Gaussian Fading Channels Research Articles

A Sphere Packing Bound for Vector Gaussian Fading Channels Under Peak Amplitude Constraints

An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO channels notable results from the geometric analysis on the capacity of scalar Gaussian channels. Relying on a sphere packing argument and on the renowned Steiner’s formula, the proposed upper bound depends on the intrinsic volumes of the constraint region, i.e., functionals defining a measure of the geometric features of a convex body. The tightness of the bound is investigated at high signal-to-noise ratio (SNR) for any arbitrary convex amplitude constraint region, for any channel matrix realization, and any dimension of the MIMO system. In addition, two variants of the upper bound are proposed: one is useful to ensure the feasibility in the evaluation of the bound and the other to improve the bound’s performance in the low SNR regime. Finally, the upper bound is specialized for two practical transmitter configurations, either employing a single power amplifier for all transmitting antennas or a power amplifier for each antenna.

The impact of intentional interference on the performances of ML detector in MIMO systems

Here we address the problem of performing the resilience of Multiple Input Multiple Output (MIMO) architecture against intentional and unintentional interferences. We investigate the performance of a non-linear receiver based on the Maximum Likelihood (ML) detector in MIMO systems over Gaussian fading channels in the presence of interfering signals. Using the properties of the Gaussian matrix, a finite expression of the Probability Density Function (PDF) for the Signal to Interference plus Noise Ratio (SINR) is obtained as a function of the brute jammer power budget and the number of affected antennas. By considering a particular closed-form of intelligent jamming strategies against MIMO architecture presented in the literature, approximated upper limits of the Bit Error Rate (BER) are performed under different jamming scenarios depending on the Channel State Information (CSI) availability. These results enable us to characterize the consequences of such conflicting attacks on the quality of the legitimate link. Furthermore, extensive simulations are carried out to justify the performance of the ML detector and validate the obtained results.

Joint Communication and State Estimation Over a State-Dependent Fading Gaussian Channel

A joint message and state communication problem over a fading Gaussian channel with additive state is considered. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and known non-causally at the transmitter, while the instantaneous fading gain is assumed to be known at both the encoder and the decoder. The receiver not only has to decode the message from the transmitter, but also needs to estimate the state process to meet a prescribed distortion limit. A complete characterization of the optimal rate versus distortion performance is provided. Moreover, the converse proof presented here might be of independent interest, since it gives a simpler and more compact way of establishing the converse for settings with non-fading links studied in the literature – by virtue of relying only upon the differential entropy maximizing property of Gaussian random variables for a given variance.

Enhanced LDM for Next-Generation Digital Broadcasting Transmission

In the traditional layered division multiplexing (LDM) system, by simply adjusting the injection level, the reception performance of the core layer (CL) mobile services will be decreased significantly, resulting in the deterioration of system coverage performance. Thus, it is necessary to improve the performance of the enhanced layer (EL) service reception without affecting the reception threshold of CL service. To achieve this, in this paper, an enhanced LDM (En-LDM) scheme that supports multi-service transmission is proposed for the next-generation broadcasting network. In this scheme, at the transmitter end, part of the low-density parity-check (LDPC) coded data stream of fixed service conveyed in the EL will be extracted out through puncturing, and then, it will be transmitted over the CL of the LDM signal along with the original CL data in a frequency domain multiplexing (FDM) manner. At the receiving end, the punctured data of the EL fixed service will be recovered with a higher signal-to-noise ratio (SNR). Compared to the traditional LDM scheme, the proposed En-LDM scheme can significantly improve the reception performance of fixed services without decreasing the SNR threshold of mobile services. Moreover, the En-LDM can achieve a higher channel capacity than that of the traditional LDM for both the fixed services and the overall services. The superiority of the proposed En-LDM scheme over the traditional LDM scheme is validated by the simulation under the additive white Gaussian noise (AWGN) and fading channels.

Convolutional Neural Network (CNN)-Based Frame Synchronization Method

A new frame synchronization technique based on convolutional neural network (CNN) is proposed for synchronized networks. To estimate the exact packet arrival time, the receiver typically uses the correlator between the received signal and the preamble or pilot in front of the transmitted packet. The conventional frame synchronization technique searches the correlation peak within the time window. In contrast, the proposed method utilizes a CNN to find the packet arrival time. Specifically, in the proposed method, the 1D correlator output is converted into a 2D matrix by reshaping, and the resulting signal is inputted to the proposed 4-layer CNN classifier. Then, the CNN predicts the packet arrival time. To verify the frame synchronization performance, computer simulation is performed for two channel models: additive white Gaussian noise and fading channels. Simulation results show that the proposed CNN-based synchronization method outperforms the conventional correlation-based technique by 2dB.

Algebraic constructions of rotated unimodular lattices and direct sum of Barnes–Wall lattices

In this paper, we construct some families of rotated unimodular lattices and rotated direct sum of Barnes–Wall lattices [Formula: see text] for [Formula: see text] and [Formula: see text] via ideals of the ring of the integers [Formula: see text] for [Formula: see text] and [Formula: see text]. We also construct rotated [Formula: see text] and [Formula: see text]-lattices via [Formula: see text]-submodules of [Formula: see text]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. The minimum product distances of such constructions are also presented here.

Ergodic capacity and symbol error rate of distributed massive MIMO systems over Rayleigh-inverse Gaussian fading channels using ZF detectors

Distributed massive multiple-input multiple-output (DM-MIMO) system has attracted significant research interest in recent years. It is regarded as a potential technology in 5G communication network because of its capability to achieve substantial improvements in energy and spectral efficiency. In this paper, we consider Rayleigh-Inverse Gaussian (RIG) composite fading channels for DM-MIMO systems and investigate ergodic capacity and symbol error rate (SER) at the output of a zero forcing (ZF) detector. The DM-MIMO system comprises of multiple base stations (BSs) distributed across the cell and an arbitrarily located mobile unit. It is shown that for the considered DM-MIMO architecture signal to noise ratio (SNR) at the ZF output involves sum of several unequal Wishart channel matrices. This increases the difficulty in evaluating its performance compared to co-located MIMO (C-MIMO). In this regard, we first determine the ergodic capacity for finite receiving antennas and obtain the closed-form expression over small-scale fading over both correlated and uncorrelated channels. The output is compared with conventional C-MIMO configurations at various user locations. For massive MIMO system, the approximated SNR is expressed as a sum of unequal inverse Gaussian random variables. In such scenario, we formulate the closed form expression of asymptotic ergodic capacity and subsequently its lower bound for more practical insights. We demonstrate here that, the lower bound is consistently tight until coefficient of variation (CV) is less than or equal to unity and the tightness progressively decreases when CV is further increased beyond unity. We also assess SER performance of ZF detectors for both finite and infinite number of receiving antennas. The impact of various parameters such as number of transmitting and receiving antennas, shadowing parameters, locations of user and BSs etc. on the performance of ZF detectors are extensively investigated. Finally, the suitability of obtained expressions is validated through a set of Monte-Carlo simulations.

Iterative Invertible Clipping Method for PAPR Reduction in Wireless MC-CDMA Communication Systems

Background & Objective: One of the disadvantages of Multi-carrier Code Division Multiple Access (MC-CDMA) system is the high value of Peak to Average Power Ratio (PAPR). This paper proposes an approach called Iterative Invertible Clipping Method (IICM) to address the PAPR for MC-CDMA signal based on wireless communication system characteristics. This is mainly concentrated in clipping function making use of a polynomial of degree three at the transmitter, and its inverse at the receiver, to recover the original signal. Method: A Fast Fourier Transform (FFT)-based frequency domain filter is employed to reduce the overall peak regrowth which is supported by measuring the Adjacent Channel Power Ratio (ACPR) after soft clipping and filtering. This technique is compared with Ragusa method using a polynomial of degree 5. Result: The simulated results of the proposed method showed better performance in terms of PAPR reduction, Bit Error Rate (BER), and computational complexity requiring two iterations only. The Complementary Cumulative Complementary Density Function (CCDF) is served to measure and improve PAPR performance of the system. Conclusion: The channel coding process is applied to strengthen the obtained results in the Additive White Gaussian Noise (AWGN) channel and fading channel (Rayleigh). The High-Power Amplifier (HPA) is used for validation purposes.

RESEARCH OF CHARACTERISTICS OF NOISE IMMUNITY WITH USE OF ORTHOGONAL CODING

In the digital communication systems for noise immunity's increase with the fixed code rate it is proposed to use an additional orthogonal coding developed by the authors. It is an analogue of convolutional coding over the rational numbers' field. Transmission of digital signals in Additive white Gaussian noise (AWGN) channel and fading channels is considered including a joint use of the orthogonal and correcting codes (block and convolutional). It is shown that losses in signal-to-noise ratio can be significantly reduced by use of orthogonal coding. By increase of matrices' order, on which basis orthogonal codes are constructed, the coding gain grows also. By use of the proposed by the authors orthogonal coding the required quality of communication is implemented with a smaller energy cost. The significant coding gain (up to 6,4 dB in the channels with the AWGN, up to 22,74 dB in the fading channels) provided by more effective use of energy of transmitted signals is reached without increase in complexity and cost of transmitting/receiving devices.

Performance assessment of correlated Rayleigh‐inverse Gaussian fading channel over distributed MIMO systems with ZF detectors

Composite fading channel modelling of terrestrial wireless propagation is crucial for the design of communication system and its performance analysis. In this study, a systematic characterisation of Rayleigh-inverse Gaussian (RIG) distribution is provided for modelling the channel of distributed multiple-input multiple-output (MIMO) systems with zero-forcing (ZF) receiver in the presence of transmit antenna correlation. At the outset, the closed-form expression for probability density function of instantaneous signal-to-noise ratio (SNR) is derived followed by its associated moments and cumulative density function. In the subsequent analysis, exact closed-form analytical expression of ergodic capacity with its bounds are derived and their asymptotic expressions are obtained in high and low SNR regime. Then the closed-form expressions are deduced for average symbol error rate (ASER) and outage probability (OP). Additionally, the authors propose to formulate simplified expressions for asymptotic ASER as well as OP and assess their approximation accuracy. Numerical results are presented to compare the performance of RIG model with the existing generic models and illustrate that RIG is superior in terms of ergodic capacity, ASER and OP. Finally, the derived analytical expressions are validated through Monte Carlo simulations which demonstrate the effectiveness of RIG model in the diverse environmental scenario for various system and channel parameters.

On CS Image Reconstruction Using LDPC Code Over Radio Mobile Channel

In this work, the effect of additive white Gaussian noise and fading channel on the compressed sensing or compressive sampling (CS) image reconstruction process are demonstrated. First, the work suggests encoding of the sensed samples by low density parity check code (LDPC) before transmission. It is well known that longer is the length of the LDPC codes better (lower) is the bit error rate (BER) performance. Thus to improve CS reconstruction a method to construct a larger length but 4 cycle free irregular LDPC code structure is also proposed. The code construction is based on the LDPC code in IEEE WiMAX standard. The proposed CS-LDPC structure is then extended for $$4^n$$ -QAM to find an optimal set of thresholds by minimizing BER (equivalently symbol error rate) using differential evolution (DE). The algorithm works on the log likelihood ratio values obtained by LDPC decoding. Extensive simulation results show the efficacy of the use of LDPC codes and the trade-off in code rate and measurements on reconstruction quality. Improved performance with the proposed DE based demodulation is also demonstrated.

Spectrum sensing based on cumulative power spectral density

This paper presents new spectrum sensing algorithms based on the cumulative power spectral density (CPSD). The proposed detectors examine the CPSD of the received signal to make a decision on the absence/presence of the primary user (PU) signal. Those detectors require the whiteness of the noise in the band of interest. The false alarm and detection probabilities are derived analytically and simulated under Gaussian and Rayleigh fading channels. Our proposed detectors present better performance than the energy (ED) or the cyclostationary detectors (CSD). Moreover, in the presence of noise uncertainty (NU), they are shown to provide more robustness than ED, with less performance loss. In order to neglect the NU, we modified our algorithms to be independent from the noise variance.

Wireless DF Relaying with Beamforming for an Unmanned Aircraft System over ??? Fading Channels

In this paper, we propose a dual-hop decode-and-forward (DF) relaying network with beamforming for an unmanned aircraft system (UAS) over ??? fading channels. The ?–? fading model is a general fading model that models wireless fading channel perfectly in line-of-sight (LOS) propagation environments and includes Nakagami-m, Rician, Rayleigh, and One-sided Gaussian fading channels as special cases. We consider an unmanned aerial vehicle (UAV) as a moving relay for forwarding the data signals from a source ground station (GS) to a destination GS. Our proposed system considers multiple antennas at the source and destination, whereas the relay has a single antenna. We derive a closed-form expression for the outage probability in terms of the generalized Marcum Q-function. We carry out the performance analysis by means of derived expression for the various antenna arrangements, distinct values of radius, and different values of fading parameters. Our results show that the number of antennas and fading parameters, ? and ?, have a positive relation with system performance. The analytical results are validated through Monte Carlo simulations.

Optimized Cross-Layered Unequal Error Protection for SPIHT Coded Wireless Video Transmission

Transmission of coded video over erroneous channels (e.g., Internet and wireless networks) is always a challenging task. Error control strategies, to combat the channel errors, are generally applied at individual network layers leading to inefficient utilization of resources. The cross-layer design has emerged as alternative for efficient utilization of the available resources, such as bandwidth, delay, and transmission power to provide best quality of the reconstructed video. Furthermore, to efficiently utilize the resources, cross-layer error control parameters need to be optimized. Since, the optimal error control parameters change with channel conditions, new optimal values need to be calculated every time the channel condition changes. However, optimization of the parameters at the time of video transmission requires very high computational processing power otherwise it may induce a large transmission delay which is intolerable in video communication. In this paper, we propose an optimized cross-layered unequal error protection (UEP) scheme targeted for hand-held devices which have low processing power, uses pre-computed look-up table (LUT) that stores the optimal cross-layer error control parameters for a range of channel conditions. LUT is constructed using offline optimization of the parameters. For real time video communication, given a channel condition, the corresponding error control parameters are read from a LUT and are passed to the corresponding network layers. Thus, the proposed transmission system is simple and delivers best end-to-end quality of the video. Simulation results show that the proposed cross-layered UEP system can achieve up to 14–17 dB and 2–4 dB improvement in video quality over individual application layer optimized UEPs in additive white Gaussian noise and fading channel respectively at very poor channel conditions. Furthermore, the proposed system outperforms other contemporary methods.

FPGA Implementation of a Nakagami-m fading channel Simulator using Random Number Generator

<p class="abstract">By realizing the concept of implementation of the radio propagation channels on simulators is the eminent intention of this work. Even though prototyping software simulators are effortless to design we prefer hardware simulators as they endeavors distinguishable quickness, compared to earlier. Prior to this work fading channels like Gaussian, Rayleigh and Rician fading channel simulators were executed on hard ware.(i.e. FPGA) The significant target of this attempt is to implement Nakagami-m fading channel on hardware as they preserved for unsubstantial consideration. While differentiating with other fading channels Nakagami-m fading channel acquires wide spread applications, as its capability of providing appropriate fit for practical fading data, as this is flexible through its size parameter ‘m’, over which representation of signal fading conditions that vary from serious to modest, to normal fading or no fading is accomplished . The proposed hardware simulator can hatches complex Nakagami variates after it was implemented on XilinxSpartan-xc3s500e-4fg320 FPGA. This is operated at 50MHz.</p>

Exact SINR Statistics in the Presence of Heterogeneous Interferers

We derive new results for the higher order moments of signal-to-interference-plus-noise ratio (SINR) in the presence of an arbitrary Poisson point process (PPP)-based heterogeneous interference field. The analysis leverages on a moment-generating-function (MGF) methodology, which only requires the statistics of intended signal and aggregate interference, thus eliminating the need for the exact distribution of SINR. We extend the existing results on interference statistics by deriving a generalized closed-form expression of the interference MGF considering Nakagami-m fading channels with exclusion region. In certain special cases, explicit expressions for the averages of different functions of SINR are found, which also lead to closed-form solutions for the probability distributions of aggregate interference reciprocal and signal-to-interference ratio. We prove that in such cases the effect of total PPP-based interference power on useful transmission is mathematically equivalent to the severe fluctuations from a one-sided Gaussian fading channel. As an application example, the proposed methodology is used together with stochastic geometry theory to characterize the average SINR and rate in heterogeneous cellular networks. The validity of our analytical derivations is confirmed via Monte Carlo simulations for various system settings. We show that with cellular network densification there exists a tradeoff between the average SINR and rate performance.

Optimized Spectrum Constrained Crest Factor Reduction Technique Using Polynomials

This paper proposes a new peak-to-average power ratio (PAPR) reduction technique using a polynomial soft clipping function identified through a nonlinear constrained optimization. The power efficiency optimization problem of a linearized power amplifier can be considered as the minimization of the PAPR constrained by meeting the spectral mask requirements of the signal standard. It is demonstrated that the proposed approach can reduce the PAPR from 9.9 to 5.5 dB while meeting the spectral mask of the wideband code-division multiple-access standard. To compare the results with the traditional clipping and filtering method, the 5.5-dB PAPR clipped signal using the clipping and filtering technique was compared with the soft clipped signal. With the same efficiency, the error vector magnitude (EVM) for the soft clipped signal improved from 4.5% to 1.3% using post-compensation. Later, clipping and filtering are combined with the soft clipping technique. It is shown that the combined structure can reduce the PAPR to 3.4 dB while passing the adjacent channel power ratio and EVM requirements. The performance of the proposed method in the presence of additive white Gaussian noise and fading channels has been evaluated for 64QAM modulations using orthogonal frequency-division multiplexing modulated symbols.

Error exponents analysis of dual‐hop η ‐ μ and κ ‐ μ fading channel with amplify‐and‐forward relaying

In this study, the authors investigate the Gallager's error exponents of dual-hop amplify-and-forward systems over generalised η-μ and κ-μ fading channels, two versatile channel models which encompass a number of popular fading channels such as Rayleigh, Rician, Nakagami-m, Hoyt and one-sided Gaussian fading channels. The authors present new analytical expressions for the probability density function of the end-to-end signal-to-noise-ratio (SNR) of the system. These analytical expressions are then applied to analyse the system performance through the study of Gallager's exponents, which are classical tight bounds of error exponents and present the tradeoff between practical information rate and the reliability of communication. Two types of Gallager's exponents, namely, random coding error exponent and expurgated error exponent, are studied. Based on the newly derived analytical expressions, the authors provide an efficient method to compute the required codeword length to achieve a predefined upper bound of error probability. In addition, the analytical expressions are derived for the cutoff rate and ergodic capacity of the system. Moreover, simplified expressions are presented at the high SNR regime. All the analytical results are verified via Monte–Carlo simulations.

A Log-Det Inequality for Random Matrices

We prove a new inequality for the expectation $E\left[\log\det\left(\mathbf{W}\mathbf{Q}+\mathbf{I}\right)\right]$, where $\mathbf{Q}$ is a nonnegative definite matrix and $\mathbf{W}$ is a diagonal random matrix with identically distributed nonnegative diagonal entries. A sharp lower bound is obtained by substituting $\mathbf{Q}$ by the diagonal matrix of its eigenvalues $\mathbf{\Gamma}$. Conversely, if this inequality holds for all $\mathbf{Q}$ and $\mathbf{\Gamma}$, then the diagonal entries of $\mathbf{W}$ are necessarily identically distributed. From this general result, we derive related deterministic inequalities of Muirhead- and Rado-type. We also present some applications in information theory: We derive bounds on the capacity of parallel Gaussian fading channels with colored additive noise and bounds on the achievable rate of noncoherent Gaussian fading channels.

Space Time Block Code Analysis for MIMO-OFDM System

The growth in high data rate mobile data transmission in recent years is due to the tremendous achievements in Digital Communication especially Digital Modulation Techniques starting from Second Generation system (2G) in early 80’s to today 4G (LTE – Advanced). To achieve the goal towards Shannon’s Channel Capacity, a no. of modulation techniques are developed during these years. With the tremendous growth in the Very Large Scale Integrated Circuits (VLSI), a no. of digital modulation techniques is easier to implement in convenient manner. Orthogonal Frequency Division Multiplexing (OFDM), one of the latest techniques became feasible and economical due to the high processing speed. OFDM in combination with other techniques like Space Time Block Code (STBC)Phase shift key (PSK) and Quadrature Amplitude Modulation (QAM) give better performances in case of Multiinput Multi-output System (MIMO). This paper presents (STBC) technique for multiple transmission antennae (OFDM) system. Generally in Multiinput Multioutput (MIMO) system code selection across the space and time is difficult to get minimum Bit Error (BER) to achieve maximum output. In adaptive White Gaussian (AWGN) fading channels, STBC is best breakthrough to reduce the BER and obtain maximum output. Like AWGN fading channel the analysis is done for OFDM system using STBC at transmitter end. Various modulation techniques like Binary Phase Shift Key (BPSK) and Quadrature Amplitude Modulation are implemented using mentioned techniques. The Bit Error Rate (BER) versus different Signal to Noise (SNR) ratio are studies for above modulation techniques.