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Error Probability for rician fading multipath reception of binary and N-ary signals
Abstract
Performance characteristics are derived for two different forms of multireceivers (the coherent and noncoherent) which are used with binary and N -ary signaling through the Rician fading multichannel. The coherent multireceiver is capable of perfectly measuring the channel amplitudes and phases whereas, at the other extreme, the noncoherent multireceiver implies a receiver which requires no channel measurement whatsoever. The multichannel model presumes that each transmission mode supports a specular or fixed component and a random or scatter component which fades according to the Rayleigh distribution. Heretofore, performance analyses of multichannel links have assumed that the fading obeys the Rayleigh law. This multichannel model is sufficiently general to include four practical types: the Rician and the Rayleigh fading multichannels, multichannels whose propagation modes do not fade, and those which simultaneously contain Rician and Rayleigh fading propagation paths or the so called mixed-mode multichannel. Error probabilities are graphically illustrated and compared for various multichannel models. It is found that the effectiveness of multichannel reception is highly dependent on the strength of the specular channel component relative to the mean squared value of the random channel component. In particular, multichannel reception is more effective when applied to the completely random multichannel. For special cases the error-rate expressions reduce to well-known results.
... O modelo deste canal para interface aérea pode ser dividido em duas componentes: uma componente fixa, também conhecida como componente especular do sinal e uma componente aleatória, com o mesmo comportamento de um canal do tipo Rayleigh. Tem-se então que a resposta ao impulso para o mésimo canal do k-ésimo usuário da interface aérea modelada com desvanecimento do tipo Rice é dada por [4], [6]: , a somatória normalizada das médias quadráticas dos ganhos das partes especular e aleatória (em relação ao l-ésimo caminho tomado como referência) dos L caminhos percorridos pelo sinal. As expressões para o cálculo da probabilidade de erro (BER) para um receptor coerente sem diversidade num canal modelado com desvanecimento do tipo Rice [4], são dadas por: Q(u,w) é a função de Marcum (Marcum Q-function) e I n (x) é a função de Bessel de ordem n de x. ...
... Tem-se então que a resposta ao impulso para o mésimo canal do k-ésimo usuário da interface aérea modelada com desvanecimento do tipo Rice é dada por [4], [6]: , a somatória normalizada das médias quadráticas dos ganhos das partes especular e aleatória (em relação ao l-ésimo caminho tomado como referência) dos L caminhos percorridos pelo sinal. As expressões para o cálculo da probabilidade de erro (BER) para um receptor coerente sem diversidade num canal modelado com desvanecimento do tipo Rice [4], são dadas por: Q(u,w) é a função de Marcum (Marcum Q-function) e I n (x) é a função de Bessel de ordem n de x. Para um receptor coerente, com diversidade L d , num canal modelado com desvanecimento do tipo Rice, a probabilidade de erro é dada por [4]: ...
... As expressões para o cálculo da probabilidade de erro (BER) para um receptor coerente sem diversidade num canal modelado com desvanecimento do tipo Rice [4], são dadas por: Q(u,w) é a função de Marcum (Marcum Q-function) e I n (x) é a função de Bessel de ordem n de x. Para um receptor coerente, com diversidade L d , num canal modelado com desvanecimento do tipo Rice, a probabilidade de erro é dada por [4]: ...
... Next, to find the correlations between throughput performance with routing and congestion control that influence by the fading channel, we calculated the probability of error based on SNR in Rician and Rayleigh fading channel. In Rician fading channel, we used the probability of error as a BER function in [20], [21] and is given as: ...
... where ̅ [ ] is the average signal-to-noise ratio, and the random variable represents the instantaneous power of the fading channel. Now, we can rewrite Equation (21) or Rayleigh fading channel by: ...
... Maximum node speeds were 2 m/s, 4 m/s, 6 m/s, 8 m/s and 10 m/s and numbers of nodes were 20, 25, 30, 35, 40, 45 and 50, respectively. The environment used Rician with completely random channel [21], and Rayleigh fading propagation model. We used mobile-to-mobile channel model as described in [23]- [25]. ...
Routing protocol and congestion control in Transmission Control Protocol (TCP) have important roles in wireless mobile network performance. In wireless communication, the stability of the path and successful data transmission will be influenced by the channel condition. This channel condition constraints come from path loss and the multipath channel fading. With these constraints, the algorithm in the routing protocol and congestion control is confronted with the uncertainty of connection quality and probability of successful packet transmission, respectively. It is important to investigate the reliability and robustness of routing protocol and congestion control algorithms in dealing with such situation. In this paper, we develop a detailed approach and analytical throughput performance with a cross layer scheme (CLS) between routing and congestion control mechanism based on signal to noise ratio (SNR) in Rician and Rayleigh as multipath fading channel. We proposed joint routing and congestion control TCP with a cross layer scheme model based on SNR (RTCP-SNR). We compare the performance of RTCP-SNR with conventional routing-TCP and routing-TCP that used CLS with routing aware (RTCP-RA) model. The analyses and the simulation results showed that RTCP-SNR in a multipath channel outperforms conventional routing-TCP and RTCP-RA. Copyright © 2018 Institute of Advanced Engineering and Science. All rights reserved.
... Some examples of sharp integrand approximations, however not including the integration of the conditional error probability, are given in [12]- [14] and [15]. We also want to mention some pioneering works, like [16]- [21] and [22], which include the error probability and some corresponding approximations in terms of special functions and finite or infinite series. These approximations are rather useful for numerical evaluations. ...
... which enables us to evaluate the value of g(p, x), for certain p and x, numerically more accurate than the evaluation of g(p, x) by equation (16). There are three reasons for this fact. ...
... As shown in (17) from our previous work [1, Theorem 6], we have found new representations for the Beta-Nakagami integral (BeNaI) with considerable consequences. On the one hand, equation (17) does not include any special functions and is thus simpler to handle than (16). On the other hand, by the new representation (17) we have been able to deduce a proper class of functions for determining accurate bounds in closed-form for the BeNaI. ...
We investigate the average error probability of data communication over Nakagami fading channels. First, we discuss some new identities and properties of a certain integral representation of the average error probability. Second, we propose novel lower and upper bounds. Both bounds are sharp, and they have a simple closed-form representation. We also demonstrate that the bounds are very precise for a wide range of parameters. A relative error of less than 1.2% is achieved. Finally, the mathematical structure of the bounds is investigated. For both bounds, parameters can be adapted to achieve a simpler form, however, at the price of a reduced precision. The channel capacity for Nakagami fading is hard to determine in general. It is expected that by using the accurate bounds developed in this work precise approximations of the capacity can be achieved.
... is the Marcum Q-function [27] and I 0 (·) is given by (5). Given a transmission probability q, and the Rician parameters K and Ω, the threshold m can be obtained recursively from (12). ...
... (8.350.1)]. Thus, replacing (27) in (20), we obtain an approximate expression to evaluate the ABEP of opportunistic systems operating with S-QAM in Rician fading channels, given by ...
Opportunistic systems take advantage of the wireless communication channel random behavior, since transmission is made only when fading amplitude is above a threshold value, which is calculated based on a transmission probability. This type of transmission draws attention because improves the system performance, and it is an interesting scheme for primary users in cognitive radio networks or is also an option for physical layer security. In this paper, we analyze the performance of opportunistic transmissions in Rician fading channels considering square-quadrature-amplitude-modulation (S-QAM) and non-square-quadrature-amplitude-modulation (NS-QAM). Exact closed-form expressions and approximations are derived to evaluate the average bit error probability (ABEP). An expression to calculate the mean spectral efficiency (SE) is also derived considering that a target ABEP must be guaranteed. The SE is calculated using the coverage radius obtained for each modulation used in the system. Hence, an algorithm for the radii calculation is also presented, which considers that the parameters of the Rician fading channel change in the cellular area. The results show that opportunistic transmission (OpT) mitigates the fading effects once the ABEP decays exponentially as the signal to noise ratio (SNR) is increased. Additionally, the proposed algorithm, along with the derived expressions, determine the scenarios where the SE is maximized.
... It is again assumed that the explored radio channel exhibits slow fading allowing the phase shift θ to be estimated without error. The probability of bit error Pb, obtained by averaging over the probability density function p(r), could be given by [6]: ...
... where ̅̅̅ is the average signal-to-noise ratio; I0(ab) is a zero-order Bessel function of first kind , Q(a,b) is the "Q-function" (error function "erfc") with parameters a and b as follows [6]: ...
Modern communication systems use quadrature or phase modulations for data transfer. Imposed noise processes and conducted interference in the channel destroy the transmitted signal. In this paper the author observes the resistance of a channel link with QPSK for wideband (5MHz) data signal. Variations in transmit level are made in order to change the signal-to-noise ratio. Adjacent channel interference had influenced the transmitted signal. A table of BER vs. SNR is shown. The results are obtained and discussed based on real-time Bit Error Rate analysis.
... The analysis for M -ary DS-CDMA with non-coherent reception has common aspects with that for the square-law combining diversity systems. The exact BER probabilities of the diversity systems for Rayleigh and Nakagami-Rice fading channels are provided in [11,12,13,14]. The analysis takes into account these studies and derives the BER probabilities in two ways. ...
... All decision variables are mutually statistically independent and decision variables for the incorrect codes have identical distribution. By subtracting the M − 1 power of the correct detection probability P (x 1 > x 2 ) from unity and averaging, the exact expression of the error probability is derived in the closed-form as [13] ...
The bit-error-rate performance of M-ary direct-sequence code-division multiple-access (DS-CDMA) systems with square-law combination in multipath Nakagami-Rice fading channels is analyzed. The signal is modulated by using the M orthogonal signals to enhance the spectral efficiency. Rake combining for square-law detection is applied to improve the performance in the multipath channel. The bit-error-rate probability is derived in closed-form under the assumption that each user is assigned a random signature code. The bit-error-rate performance is evaluated in terms of the number of users and rake fingers.
... By following [40,Eq. (8.177)] and [44], the average BER can be expressed as ...
... (2) Obstructed (OBS) with varying degrees of clutter. The signal loss model can be represented by Path-loss and fading [23], Hospital environment (indoor) can be most accurately represented by Rician fading and ITU path-loss model. The PDF of SNR received in Rician fading channel is given by [24] ...
This paper presents a new low delay centralized cooperative spectrum sensing method based on dynamic voting rule using multiple threshold level, for indoor hospital environment, where fading and direct path loss both are together responsible for variation in signal strength. In the proposed algorithm, weights of Cognitive Radios (CRs) in terms of assigned vote-count are estimated based on the sensed energy values with respect to multiple fixed threshold levels, so that the direct path loss can be dealt without further increasing the error, which occurs due to fading. For indoor hospital like environment , Rician fading model is more appropriate. Therefore, formulation, evaluation and analysis of various sensing performance parameters have been carried out considering Rician fading model. Comparative analysis and trade-off among three optimum parameters-energy threshold, total number of CRs participating in sensing and total error rate, are presented with respect to signal to noise ratio (SNR). Finally, the Monte Carlo simulation is designed and implemented considering the two conditions-only fading environment and fading along with direct path loss environment. It can be observed that in both cases, the proposed spectrum sensing rule outperforms the other contemporary rules.
... Therefore, γ i is also non chi-square distributed. Thus, the PDF of γ i from (11) in [16] and [2, eq.(2.3−29)], shows that the PDF, p(γ 4 ), is given by the PDF of γ 4 and is given as [17] p( ...
In this paper, we derive an analytical expression for the average symbol error rate for the 4/16-QAM hierarchical modulation (HM), of the mapped signal at the relay during the up-link phase, for the HP and LP streams, respectively, in Rician fading environments. Furthermore, by utilizing HM for the proposed HM-PLNC system, we minimize the computational complexity at the relay node by reducing the number of Euclidean distance computations (EDCs) to 32 EDCs in fading channels. Performance evaluations show that the proposed system can significantly enhance E2E throughput for the TWRN systems compared to an equivalent 16-QAM based PLNC system. The results present a closed-form solution for HP and LP streams over slow, flat, Rician fading channels.
... LogDistancePropagationLossModel[17] (γ = 2.0) plus Rician fast fading[18]. With γ = 2.0 the LogDistance model has the same output as the Friis model; this model adds the Rician fast fading by configuring the NakagamiPropagation-LossModel[19] with m = 1.25. ...
... An alternative approach is to bypass the problem of characterizing the polarization fraction by working with the Stokes parameters of the observed polarized emission directly (e.g., Herron et al. 2018). The Rice distribution is discussed extensively in the electrical engineering literature due to its relevance to signal processing (e.g., Lindsey 1964;Sijbers et al. 1998;Abdi et al. 2001). ...
The dependence of the polarization fraction p on total intensity I in polarized submillimeter emission measurements is typically parameterized as p ∝ I − α ( α ≤ 1) and used to infer dust grain alignment efficiency in star-forming regions, with an index α = 1 indicating near-total lack of alignment of grains with the magnetic field. In this work, we demonstrate that the non-Gaussian noise characteristics of the polarization fraction may produce apparent measurements of α ∼ 1 even in data with significant signal-to-noise in Stokes Q , U , and I emission, and so with robust measurements of polarization angle. We present a simple model demonstrating this behavior and propose a criterion by which well-characterized measurements of the polarization fraction may be identified. We demonstrate that where our model is applicable, α can be recovered by fitting the p – I relationship with the mean of the Rice distribution without statistical debiasing of the polarization fraction. We apply our model to JCMT BISTRO Survey POL-2 850 μ m observations of three clumps in the Ophiuchus molecular cloud, finding that in the externally illuminated Oph A region, α ≈ 0.34, while in the more isolated Oph B and C, despite their differing star formation histories, α ∼ 0.6–0.7. Our results thus suggest that dust grain alignment in dense gas is more strongly influenced by the incident interstellar radiation field than by star formation history. We further find that grains may remain aligned with the magnetic field at significantly higher gas densities than has previously been believed, thus allowing investigation of magnetic field properties within star-forming clumps and cores.
... The Rice distribution is discussed extensively in the electrical engineering literature, due to its relevance to signal processing (e.g. Lindsey 1964;Sijbers et al. 1998;Abdi et al. 2001). ...
The dependence of polarization fraction $p$ on total intensity $I$ in polarized submillimeter emission measurements is typically parameterized as $p\propto I^{-\alpha}$ $(\alpha \leq 1)$, and used to infer dust grain alignment efficiency in star-forming regions, with an index $\alpha=1$ indicating near-total lack of alignment of grains with the magnetic field. In this work we demonstrate that the non-Gaussian noise characteristics of polarization fraction may produce apparent measurements of $\alpha \sim 1$ even in data with significant signal-to-noise in Stokes $Q$, $U$ and $I$ emission, and so with robust measurements of polarization angle. We present a simple model demonstrating this behavior, and propose a criterion by which well-characterized measurements of polarization fraction may be identified. We demonstrate that where our model is applicable, $\alpha$ can be recovered by fitting the $p-I$ relationship with the mean of the Rice distribution, without statistical debiasing of polarization fraction. We apply our model to JCMT BISTRO Survey POL-2 850$\mu$m observations of three clumps in the Ophiuchus Molecular Cloud, finding that in the externally-illuminated Oph A region, $\alpha\approx 0.34$, while in the more isolated Oph B and C, despite their differing star formation histories, $\alpha \sim 0.6-0.7$. Our results thus suggest that dust grain alignment in dense gas is more strongly influenced by incident interstellar radiation field than by star formation history. We further find that grains may remain aligned with the magnetic field at significantly higher gas densities than has previously been believed, thus allowing investigation of magnetic field properties within star-forming clumps and cores.
... LogDistancePropagationLossModel[16] (γ = 2.0) plus Rician fast fading[17]. With γ = 2.0 the LogDistance model has the same output as the Friis model; this model adds the Rician fast fading by configuring the NakagamiPropagation-LossModel[18] with m = 1.25.3) ...
To properly validate wireless networking solutions we depend on experimentation. Simulation very often produces less accurate results due to the use of models that are simplifications of the real phenomena they try to model. Networking experimentation may offer limited repeatability and reproducibility. Being influenced by external random phenomena such as noise, interference, and multipath, real experiments are hardly repeatable. In addition, they are difficult to reproduce due to testbed operational constraints and availability. Without repeatability and reproducibility, the validation of the networking solution under evaluation is questionable. In this paper, we show how the Trace-based Simulation (TS) approach can be used to accurately repeat and reproduce real experiments and, consequently, introduce a paradigm shift when it comes to the evaluation of wireless networking solutions. We present an extensive evaluation of the TS approach using the Fed4FIRE+ w-iLab.2 testbed. The results show that it is possible to repeat and reproduce real experiments using ns-3 trace-based simulations with more accuracy than in pure simulation, with average accuracy gains above 50%.
... The error probability estimates for linear BPSK signaling in Rician fading channels are well documented in [11] and is given as ...
Orthogonal Frequency Division Multiplexing (OFDM) is a very efficient multicarrier technique. OFDM is used more and more in recent wideband digital communications. It has numerous advantages such as the ability to handle severe channel conditions, efficient spectral usage, reduced inter symbol interference (ISI), and high data rate. Therefore, it has been utilized in many future wired and wireless communication systems 4G LTE mobile communications. In this paper, mainly focus on the performance evaluation and study of OFDM system over multipath fading channels such as AWGN, Rician and Rayleigh fading channels. Based on simulation results will make us understand some of these effects and signal-to-noise ratios (SNRs), channels are compared together in order to rank them according to the delivered signal. Quality of the signals, bit-error rates (BERs), and peak signal-to-noise ratios (PSNRs) of the received signals are the aspects in which system performance is evaluated.
... The BER performance of any digital modulation scheme generally defined as: BER= (1) From [13] we determine the probability of error for linear BPSK signaling in Rician fading channels is given as (2) ...
This paper, focus on the performance evaluation of cognitive radio network in terms of BER VS SNR
for M-ary PSK modulation schemes, such as BPSK, QPSK, 8-PSK, 16-PSK, 32-PSK, and 64-PSK over AWGN
and Rician fading channel. The cognitive radio network was designed firstly as a computer model showing the
sequence of processes in cognitive radio system and then the Simulation of cognitive radio work was performed using MATLAB simulation. The results were obtained in terms of BER VS SNR for M-PSK modulation. The results show that as the number of M-ary increase the BER increased while the BER decreased as the SNR increased, although as Spectrum efficiency increase.
... where γ b,i is the average SNR per bit. With BPSK over Rician fading channel, the average BER is given by [49], ...
In this paper, we investigate a hybrid automatic repeat request (ARQ) scheme for reliable data transfer in multi-hop underwater acoustic sensor networks (UASNs). The proposed scheme combines Reed-Solomon-based packet level erasure coding and selective retransmissions to achieve high reliability and energy efficiency. We also describe how to select the code rate (i.e., number of encoded packets) for a given message block consisting of m packets. The paper evaluates the performance of the proposed scheme by taking into account the underwater-specific characteristics such as distance dependent bandwidth, acoustic spreading effects, propagation loss, and fading effects. Simulation results demonstrate that the proposed scheme can significantly improve the network throughput and energy efficiency while reducing the end to end delay considerably.
... However, for hard decision decoding, the capacity can be more easily computed. By manipulating the equations in [6], we can find the probability of error, P e , for Rician fading under hard decision decoding, when using this strategy: ...
... For binary modulations the SEP becomes nothing but BEP and this BEP for DBPSK, BPSK and BFSK for different K values are shown in Figure 3. The results for BPSK and BFSK matches exactly with available results (Lindsey, 1964) and have been included for comparison purpose. Like the M-QAM case, for every modulation scheme in Figure 3, a similar effect of changing the K value is visible. ...
Simple closed-form solutions for the average error rate of several coherent modulation schemes including square M-QAM, DBPSK and QPSK operating over slow flat Rician fading channel are derived. Starting from a novel unified expression of conditional error probability the error rates are analysed using PDF based approach. The derived end expressions composed of infinite series summations of Gauss hypergeometric function are accurate, free from any numerical integration and general enough, as it encompasses as special situations, some cases of non-diversity and Rayleigh fading. Error probabilities are graphically displayed for the modulation schemes for different values of the Rician parameter K. In addition, to examine the dependence of error rate performance of M-QAM on the constellation size, numerical results are plotted for various values of M. The generality of the analytical results presented offers valuable insight into the performance evaluation over a fading channel in a unified manner.
... For robotic teams, accurate prediction of received signal strength and communication channel capability requires consideration of these effects since the nodes are operating in possibly cluttered environments and are mobile [74]. Fortunately, it has been observed that small-scale fading for particular environments can be approximated as a random variable with log-normal [55], Rician [62], or Rayleigh [12] distribution. ...
There are a large class of problems, from search and rescue to environmental monitoring, that can benefit from teams of mobile robots in environments where there is no existing infrastructure for inter-agent communication. We seek to address the problems necessary for a team of small, low-power, low-cost robots to deploy in such a way that they can dynamically provide their own multi-hop communication network. To do so, we formulate a situational awareness problem statement that specifies both the physical task and end-to-end communication rates that must be maintained. In pursuit of a solution to this problem, we address topics ranging from the modeling of point-to-point wireless communication to mobility control for connectivity maintenance. Since our focus is on developing solutions to these problems that can be experimentally verified, we also detail the design and implantation of a decentralized testbed for multi-robot research. Experiments on this testbed allow us to determine data-driven models for point-to-point wireless channel prediction, test relative signal-strength-based localization methods, and to verify that our algorithms for mobility control maintain the desired instantaneous rates when routing through the wireless network. The tools we develop are integral to the fielding of teams of robots with robust wireless network capabilities.
... Some examples of sharp integrand approximations, however not including the integration of the conditional error probability, are given in [73][74][75] and [76]. We also want to mention some pioneering works, like [77][78][79][80][81][82] and [83], in which the error probability and some corresponding approximations in terms of special functions and finite or infinite series are investigated. These approximations are rather useful for numerical evaluations. ...
... we have (18) Plugging (18) into (17) yields (19) where we have used the equality . Further, the complementary CDF (tail distribution) of under is (20) Before proceeding, we introduce an integral formula as follows: (21) The derivation of (21) is given in Appendix A. ...
Our aim in this work is to analyze the detection performance of a constant false alarm rata matched filter (CFAR-MF) which was developed for the detection problem in white Gaussian noise with unknown noise power. An exact expression for the detection probability of the CFAR-MF is derived in the mismatched case where mismatch exists between the actual signal steering vector and the nominal one. This theoretical expression can be used to facilitate the performance evaluation of the CFAR-MF in real-world scenarios when signal mismatch cannot be neglected.
The objective of this article is to analyze the behavior of channels in mobile radio transmission chains and propose a solution for reducing propagation attenuation and ensuring Quality of Service (QoS) in telecommunications. As network coverage and throughput demands continue to grow, a thorough characterization of channels is essential. The primary contribution of this work is to investigate the different phases of the digital transmission chain jointly to achieve optimal reliability and QoS. Spatial and temporal representations must be considered at the same level when characterizing and modeling MIMO system channels. Accurate and realistic modeling can be achieved through transmission channel characterization in the spatial domain, which is critical in a MIMO context to improve throughput and performance compared to conventional systems. The article explores the behavior of information carriers in the propagation environment and the impact of fading, diversity, multiplexing, and multipath phenomena.
The four short years since Digital Communication over Fading Channels became an instant classic have seen a virtual explosion of significant new work on the subject, both by the authors and by numerous researchers around the world. Foremost among these is a great deal of progress in the area of transmit diversity and space-time coding and the associated multiple inputmultiple output (MIMO) channel. This new edition gathers these and other results, previously scattered throughout numerous publications, into a single convenient and informative volume. Like its predecessor, this Second Edition discusses in detail coherent and noncoherent communication systems as well as a large variety of fading channel models typical of communication links found in the real world. Coverage includes single- and multichannel reception and, in the case of the latter, a large variety of diversity types. The moment generating function (MGF)based approach for performance analysis, introduced by the authors in the first edition and referred to in literally hundreds of publications, still represents the backbone of the book's presentation. Important features of this new edition include:
An all-new, comprehensive chapter on transmit diversity, space-time coding, and the MIMO channel, focusing on performance evaluation
Coverage of new and improved diversity schemes
Performance analyses of previously known schemes in new and different fading scenarios
A new chapter on the outage probability of cellular mobile radio systems
A new chapter on the capacity of fading channels
And much more
Digital Communication over Fading Channels, Second Edition is an indispensable resource for graduate students, researchers investigating these systems, and practicing engineers responsible for evaluating their performance.
The main objective of this study was to study, analyze and address the channel behavior in a mobile radio transmission chain. One of the major challenges in telecommunications networks (5G) is to minimize the propagation attenuation and consequently guarantee good Quality of Services. With the increased demand in terms of throughput and etwork coverage, a rigorous characterization of channels is demanded. In this article, a new characterization method that uses an analytical modeling approach based on Multiple Input Multiple Output (MIMO) channels is proposed. Definitely, the channel characterization and modeling for a MIMO system must take into account at the same level the spatial and temporal representations. In the spatial domain, the transmission channel characterization allows realistic and accurate modeling. In a MIMO context, this modeling is important since it gives a gain in throughput and, consequently, a good performance relatively to conventional and classical systems. Here, it is studied the behavior of these information carriers deploying the context of propagation environment as well as the effect of fading, diversity, multiplexing and multipath phenomenon. Hence, a specific study based on Rayleigh and Additive White Gaussian Noise channels is presented.
Internet of Underwater things (IoUT) is growing into one of the most important research interests since the last few decades. The primary objective of IoUT is to develop a worldwide network of smart underwater-interconnected objects. It has wide-ranging aquatic applications, including surveillance, pollution reduction, monitoring offshore oil and gas pipelines, disaster prevention, and navigation assistance, making it as important as a terrestrial communication system. The underwater communication channel poses unique acoustic communication challenges that suffer from long propagation delay, low bandwidth, multipath, and fading. IoUT significantly differs from the conventional Internet of Things (IoT) due to disparate environmental conditions under the ocean that require re-designing the underwater communication channel model. In addition to the challenges mentioned above, end-to-end delay and efficient energy utilization are also of great concern. Therefore, in this research paper, diverse attributes of underwater acoustic communication, including the speed of sound, transmission loss, absorption, and ambient noise, are analyzed to design a channel model for underwater communication. These environmental conditions also make underwater acoustic channels highly variable, so efficient resources, including bandwidth and power, are required. Adaptive modulation is proposed to make the communications system efficient by considering the distance between nodes and the signal-to-noise ratio as channel state information. The proposed channel model critically analyzed the CSI factors, results show efficient bandwidth utilization and appropriate power consumption for the well-suited route. The proposed research also aims to reduce end-to-end propagation delay by considering vertical angle-based shortest path (efficient route) in the Multilevel rotating priority MRP-routing algorithm.
Unmanned aerial vehicle (UAV) is an emerging technology with high mobility and flexible reconfiguration. In this paper, an UAV-assisted spatial modulation (SM) system with amplify-and-forward (AF) protocol is presented, and the corresponding bit error rate (BER) performance is investigated over Rician fading channels, where the UAV is employed as a half-duplex relay and remains stationary over a given area, the path loss exponent and Rician factor depend on the position of the UAV. Based on the imperfect channel state information (CSI) available, the effective signal-to-noise ratio (SNR) of the system is firstly derived. Then, with this result, we analyze the BER performance of the system, and deduce an upper bound of average BER for evaluation. On these bases, the asymptotic performance under large SNR is analyzed, and asymptotic expression of BER bound is derived to attain the diversity gain which is zero for imperfect CSI and one for perfect CSI. Simulation results demonstrate the effectiveness of the presented performance analysis, and reveal that the degradation arisen from estimation error and multiple antennas at the transmitter in BER performance is serious while the improvement brought by spatial diversity at the receiver is relatively modest. Specifically, the increase of 0.04 in estimation error variance results in the diminution of 12.5dB in performance gain, and the use of eight transmit antennas is 8dB worse than two transmit antennas. At the receiver, the increase in performance gain offered by going from ND=1 to ND=6 is about 4dB. Furthermore, according to the simulation, the optimal BER performance can be reached by adjusting the UAV position and power allocation factor. At last, the open issues and challenges focusing on both the deployment and architecture of this system are highlighted.
This paper is on a coverage estimation procedure for the deployment of outdoor Internet of Things (IoT). In the first part of the paper, a data-driven coverage estimation technique is proposed. The estimation technique combines multiple machine-learning-based regression ideas. The proposed technique achieves two purposes. The first purpose is to reduce the bias in the estimated received signal strength arising from estimations performed only on the successfully received packets. The second purpose is to exploit commonality of physical parameters, e.g. antenna-gain, in measurements that are made across multiple propagation environments. It also provides the correct link function for performing a nonlinear regression in our communication systems context. In the second part of the paper, a method to use readily available geographic information system (GIS) data (for classifying geographic areas into various propagation environments) followed by an algorithm for estimating received signal strength (which is motivated by the first part of the paper) is proposed. Together they enable quick and automated estimation of coverage in outdoor environments. It is anticipated that these will lead to faster and more efficient deployment of outdoor Internet of Things.
In this chapter, bit error rate (BER) performance of some of digital modulation schemes and different wireless communication techniques is evaluated in AWGN and fading channels. Further, the BER performance of different diversity techniques such as selective diversity, EGC, and MRC is also evaluated in Rayleigh fading channel.
A proposition is described in this paper regarding the use of algebraic space-time code (ASTC) and minimum mean square error equalizer (MMSE) for the amelioration of the bit error rate (BER) in the orthogonal frequency division multiplexing (OFDM) and multiple-input multiple-output (MIMO) systems so as to deduce the desired outcomes. The MATLAB SIMULINK R2012.a is incorporated here for the modeling and simulation results and the same are plotted for BER performance of OFDM in MIMO system Vs Eb/No. Also the different fading channels i.e. additive white Gaussian noise, Rayleigh and Rician channel have been inculcated and the BER performance ameliorates overwhelmingly thereby depicting the desired enhancement incorporating MMSE equalizers and ASTC encoder in several fading channels, i.e. approximately 10% – 20% in OFDM and in MIMO-OFDM it improve up to 15% approximately. The relative analysis of the conclusion and observations described in the recommended system show an improvement than the MMSE equalizer tremendously.
Orthogonal frequency division multiplexing modulation technique plays an important role in long distance communication. The OFDM is a multi-carrier modulation scheme which enables transmission of multiple signals; simultaneously over a single transmission path. The proposed work is based on peak to average power ratio (PAPR) reduction by the implementation of Selective Mapping Technique (SLM) and Partial Transmit Sequence (PTS) methods. The work is extended by modifying the SLM and PTS of PAPR by reducing their complexity of the OFDM system [1]. But in this paper, further increase the work to reduce complexity of OFDM system and also decrease the value of PAPR by using ACO algorithm with PTS and SLM. Keywords— OFDM, ACO, SLM, PTS PAPR, ISI and ICI I. INTRODUCTION In this high-speed wireless and mobile communications era, the concept of multi carrier transmission provides high data rates in communication channel. Thus OFDM is a special kind of multi carrier transmission technique that divides the communication channel into several equally spaced frequency bands. The bit streams are divided into many sub streams and send the information over different sub channels. And sub-carrier carrying the user information is transmitted in each band. Therefore each sub carrier is orthogonal with other sub carrier and it is carried out by a modulation scheme. The data's are transmitted simultaneously in super imposed and parallel form. Then sub carriers are closely spaced and overlapped to achieve high bandwidth efficiency [2]. The main disadvantage of OFDM is high peak to average power ratio. Thus peak values of some of the transmitted signals are larger than the typical values The main work of this paper is to reduce the high peak powers in OFDM systems. Several methods are there to reduce PAPR effectively. In this study the concept of selective mapping (SLM)and partial transmit sequence(PTS) technique is applied to the OFDM symbols to reduce high peak signals[10]The results state that the proposed new SLM and PTS method attains a good PAPR reduction and the encoding complexity is reduced by applying the new schemes.
In wireless communication, it is of significance that the receiving information should be identical to the transmitted information. With this regards, an application of error correction coding (ECC) is one suitable method for maintaining the information precision between the transmission channels. With similar objectives, the diversity techniques are used to moderate the devaluation in the error performance due to the fading impairment by using multiple communication branches. This paper, we propose the application of concatenate codes combined with space diversity technique as maximal ratio combining. We focused on the bit error rate (BER) performance and the impact of Rician fading channel on wireless body area network (WBAN). The finding shows that the proposed scheme can provide considerable improvement on the BER performance compared with that of the traditional system. The concatenate code with MRC outperformed conventional ones, either RS or convolutional codes. At 10−4 of BER, the designed scheme is better than RS code by1.3 dB and convolutional code by2.2dB.
In this chapter, bit error rate (BER) performance of some of digital modulation schemes and different wireless communication techniques is evaluated in additive white Gaussian noise (AWGN) and fading channels. Further, the BER performance of different diversity techniques such as selective diversity, EGC, and MRC is also evaluated in Rayleigh fading channel.
The final closed-form expression of the bit error rate (BER) is presented for a DS-CDMA system using a maximal ratio combining (MRC) diversity in conjunction with simple channel coding over a Rician fading channel. The accuracy of the BER evaluated by this expression is verified through comparison with a semi-analytic simulation result. The effect of diversity order and channel coding on the bit error rate performance is also considered for typical multipath delay profiles with different Rician ratios.
This paper presents a statistical analysis of the decision threshold for direct-sequence spread-spectrum (DS-SS) parallel Pseudo-Noise (PN) code acquisition with a reference filter. The probabilities of detection and false alarm are derived, and the mean acquisition time is evaluated as a measure of the system performance in both nonfading and Rician fading channels. From the statistical results, it is shown that in the performance analysis of the parallel acquisition system with reference filtering, the statistical evaluation of the decision threshold seems more appropriate than the approximation of the decision threshold adopted in other schemes [4,5]. It is also shown that the parallel acquisition scheme provides a sub- optimal threshold value for a wide range of SNR such that the mean acquisition time is minimized.
Wireless sensor networks has been one of the major research topics in recent years because
of its great potential for a wide range of applications. In some application scenarios, sensor
nodes intend to report the sensing data to a far-field destination, which cannot be realized by
traditional transmission techniques. Due to the energy limitations and the hardware constraints
of sensor nodes, distributed transmit beamforming is considered as an attractive candidate for
long-range communications in such scenarios as it can reduce energy requirement of each sensor
node and extend the communication range. However, unlike conventional beamforming,
which is performed by a centralized antenna array, distributed beamforming is performed by
a virtual antenna array composed of randomly located sensor nodes, each of which has an
independent oscillator. Sensor nodes have to coordinate with each other and adjust their transmitting
signals to collaboratively act as a distributed beamformer. The most crucial problem of
realizing distributed beamforming is to achieve carrier phase alignment at the destination. This
thesis will investigate distributed beamforming from both theoretical and practical aspects.
First, the bit error ratio performance of distributed beamforming with phase errors is analyzed,
which is a key metric to measure the system performance in practice. We derive two distinct
expressions to approximate the error probability over Rayleigh fading channels corresponding
to small numbers of nodes and large numbers of nodes respectively. The accuracy of both
expressions is demonstrated by simulation results. The impact of phase errors on the system
performance is examined for various numbers of nodes and different levels of transmit power.
Second, a novel iterative algorithm is proposed to achieve carrier phase alignment at the destination
in static channels, which only requires one-bit feedback from the destination. This
algorithm is obtained by combining two novel schemes, both of which can greatly improve the
convergence speed of phase alignment. The advantages in the convergence speed are obtained
by exploiting the feedback information more efficiently compared to existing solutions.
Third, the proposed phase alignment algorithm is modified to track time-varying channels. The
modified algorithm has the ability to detect channel amplitude and phase changes that arise over
time due to motion of the sensors or the destination. The algorithm can adjust key parameters
adaptively according to the changes, which makes it more robust in practical implementation.
There are critical requirements for security in Big Data collection and transmission of Big Data through a communication network. A new secure transmission for Big Data based on nested sampling and co-prime sampling is proposed in this paper. With nested sampling and coprime sampling, Big Data could also achieve higher PSD for BFSK signal. When the sampling spacing pairs bigger enough, the spectrum of BFSK signal performs like frequency hopping. With the same independent multitone interfering signal added to FH/BFSK system, the error probability becomes much lower using nested sampling and coprime sampling compared with the original FH/BFSK signal. This property has great advantage in the security of Big Data collection and transmission using FH/BFSK based on nested sampling and coprime sampling.
The presence of the Line-Of-Sight (LOS) component will increase the condition number of the multi antenna channel matrix, and severely reduce detection performance of the synchronous multi-carrier layered space-time code. As a remedy to this problem, a multi-carrier layered space-time architecture is proposed based on the asynchronous transmission of each antenna's signal in frequency domain. Closed-form Bit Error Rate (BER) expressions of the Zero Forcing (ZF) joint detection for a Ricean fading channel is derived for both coded and uncoded modulation. Comparisons are also made with those obtained in a traditional synchronous system. The theoretical analysis and simulation results show that the asynchronous multi-carrier transmission scheme can break through the antenna number limitation of synchronous multi-carrier layered space-time code system, while achieving full receive diversity with low complexity linear detector.
In this paper, the error performance of multiuser CDMA system with space-time coding is studied in Rician fading channel, and the corresponding bit error rate (BER) and symbol error rate (SER) analysis are presented. Based on the performance analysis, a simple and effective multiuser receiver scheme is developed. The scheme has linear decoding complexity when it compares to the existing scheme. Based on the performance analysis, and using mathematical manipulation, the BER and SER of multiuser space-time coded CDMA system are derived, respectively. As a result, accurate closed-form expressions of BER and SER are respectively obtained. With these expressions, the performance of multiuser CDMA system with space-time coding can be evaluated effectively. Computer simulation shows that the developed receiver scheme has almost the same performance as the existing scheme, and the theoretical BER and SER can match the corresponding simulation results well
The book discusses modern channel coding techniques for wireless communications such as turbo codes, low parity check codes (LDPC), space-time coding, Reed Solomon (RS) codes and convolutional codes. Many illustrative examples are included in each chapter for easy understanding of the coding techniques. The text is integrated with MATLAB-based programs to enhance the understanding of the subject’s underlying theories. It includes current topics of increasing importance such as turbo codes, LDPC codes, LT codes, Raptor codes and space-time coding in detail, in addition to the traditional codes such as cyclic codes, BCH and RS codes and convolutional codes. MIMO communications is a multiple antenna technology, which is an effective method for high-speed or high-reliability wireless communications. PC-based MATLAB m-files for the illustrative examples are included and also provided on the accompanying CD, which will help students and researchers involved in advanced and current concepts in coding theory. Channel coding, the core of digital communication and data storage, has undergone a major revolution as a result of the rapid growth of mobile and wireless communications. The book is divided into 11 chapters. Assuming no prior knowledge in the field of channel coding, the opening chapters (1 - 2) begin with basic theory and discuss how to improve the performance of wireless communication channels using channel coding. Chapters 3 and 4 introduce Galois fields and present detailed coverage of BCH codes and Reed-Solomon codes. Chapters 5-7 introduce the family of convolutional codes, hard and soft-decision Viterbi algorithms, turbo codes, BCJR algorithm for turbo decoding and studies trellis coded modulation (TCM), turbo trellis coded modulation (TTCM), bit-interleaved coded modulation (BICM) as well as iterative BICM (BICM-ID) and compares them under various channel conditions. Chapters 8 and 9 focus on low-density parity-check (LDPC) codes, LT codes and Raptor codes. Chapters 10 and 11 discuss MIMO systems and space-time (ST) coding.
Presented in this paper are ideal asymptotic performance characteristics for two types of multireceivers, the coherent adaptive multireceiver and the noncoherent multireceiver. The transmitter, for the system, is one which selects for transmission one of two equiprobable, equal energy correlated waveforms. The selected waveform is transmitted into the Rician fading multichannel with additive Gaussian noise superposed at the receiver end. The multichannel may take on one of four forms, i.e., it may change from one of a completely random nature to that of a completely fixed nature. All intermediate forms are permissible.
The purpose of this note is to point out that for either frequency diversity or time diversity, the dependence of required transmitted power on number of branches is quite different than for space diversity. For both frequency- and time-diversity techniques the saving of transmitter power can come only from the first factor above (that is, the averaging of fluctuations), since the total mean received power is a fixed fraction of the scattered power. It will be shown that as a consequence: 1) The minimum required transmitter power for a specified reliability is strictly larger than zero. 2) Both the value of this minimum and the number of diversity branches yielding the minimum depend upon the diversity-combining method used.
This paper is concerned with various aspects of the characterization of randomly time-variant linear channels. At the outset it is demonstrated that time-varying linear channels (or filters) may be characterized in an interesting symmetrical manner in time and frequency variables by arranging system functions in (timefrequency) dual pairs. Following this a statistical characterization of randomly time-variant linear channels is carried out in terms of correlation functions for the various system functions. These results are specialized by considering three classes of practically interesting channels. These are the wide-sense stationary (WSS) channel, the uncorrelated scattering (US) channel, and the wide-sense stationary uncorrelated scattering (WSSUS) channel. The WSS and US channels are shown to be (time-frequency) duals. Previous discussions of channel correlation functions and their relationships have dealt exclusively with the WSSUS channel. The point of view presented here of dealing with the dually related system functions and starting with the unrestricted linear channels is considerably more general and places in proper perspective previous results on the WSSUS channel. Some attention is given to the problem of characterizing radio channels. A model called the Quasi-WSSUS channel is presented to model the behavior of such channels. All real-life channels and signals have an essentially finite number of degrees of freedom due to restrictions on time duration and bandwidth. This fact may be used to derive useful canonical channel models with the aid of sampling theorems and power series expansions. Several new canonical channel models are derived in this paper, some of which are dual to those of Kailath.
Considerable attention has been given in the past to the design and specification of optimum (a posteriori probability computer) receivers. In this paper we consider the problem of communicating through the Rayleigh-Fading-Multipath channel with additive noise. The a posteriori probabilities necessary for specifying different receiver modes for various forms of a priori channel knowledge are derived. System performance is analyzed and computed for several modes of operation and the results presented in graphical form, allowing one to determine the importance of making measurements on the unknown channel state.
Multiple frequency shift keying (MFSK) is a modulation suitable for transmitting digital data under fading conditions. A quantitative analysis of MFSK-with-diversity is presented. The MFSK signals on the several diversity channels are presumed to be perturbed independently by Rayleigh fading and additive white Gaussian noise. Also, it is assumed that fading is slow and that envelope, cross-correlation (matched filter) detection is used. The diversity combining method is chosen so that the receiver performs a likelihood-ratio test in deciding which one of K frequencies was transmitted. This optimum comibining method is to square and add the detected outputs of corresponding filters from each diversity channel. Theoretical error probability as a function of signal-energy-per-bit received is derived, and curves are plotted for two-, four-, and eight-frequency MFSK-with-diversity. Bandwidth requirements, as a function of type and order of diversity, are determined. Eight-frequency MFSK with triple diversity has a 21.8-db advantage over simple FSK for transmitting 6-bit characters with a 0.001 error probability.
In a previous paper the structure of the optimal multi-diversity receiver for a fading, noisy diversity channel was determined under the assumption that the memory of the receiver does not extend beyond the time interval of the signal currently being received. The probability of error for such a receiver is determined herein under the following assumptions: the channel is binary and symmetric; the (Gaussian) noises in the various diversity links are white and independent; and the fadings in the various links are Rayleigh distributed and slow, but not necessarily independent. Detailed curves of this probability of error are given for various orders of diversity in the two cases of independent fadings and "exponentially correlated" fadings. Since the optimal receiver may be difficult to implement, a more easily implemented "square-law combining" receiver is also considered, and it is shown that for all practical purposes this simpler receiver behaves optimally. Finally the effect of the assumption that the receiver has a short memory is considered by comparing its performance with that of a longer-memory receiver studied by Pierce and Stein.
The effective use of predetection (or IF) linear combining of diversity channels requires that all frequency components be added in = phase. In view of the time-variant phase characteristics of fading channels, some form of instantaneous phase correction must be provided prior to the diversity combining so that proper in-phase addition will result. If the instantaneous fading is not uniform over the width of the channel, the resulting channel incoherence will reduce the efficacy of the phase correction. One way to avoid this difficulty is to divide the selectively fading channel into "flatly" fading subchannels and perform the necessary phasing and combining operations per subchannel. The question arises as to how much frequency selective fading can be tolerated within a channel, or a subchannel, before serious deterioration in performance results. This paper considers this question with reference to FDM-SSB binary data transmission and matched filter reception, wherein a pilot tone is used both for deriving proper phase correction and for providing the weighting necessary for maximal ratio combining. Analytical expressions are derived for error probabilities which show the deleterious effects of frequency selectivity and pilot tone additive noise.
The fading of radio waves of medium and high frequencies returned from the ionosphere is analysed. The experimental data on high frequencies were recorded by the author at normal incidence using a pulse transmitter, and, when necessary, a circularly polarized receiving aerial. The medium-frequency records were made by the B.B.C. using continuous-wave transmissions from broadcasting stations at different distances up to 1 500 kilometres. A review is given of some theories suggested to explain the production of fading in terms of an ionosphere with varying irregularities in the horizontal plane. The theoretical nature of the fading curve, both with regard to the distribution of amplitude and the variation with time, is indicated, and is compared with experimental results. It is shown that all fading curves can be explained in terms of a wave which is the sum of a steady, specularly reflected component, and a random component with a Rayleigh distribution of amplitude. The relative magnitudes of these two components have been determined for a series of different conditions, and the results are summarized. It is also shown that the rate of variation of the amplitude of the received signal is approximately, but not exactly, in accord with the theories, and from this rate of change it is possible to calculate the ¿effective velocity¿ of the irregularities in the ionosphere. If the fading is caused by irregular ¿turbulent¿ motions of the irregularities, the ¿effective velocity¿ is the r.m.s. velocity of these motions; if it is due to a steady drift of the irregular ionosphere as a whole with a velocity vw, then the ¿effective velocity¿ is approximately equal to vw/14. The ¿effective velocities¿ deduced from 122 records made at vertical incidence, and 55 made at oblique incidence, lie between 0.3 and 8.0 m/sec and have an average value of 1.9 m/sec.
In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22
Thesis (Sc.D.) Massachusetts Institute of Technology. Dept. of Electrical Engineering, 1956. Vita. Bibliography: leaves 97-98. by George Lewis Turin. Sc.D.
Description and performance are given for two slightly different forms of an adaptive receiver that is used with binary signaling in a multichannel communication system. Each channel has a non-dispersive, nonfading propagation path and additive white gaussian noise that is independent of, and equal in intensity to, the other channel noises. Either phase-independent orthogonal signaling (such as FSK) or phase-reversal-comparison signaling is employed to convey to the receiver both the message and information about the path strengths and phases. The receiver measures the path parameters and applies the results to the detection processing as though they were perfectly accurate; it is shown that this procedure is a natural extension of non-adaptive reception. Results are given without derivation for the probability of binary decision error, which depends on the type of signaling, the ratio of the total noise-exclusive signaling energy received to the noise intensity, the number of channels, and the ratio of the effective measurement time to the binary signal duration. The distribution of the received signaling energy among the channels is immaterial. Graphs of error probability are presented for selected system parameters. A novel by-product of the study is an error-probability expression for non-adaptive multichannel reception of quite general binary signaling. Optimal adjustment of the adaptive receiver for fading-path situations is also considered, but corresponding error probabilities have not yet been derived.
Detection of a binary transmission by both optimum and suboptimum nonlinear and linear multireceivers is considered by comparing their asymptotic performance characteristics. The multichannel model is presumed to be of the Rician type. Particularly, we consider Turin's nonlinear specular-coherent multi-receiver and the nonlinear noncoherent Pierce-Stein multireceiver. These two termination error rate characteristics are graphically compared for low and high output signal-to-noise ratios. The performance characteristics of two other coherent linear multireceivers, one optimum and one easier implemented suboptimum, are derived and compared with the above-mentioned nonlinear multireceivers. The numerical results indicate system design trends and provide information on the degradation or improvement afforded by employing nonlinear detection systems as compared with linear detection systems. In particular, the optimum nonlinear coherent multireceiver is difficult to implement. It is shown that, for multichannels which are largely specular in nature, a more easily implemented linear coherent unit behaves optimally for all practical purposes. For channels which are largely scatter in nature it is shown that the linearized suboptimum system performance is highly inferior to the corresponding optimum coherent unit. In these situations, the noncoherent "square-law combining" system would be more reliable than the suboptimum coherent unit. In fact, for large scatter components we find that the noncoherent unit performs almost identically to the nonlinear coherent unit. This is due to the signal suppression effects known to occur in all nonlinear detectors throughout the field of statistical detection theory.
Previous analyses of diversity techniques are extended to include the performance of an optimum (maximal-ratio) combiner in the case of nonindependent signal fading fluctuations, for an arbitrary number of diversity branches. The analysis includes the general possibility of correlations among the quadrature components of the various signals. Some computational simplifications for certain cases of physical interest are given, as well as a specific application to two problems in digital communications.
One of two correlated, equal energy, equiprobable waveforms is transmitted through a channel during a given time interval. The signal is corrupted in the channel by slowly-varying, frequency-nonselective fading and by additive, Gaussian noise. On reception, the corrupted signal is processed by an ideal receiver, which guesses that the transmitted waveform was the one which it computes to be a posteriori most probable. Expressions for the probability of committing an error in making such a guess are derived for both coherent and noncoherent receivers; these are studied in detail, and some general trends and system design considerations are noted. In an illustrative example, the results are applied to binary frequency-shift keyed (FSK) systems with various pulse shapes and frequency separations.
Methods of using diversity to improve frequencyshift keyed receptions in the presence of Rayleigh fading are analyzed. In the absence of prior information about signal amplitude and phase, square-law combination is optimum; the error rate for this combination method has been found. If signal amplitude and phase are exactly known prior to reception of the signal, coherent combination and detection are optimum; at low error probability this yields only a 3-db improvement. Nonoptimum switch diversity yields only slightly less diversity gain than square-law combination. For dual diversity, correlation of the fading on the separate antennas does not give a large loss if the correlation coefficient is moderate. Correlated noise yields a similar small loss.
Frequency-shift, phase-shift, and on-off amplitude modulation are examined as mechanisms. Curves of fractional error as a function of average carrier-to-noise ratio are derived for fading and non-fading carriers. The results are applicable to telegraph, teletype, and other binary-coded signals.
Higher Transcendental Function Predetection diversity combining with selectively fading channels
- A February
- Erdelyi
February, 1954. A. Erdelyi, et al., " Higher Transcendental Function, " vol. I and II, McGraw-Hill Book Co., Inc., New York, N. Y.; 1953. P. Bell and B. D. Nelin, " Predetection diversity combining with selectively fading channels, " IRE TRANS. ON COM-MUNICATIONS SYSTEMS, vol. CS-10, pp. 32-42;
Error rates in data transmission
- reiger
January, S. Reiger, " Error rates in data transmission, " PROC. IRE, (Correspondence), vol. 46, pp. 919-920;
Table of & Function Santa Monica, Calif., Rept. No., RM-339 Also see .J. I. Marcum and P. Swerline Studies of Target Detection by Pulsed Radar
- J I December
- Marcum
December, 1963. J. I. Marcum, " Table of & Function, " RAND Corp., Santa Monica, Calif., Rept. No., RM-339; January 1, 1950. Also see.J. I. Marcum and P. Swerline. " Studies of Target Detection by Pulsed Radar, " IRE TR.&. ON INBORMAT~ON THEORY, vol. IT-6;
Theory of Bessel Function Infinite integrals containing Bessel function products Also see " Space Programs Summary Characterization of randomly time-variant linear channels
- G N June
- P A Watson
- Bello
June, 1964. G. N. Watson, " Theory of Bessel Function, " Cambridge University Press, New York, N. Y.; 1958. W. C. Lindsey, " Infinite integrals containing Bessel function products, " J. Sot. Indust. Appl. Math., June, 1964. Also see " Space Programs Summary, " No. 37-22, vol. IV, Jet Propulsion Lab., Pasadena, Calif.; July, 1963. P. A. Bello, " Characterization of randomly time-variant linear channels, " IEEE TRANS. ON COMMUNICATIONS SYSTEMS, vol. CS-11, pp. 360-393;
Probability Distribution for Practical Applications
- W C Lindsey
Exploration of the moon's surface
- shoemaker
The autocorrelogram of a complete carrier wave received over the ionosphere at oblique incidence
- price
Studies of Target Detection by Pulsed Radar
- marcum
Error Probability of Binary Data Transmission Systems in the Presence of Random Noise
- reiger