows the synthesis of practical transmitting filter characteristics for any given amplitude characteristic of the transmission medium, without requiring ideal rectangular filters.
4) The amplitude and phase characteristics of the transmitting filters can be designed independently, and the received signals remain orthogonal regardless
Bit Error Rate Performance of MIMO Spatial Multiplexing with MPSK Modulation ...ijsrd.com
Wireless communication is one of the most effective areas of technology development of our time. Wireless communications today covers a very wide array of applications. In this, we study the performance of general MIMO system, the general V-BLAST architecture with MPSK Modulation in Rayleigh fading channels. Based on bit error rate, we show the performance of the 2x2 schemes with MPSK Modulation in noisy environment. We also show the bit error rate performance of 2x2, 3x3, 4x4 systems with BPSK modulation. We see that the bit error rate performance of 2x2 systems with QPSK modulation gives us the best performance among other schemes analysed here.
Introduction to Modulation and Demodulation.pptxNiharranjanAdit
1) The document discusses various modulation techniques used in communication systems including amplitude modulation (AM), frequency modulation (FM), phase modulation (PM), pulse amplitude modulation (PAM), frequency-shift keying (FSK), phase-shift keying (PSK), and their derivatives.
2) It explains the basic concepts of modulation such as using a message signal to control parameters of a carrier signal to transmit information.
3) Key modulation types covered are AM, which varies the amplitude of a carrier signal; FSK and PSK, which are used for digital modulation by shifting the frequency or phase of a carrier.
Study and Analysis Capacity of MIMO Systems for AWGN Channel Model ScenariosIJERA Editor
Future wireless communication systems can utilize the spatial properties of the wireless channel to enhance the spectral efficiency and therefore increases its channel capacity. This can be designed by deploying multiple antennas at both the transmitter side and receiver side. The basic measure of performance is the capacity of a channel; the maximum rate of communication for which arbitrarily small error probability can be achieved. The AWGN (additive white Gaussian noise) channel introduces the notion of capacity through a heuristic argument. The AWGN channel is then used as a basic building block to check the capacity of wireless fading channels in contrast to the AWGN channel. There is no single definition of capacity for fading channels that is applicable in all situations. Several notions of capacity are developed, and together they form a systematic study of performance limits of fading channels. The various capacity measures allow us to observe clearly the various types of resources available in fading channels: degrees of freedom, power and diversity. The MIMO systems capacity can be enhanced linearly with large the number of antennas. This paper elaborates the study of MIMO system capacity using the AWGN Channel Model, Channel Capacity, Channel Fast Fading, Spatial Autocorrelation and Power delay profile for various channel environments.
Deterministic MIMO Channel Capacity
• CSI is Known to the Transmitter Side
• CSI is Not Available at the Transmitter Side
Channel Capacity of Random MIMO Channels
Iaetsd a novel scheduling algorithms for mimo based wireless networksIaetsd Iaetsd
This document proposes new scheduling algorithms for MIMO wireless networks to improve system performance. It discusses designing practical user scheduling algorithms to maximize capacity in MIMO systems. Various MAC scheduling policies are implemented and modified to provide distributed traffic control, robustness against interference, and increased efficiency of resource utilization. Simulations using MATLAB compare the different policies and draw important results and conclusions. The paper suggests new priority scheduling and partially fair scheduling algorithms incorporating awareness of interference to improve system-level performance in MIMO wireless networks.
This document provides a summary of a lecture on multipath fading channels for mobile communication systems. It discusses various topics related to multipath fading including shadowing (slow fading), fast fading channels, mathematical models, and probability models. Specific topics covered include the lognormal distribution of shadowing, the two ray model, modeling the wireless channel as a black box, an introduction to fast fading, and Doppler shift. References several papers on topics like fading channels, narrowband land mobile channels, and the WSSUS channel model.
PERFORMANCE ANALYSIS OF 2*2 MIMO CHANNEL USING ZF EQUALIZER VaishaliVaishali14
The following content are present related to performance analysis of 2*2 mimo channel equalization technique
OBJECTIVE
INTRODUCTION
MIMO
2X2 MIMO CHANNEL
2X2 MIMO CHANNEL WITH ZF EQUALIZER
BER OF 2x2 MIMO CHANNEL WITH ZF EQUALIZER
PROGRAM AND SIMULATION OUTPUTS
RESULTS AND DISCUSSION
CONCLUSION
REFERENCES
This document contains a syllabus for a Communication Electronics course. The syllabus covers 6 units:
1) Amplitude Modulation
2) Angle Modulation
3) Pulse Modulation
4) Noise
5) AM and FM Receivers
6) Broadband Communication Links and Multiplexing
The syllabus provides an overview of the key topics that will be covered in each unit, including the concepts, mathematical analysis, generation methods, and applications of various modulation techniques. It also lists recommended textbooks and reference books for the course.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
john krisinger-the science and history of the alcoholic beverage.pptx
lecture2.ppt
1. Postacademic Course on
Telecommunications
20/4/00
p. 1
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Lecture-2: Limits of Communication
• Problem Statement:
Given a communication channel (bandwidth B),
and an amount of transmit power, what is the
maximum achievable transmission bit-rate
(bits/sec), for which the bit-error-rate is (can be)
sufficiently (infinitely) small ?
- Shannon theory (1948)
- Recent topic: MIMO-transmission
(e.g. V-BLAST 1998, see also Lecture-1)
2. Postacademic Course on
Telecommunications
20/4/00
p. 2
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Overview
• `Just enough information about entropy’
(Lee & Messerschmitt 1994)
self-information, entropy, mutual information,…
• Channel Capacity (frequency-flat channel)
• Channel Capacity (frequency-selective channel)
example: multicarrier transmission
• MIMO Channel Capacity
example: wireless MIMO
3. Postacademic Course on
Telecommunications
20/4/00
p. 3
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
`Just enough information about entropy’(I)
• Consider a random variable X with sample space
(`alphabet’)
• Self-information in an outcome is defined as
where is probability for (Hartley 1928)
• `rare events (low probability) carry more information
than common events’
`self-information is the amount of uncertainty
removed after observing .’
M
,...,
,
, 3
2
1
K
)
(
log
)
( 2 K
X
K p
h
K
)
( K
X
p
K
4. Postacademic Course on
Telecommunications
20/4/00
p. 4
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
`Just enough information about entropy’(II)
• Consider a random variable X with sample space
(`alphabet’)
• Average information or entropy in X is defined as
because of the log, information is measured in bits
M
,...,
,
, 3
2
1
K
K
X
K
X p
p
X
H
)
(
log
).
(
)
( 2
5. Postacademic Course on
Telecommunications
20/4/00
p. 5
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
`Just enough information about entropy’ (III)
• Example: sample space (`alphabet’) is {0,1} with
entropy=1 bit if q=1/2 (`equiprobable symbols’)
entropy=0 bit if q=0 or q=1 (`no info in certain events’)
q
p
q
p X
X
1
)
0
(
,
)
1
(
q
H(X)
1
1
0
6. Postacademic Course on
Telecommunications
20/4/00
p. 6
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
`Just enough information about entropy’ (IV)
• `Bits’ being a measure for entropy is slightly
confusing (e.g. H(X)=0.456 bits??), but the
theory leads to results, agreeing with our intuition
(and with a `bit’ again being something that is
either a `0’ or a `1’), and a spectacular theorem
• Example:
alphabet with M=2^n equiprobable symbols :
-> entropy = n bits
i.e. every symbol carries n bits
7. Postacademic Course on
Telecommunications
20/4/00
p. 7
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
`Just enough information about entropy’ (V)
• Consider a second random variable Y with sample
space (`alphabet’)
• Y is viewed as a `channel output’, when X is
the `channel input’.
• Observing Y, tells something about X:
is the probability for after
observing
N
,...,
,
, 3
2
1
)
,
(
| K
K
Y
X
p
K
K
8. Postacademic Course on
Telecommunications
20/4/00
p. 8
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
`Just enough information about entropy’ (VI)
• Example-1 :
• Example-2 : (infinitely large alphabet size for Y)
+
noise decision
device
X Y
00
01
10
11
+
noise
X Y
00
01
10
11
00
01
10
11
9. Postacademic Course on
Telecommunications
20/4/00
p. 9
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
`Just enough information about entropy’(VII)
• Average-information or entropy in X is defined as
• Conditional entropy in X is defined as
Conditional entropy is a measure of the average uncertainty
about the channel input X after observing the output Y
K
K
X
K
X p
p
X
H
)
(
log
).
(
)
( 2
K K
K
K
Y
X
K
K
Y
X
K
Y p
p
p
Y
X
H
)
|
(
log
).
|
(
)
(
)
|
( |
2
|
10. Postacademic Course on
Telecommunications
20/4/00
p. 10
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
`Just enough information about entropy’(VIII)
• Average information or entropy in X is defined as
• Conditional entropy in X is defined as
• Average mutual information is defined as
I(X|Y) is uncertainty about X that is removed by observing Y
K
K
X
K
X p
p
X
H
)
(
log
).
(
)
( 2
K K
K
K
Y
X
K
K
Y
X
K
Y p
p
p
Y
X
H
)
|
(
log
).
|
(
)
(
)
|
( |
2
|
)
|
(
)
(
)
|
( Y
X
H
X
H
Y
X
I
11. Postacademic Course on
Telecommunications
20/4/00
p. 11
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (I)
• Average mutual information is defined by
-the channel, i.e. transition probabilities
-but also by the input probabilities
• Channel capacity (`per symbol’ or `per channel
use’) is defined as the maximum I(X|Y) for all
possible choices of
• A remarkably simple result: For a real-valued
additive Gaussian noise channel, and infinitely
large alphabet for X (and Y), channel capacity is
)
,
(
| K
K
Y
X
p
)
( K
X
p
)
( K
X
p
)
1
(
log
.
2
1
2
2
2
n
x
signal
(noise)
variances
12. Postacademic Course on
Telecommunications
20/4/00
p. 12
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (II)
• A remarkable theorem (Shannon 1948):
With R channel uses per second, and channel
capacity C, a bit stream with bit-rate C*R
(=capacity in bits/sec) can be transmitted with
arbitrarily low probability of error
= Upper bound for system performance !
13. Postacademic Course on
Telecommunications
20/4/00
p. 13
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (II)
• For a real-valued additive Gaussian noise
channel, and infinitely large alphabet for X (and
Y), the channel capacity is
• For a complex-valued additive Gaussian noise
channel, and infinitely large alphabet for X (and
Y), the channel capacity is
)
1
(
log 2
2
2
n
x
)
1
(
log
.
2
1
2
2
2
n
x
14. Postacademic Course on
Telecommunications
20/4/00
p. 14
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (III)
Information I(X|Y) conveyed by a real-valued channel with
additive white Gaussian noise, for different input alphabets,
with all symbols in the alphabet equally likely
(Ungerboeck 1982)
2
2
n
x
SNR
15. Postacademic Course on
Telecommunications
20/4/00
p. 15
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (IV)
Information I(X|Y) conveyed by a complex-valued channel
with additive white Gaussian noise, for different input
alphabets, with all symbols in the alphabet equally likely
(Ungerboeck 1982)
16. Postacademic Course on
Telecommunications
20/4/00
p. 16
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (V)
This shows that, as long as the alphabet is
sufficiently large, there is no significant loss in
capacity by choosing a discrete input alphabet,
hence justifies the usage of such alphabets !
The higher the SNR, the larger the required
alphabet to approximate channel capacity
17. Postacademic Course on
Telecommunications
20/4/00
p. 17
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (frequency-flat channels)
• Up till now we considered capacity `per symbol’ or
`per channel use’
• A continuous-time channel with bandwidth B (Hz)
allows 2B (per second) channel uses (*), i.e. 2B
symbols being transmitted per second, hence
capacity is
(*) This is Nyquist criterion `upside-down’ (see also Lecture-3)
second
bits
)
1
(
log
2
1
.
2 2
2
2
n
x
B
received signal (noise) power
18. Postacademic Course on
Telecommunications
20/4/00
p. 18
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (frequency-flat channels)
• Example: AWGN baseband channel
(additive white Gaussian noise channel)
n(t)
+
channel
s(t) r(t)=Ho.s(t)+n(t)
Ho
f
H(f)
B
-B
Ho
second
bits
)
1
(
log
. 2
2
2
0
2
n
x
H
B
B
N
B
Es
n
x
.
2
.
0
2
2
19. Postacademic Course on
Telecommunications
20/4/00
p. 19
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (frequency-flat channels)
• Example: AWGN passband channel
passband channel with bandwidth B accommodates
complex baseband signal with bandwidth B/2 (see Lecture-3)
n(t)
+
channel
s(t) r(t)=Ho.s(t)+n(t)
Ho
f
H(f)
x
Ho
second
bits
)
1
(
log
2
.
2 2
2
2
0
2
n
x
H
B
x+B
20. Postacademic Course on
Telecommunications
20/4/00
p. 20
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (frequency-selective channels)
n(t)
+
channel
s(t) R(f)=H(f).S(f)+N(f)
H(f)
• Example: frequency-selective AWGN-channel
received SNR is frequency-dependent!
f
H(f)
B
-B
21. Postacademic Course on
Telecommunications
20/4/00
p. 21
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (frequency-selective channels)
• Divide bandwidth into small bins of width df,
such that H(f) is approx. constant over df
• Capacity is
optimal transmit power spectrum?
f
H(f)
B
-B
second
bits
).
)
(
)
(
)
(
1
(
log 2
2
2
2
df
f
f
f
H
n
x
0
B
22. Postacademic Course on
Telecommunications
20/4/00
p. 22
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (frequency-selective channels)
Maximize
subject to
solution is
`Water-pouring spectrum’
df
f
f
f
H
n
x
).
)
(
)
(
)
(
1
(
log 2
2
2
2
Available Power
df
f
x
x ).
(
2
2
)
)
(
)
(
,
0
max(
)
( 2
2
2
f
H
f
L
f n
x
B
L
)
(
)
(
2
2
f
H
f
n
area 2
x
23. Postacademic Course on
Telecommunications
20/4/00
p. 23
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Channel Capacity (frequency-selective channels)
Example : multicarrier modulation
available bandwidth is split up into different `tones’, every
tone has a QAM-modulated carrier
(modulation/demodulation by means of IFFT/FFT).
In ADSL, e.g., every tone is given (+/-) the same power,
such that an upper bound for capacity is (white noise case)
(see Lecture-7/8)
second
bits
).
).
(
1
(
log 2
2
2
2
df
f
H
n
x
24. Postacademic Course on
Telecommunications
20/4/00
p. 24
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (I)
• SISO =`single-input/single output’
• MIMO=`multiple-inputs/multiple-outputs’
• Question:
we usually think of channels with one transmitter
and one receiver. Could there be any advantage
in using multiple transmitters and/or receivers
(e.g. multiple transmit/receive antennas in a
wireless setting) ???
• Answer: You bet..
25. Postacademic Course on
Telecommunications
20/4/00
p. 25
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (II)
• 2-input/2-output example
A
B
C
D
+
+
X1
X2 Y2
Y1
N1
N2
2
1
2
1
.
2
1
N
N
X
X
D
C
B
A
Y
Y
26. Postacademic Course on
Telecommunications
20/4/00
p. 26
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (III)
Rules of the game:
• P transmitters means that the same total power
is distributed over the available transmitters
(no cheating)
• Q receivers means every receive signal is
corrupted by the same amount of noise
(no cheating)
Noises on different receivers are often assumed to be
uncorrelated (`spatially white’), for simplicity
...
)
(
)
( 2
2
2
2
1
df
f
df
f X
X
X
...
2
2
2
2
1
N
N
N
27. Postacademic Course on
Telecommunications
20/4/00
p. 27
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (IV)
2-in/2-out example, frequency-flat channels
Ho
0
0
Ho
+
+
X1
X2 Y2
Y1
N1
N2
2
1
2
1
.
0
0
2
1
N
N
X
X
Ho
Ho
Y
Y
first example/attempt
28. Postacademic Course on
Telecommunications
20/4/00
p. 28
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (V)
2-in/2-out example, frequency-flat channels
• corresponds to two separate channels, each
with input power and additive noise
• total capacity is
• room for improvement...
2
1
2
1
.
0
0
2
1
N
N
X
X
Ho
Ho
Y
Y
2
2
X
2
N
second
bits
)
.
2
1
(
log
.
.
2 2
2
2
0
2
n
x
H
B
29. Postacademic Course on
Telecommunications
20/4/00
p. 29
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (VI)
2-in/2-out example, frequency-flat channels
Ho
Ho
-Ho
Ho
+
+
X1
X2 Y2
Y1
N1
N2
2
1
2
1
.
2
1
N
N
X
X
Ho
Ho
Ho
Ho
Y
Y
second example/attempt
30. Postacademic Course on
Telecommunications
20/4/00
p. 30
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (VII)
A little linear algebra…..
2
1
2
1
.
2
1
N
N
X
X
Ho
Ho
Ho
Ho
Y
Y
2
1
2
1
.
2
1
2
1
2
1
2
1
.
.
2
0
0
.
2
N
N
X
X
Ho
Ho
Matrix V’
31. Postacademic Course on
Telecommunications
20/4/00
p. 31
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (VIII)
A little linear algebra…. (continued)
• Matrix V is `orthogonal’ (V’.V=I) which means that it
represents a transformation that conserves energy/power
• Use as a transmitter pre-transformation
• then (use V’.V=I) ...
2
1
2
1
'.
.
.
2
0
0
.
2
2
1
N
N
X
X
V
Ho
Ho
Y
Y
2
ˆ
1
ˆ
.
2
1
X
X
V
X
X
32. Postacademic Course on
Telecommunications
20/4/00
p. 32
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (IX)
• Then…
+
+ Y2
Y1
N1
N2
+
+
X^1
X^2
X2
X1
transmitter
A
B
C
D
V11
V12
V21
V22
channel receiver
33. Postacademic Course on
Telecommunications
20/4/00
p. 33
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (X)
• corresponds to two separate channels, each
with input power , output power
and additive noise
• total capacity is
2
2
X
2
N
second
bits
)
1
(
log
.
.
2 2
2
2
0
2
n
x
H
B
2
1
2
ˆ
1
ˆ
.
.
2
0
0
.
2
2
1
N
N
X
X
Ho
Ho
Y
Y
2
)
.
2
(
2
2 X
Ho
2x SISO-capacity!
34. Postacademic Course on
Telecommunications
20/4/00
p. 34
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (XI)
• Conclusion: in general, with P transmitters and
P receivers, capacity can be increased with a
factor up to P (!)
• But: have to be `lucky’ with the channel (cfr.
the two `attempts/examples’)
• Example : V-BLAST (Lucent 1998)
up to 40 bits/sec/Hz in a `rich scattering
environment’ (reflectors, …)
35. Postacademic Course on
Telecommunications
20/4/00
p. 35
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (XII)
• General I/O-model is :
• every H may be decomposed into
this is called a `singular value decompostion’, and works for
every matrix (check your MatLab manuals)
P
QxP
Q X
X
H
Y
Y
:
.
:
1
1
'
.
. V
S
U
H
diagonal matrix
orthogonal matrix V’.V=I
orthogonal matrix U’.U=I
36. Postacademic Course on
Telecommunications
20/4/00
p. 36
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (XIII)
With H=U.S.V’,
• V is used as transmitter pre-tranformation
(preserves transmit energy) and
• U’ is used as a receiver transformation
(preserves noise energy on every channel)
• S=diagonal matrix, represents resulting,
effectively `decoupled’ (SISO) channels
• Overall capacity is sum of SISO-capacities
• Power allocation over SISO-channels (and as a
function of frequency) : water pouring
37. Postacademic Course on
Telecommunications
20/4/00
p. 37
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
MIMO Channel Capacity (XIV)
Reference:
G.G. Rayleigh & J.M. Cioffi
`Spatio-temporal coding for wireless communications’
IEEE Trans. On Communications, March 1998
38. Postacademic Course on
Telecommunications
20/4/00
p. 38
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Assignment 1 (I)
• 1. Self-study material
Dig up your favorite (?) signal processing
textbook & refresh your knowledge on
-discrete-time & continuous time signals & systems
-signal transforms (s- and z-transforms, Fourier)
-convolution, correlation
-digital filters
...will need this in next lectures
39. Postacademic Course on
Telecommunications
20/4/00
p. 39
Module-3 Transmission Marc Moonen
Lecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA
Assignment 1 (II)
• 2. Exercise (MIMO channel capacity)
Investigate channel capacity for…
-SIMO-system with 1 transmitter, Q receivers
-MISO-system with P transmitters, 1 receiver
-MIMO-system with P transmitters, Q receivers
P=Q (see Lecture 2)
P>Q
P<Q