Capacity Results for Block-Stationary Gaussian Fading Channels With a Peak Power Constraint

A peak-power-limited single-antenna block-stationary Gaussian fading channel is studied, where neither the transmitter nor the receiver knows the channel state information, but both know the channel statistics. This model subsumes most previously studied Gaussian fading models. The asymptotic channel capacity in the high signal-to-noise ratio (SNR) regime is first computed, and it is shown that the behavior of the channel capacity depends critically on the channel model. For the special case where the fading process is symbol-by-symbol stationary, it is shown that the codeword length must scale at least logarithmically with SNR in order to guarantee that the communication rate can grow logarithmically with SNR with decoding error probability bounded away from one. An expression for the capacity per unit energy is also derived. Furthermore, it is shown that the capacity per unit energy is achievable using temporal on–off signaling with optimally allocated on symbols, where the optimal on-symbol allocation scheme may depend on the peak power constraint.      

Capacity Bounds for MIMO Nakagami- $m$ Fading Channels

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami- $m$ fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter $m$ on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-$m$ and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MIMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds.      

Interference Analysis in Downlink OFDM Considering Imperfect Intercell Synchronization

This paper presents a theoretical performance analysis of downlink orthogonal frequency-division multiplexing (OFDM) cellular radio communication systems. An accurate interference model that takes into account the cochannel and interchannel interference caused by both frequency and timing synchronization errors in adjacent and cochannel cells is developed. The effect of frequency-selective fading on the interfering signals has also accurately been taken into consideration. Based on this model, accurate expressions are given for average bit error rates (BERs) of OFDM-based $M$-ary quadrature amplitude modulation (QAM). These are extended to include multichannel reception with maximal ratio combining diversity.      

Performance Analysis and Design Criteria of BICM-ID With Signal Space Diversity for Keyhole Nakagami-$m$ Fading Channels

This paper generalizes the application bit-interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) over keyhole Nakagami-$m$ fading channels. The tight union bound on the asymptotic error performance is first analytically derived. The near-optimal rotation matrix with respect to both the asymptotic performance and the convergence behavior is then determined. In particular, it is demonstrated that the suitable rotation matrix is the one that has 1) all entries equal in magnitude, 2) a high diversity order, and 3) a large minimum product of the ratios between squared distances to the power $m$ and log-squared distances to the power $m$ of the rotated constellation scaled by factors of signal-to-noise ratio (SNR) and the parameter $m$ . Various analytical and simulation results show that by employing SSD with a sufficiently large dimension, the error performance can closely approach that over an additive white Gaussian noise (AWGN) channel, even in the worst case of keyhole fading.      

What is a Spectrum Hole and What Does it Take to Recognize One?

“Spectrum holes” represent the potential opportunities for noninterfering (safe) use of spectrum and can be considered as multidimensional regions within frequency, time, and space. The main challenge for secondary radio systems is to be able to robustly sense when they are within such a spectrum hole. To allow a unified discussion of the core issues in spectrum sensing, the “weighted probability of area recovered” (WPAR) metric is introduced to measure the performance of a sensing strategy; and the “fear of harmful interference” $F_{rm HI}$ metric is introduced to measure its safety. These metrics explicitly consider the impact of asymmetric uncertainties (and misaligned incentives) in the system model. Furthermore, they allow a meaningful comparison of diverse approaches to spectrum sensing unlike the traditional triad of sensitivity, probability of false-alarm $P_{rm FA}$, and probability of missed-detection $P_{rm MD}$. These new metrics are used to show that fading uncertainty forces the WPAR performance of single-radio sensing algorithms to be very low for small values of $F_{rm HI}$, even for ideal detectors. Cooperative sensing algorithms enable a much higher WPAR, but only if users are guaranteed to experience independent fading. Lastly, in-the-field calibration for wide-band (but uncertain) environment variables (e.g., interference and shadowing) can robustly guarantee safety (low $F_{rm HI}$ ) even in the face of potentially correlated users without sacrificing WPAR.      

Packet-Based Modeling of Reed–Solomon Block-Coded Correlated Fading Channels Via a Markov Finite Queue Model

We consider the transmission of a Reed–Solomon (RS) code over a binary modulated time-correlated flat Rician fading channel with hard-decision demodulation. We define a binary packet (symbol) error sequence that indicates whether an RS symbol is successfully transmitted across the discrete (fading) channel whose input enters the modulator and whose output exits the demodulator. We then approximate the packet error sequence of the discrete channel (DC) using the recently developed queue-based channel (QBC), which is a simple finite-state Markov channel model with $M$th-order Markovian additive noise. In other words, we use the QBC to model the binary DC at the packet level. We propose a general framework for determining the probability of codeword error (PCE) for QBC models. We evaluate the modeling accuracy by comparing the simulated PCE for the DC with the numerically evaluated PCE for the QBC. Modeling results identify accurate low-order QBC models for a wide range of fading conditions and reveal that modeling the DC at the packet level is an efficient tool for nonbinary coding performance evaluation over binary channels with memory.      

A Simplified Design Model for Random Process Variability

A method for modeling the effects of random process variation through measured transistor current is introduced. The methodology culminates by modeling random current variation at a given operating point above threshold as a zero-mean Additive White Gaussian Noise (AWGN) current source with a standard deviation dependent on nominal operating current and design variables, the transistor sizes, W and L, and the transistor operating points, $V_{gs}$ and $V_{ds}$. The model has a simple posynomial form and is accurate compared to measured data within an RMS error of 5.4% for narrow-, wide-, short-, and long-channel transistors. The model's simplified form bridges the gap between existing statistical methods and circuit design. The efficacy of the model in the circuit design space will also be presented. In the analog domain, we will show that the contributions of this model can be used as a replacement for Monte Carlo methods for calculating circuit voltage and current variances. In the digital space, we will investigate the calculation of timing delay distributions. Results calculated via an alpha-power $(alpha_{p})$ law model for average current show that scaling the supply voltage by $gamma$ results in an approximately $1/gamma^{alpha_{p}+1.1}$ scaling in the path-delay standard deviation for a 65-nm process.      

Dynamic Allocation of Subcarriers and Transmit Powers in an OFDMA Cellular Network

This paper considers the problem of minimizing outage probabilities in the downlink of a multiuser, multicell orthogonal frequency division multiple access (OFDMA) cellular network with frequency selective fading, imperfect channel state information, and frequency hopping. The task is to determine the allocation of powers and subcarriers for users to ensure that the user outage probabilities are as low as possible. We formulate a min–max outage probability problem and solve it under the constraint that the transmit power spectrum at each base station is flat. In particular, we obtain a subchannel allocation algorithm that has complexity $O(L log L)$ in $L$ , the number of users in the cell. We also consider suboptimal but implementable approaches with and without the flat transmit power spectrum constraint. We conclude that the flat transmit spectrum approach has merit, and warrants further study.      

On the Analysis of Envelope Correlation and Spectra for Rician Fading Channel

Physical fading radio channels encountered in wireless mobile communication are often modeled as a complex Gaussian process whose envelope is statistically described by Rayleigh or Rician probability distribution function (PDF). In most of the literature, the accuracy of the simulation model is estimated by comparing the simulated autocorrelation function (ACF) of inphase (or quadrature phase) component of the fading process and ACF of squared envelope with the analytical ones. In this paper, we examine the performance of a sum of sinusoid (SOS) based Rician fading channel simulator on the basis of the ACF and power spectral density (PSD) of the fading envelope. We obtained simplified approximate expressions for the autocorrelation and mean value of the fading envelope which become more accurate as the value of Rice factor increases. In the simulation, the line-of-sight (LOS) component is modeled as a zero-mean random variable with pre-chosen angle of arrival (AOA) and random initial phase. We showed that the AOA of the LOS component significantly affects the level crossing rate (LCR) and average fade duration (AFD) of the fading envelope. All simulation results are compared with the analytical results and a very good agreement between them is found.

Performance of Multiuser-Coded CDMA Systems With Transmit Diversity Over Nakagami- $m$ Fading Channels

The performance of a multiple-input–multiple-output (MIMO) code-division multiple-access (CDMA) system, using space–time spreading (STS), is analyzed over a frequency-flat Nakagami- $m$ fading channel. The convolutionally space–time coded system employs a decorrelator detector with $N = 2$ and $L$ antennas at the user side and base station (BS), respectively. Assuming independent Nakagami fading channels between transmit and receive antennas, we determine the probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR) at the output of the multiuser detector and after signal combining. Considering binary phase-shift keying (BPSK) transmission, we then evaluate the pairwise error probability and the corresponding bit-error-rate (BER) upper bounds over fast-fading channels. The derived error bounds, when compared to system simulations, are shown to be accurate at all signal-to-noise ratios (SNRs) of interest. Examining the asymptotic performance of the underlying space–time multiuser system, at high SNRs, we evaluate the overall diversity gain as a function of the number of transmit and receive antennas and the minimum free distance of the convolutional code.      

On the Asymptotic Minimum Transporting Energy and Its Implication on the Wireless Network Capacity

In this paper we study the asymptotic minimum energy (which is defined as the minimum transporting energy) required to transport (via multiple hops) data packets from a source to a destination. Under the assumptions that nodes are distributed according to a Poisson point process with node density $n$ in a unit-area square and the distance between a source and a destination is of constant order, we prove that the minimum transporting energy is $Theta(n^{(1-alpha)/2})$ with probability approaching one as the node density goes to infinity, where $alpha$ is the path loss exponent.      

A Dual-Band Self-Oscillating Mixer for -Band and -Band Applications

A self-oscillating mixer that employs both the fundamental and harmonic signals generated by the oscillator subcircuit in the mixing process is experimentally demonstrated. The resulting circuit is a dual-band down-converting mixer that can operate in $C$ -band from 5.0 to 6.0 GHz, or in $X$-band from 9.8 to 11.8 GHz. The oscillator uses active superharmonic coupling to enforce the quadrature relationship of the fundamental outputs. Either the fundamental outputs of the oscillator or the second harmonic oscillator output signals that exists at the common-mode nodes are connected to the mixer via a set of complementary switches. The mixer achieves a conversion gain between 5–12 dB in both frequency bands. The output 1-dB compression points for both modes of the mixer are approximately $-{hbox{5 dBm}}$ and the output third-order intercept point for $C$ -band and $X$ -band operation are 12 and 13 dBm, respectively. The integrated circuit was fabricated in 0.13-$mu {hbox{m}}$ CMOS technology and measures ${hbox{0.525 mm}}^{2}$ including bonding pads.      

CMOS Micromachined Inductors With Structure Supports for RF Mixer Matching Networks

This letter presents the comparison of three novel structure supports for on-chip complementary metal–oxide–semiconductor (CMOS)-based micromachined inductors by using a proposed two-step maskless post-CMOS process. A 3-D electromagnetic inductor simulation model is established and calibrated with inductor fabrication. The proposed inductors are applied in the matching network of the double-balanced Gilbert mixer to improve the performance and the mechanical stability. The mixers, with and without micromachined process inductors, are fabricated in a 0.5-$muhbox{m}$ CMOS process and compared in this letter. The measurement results show a 28.12% increase in conversion gain, a 31.7% improvement in third intercept point, and a 44% reduction in the noise figure.      

Differential Maximum Ratio Combining (MRC)-Based Throughput Analysis on Dual-Fading Models of Slotted-Aloha CDMA Systems

In this paper we investigate throughputs of Slotted-ALOHA code division multiple access systems with differential detection upon L-branch antenna by means of maximum ratio combining (MRC) diversity technique. We investigate the effects of co-channel interference by employing two different fading models (i.e. between the desired signals and its interferences.) We consider systems under Nakagami/Nakagami and Rician/Nakagami fading environments. The purpose of employing MRC diversity and differential phase shift keying with L-branch antenna is to overcome multipath fading interference in order to enhance the performance of the systems. Our research indicates that the implementation of L-branch antenna in the receiver have reasonably increased the throughputs of the systems. Furthermore, we also investigate the inverse relation between interference signal and the throughputs of the systems. We further point out that the value of Nakagami fading parameter M and Rician factor K are proportional to the achievable throughputs of the systems.     

A Carrier-Independent Non-Data-Aided Real-Time SNR Estimator for M-PSK and D-MPSK Suitable for FPGAs and ASICs

We present a channel signal-to-noise ratio (SNR) estimator for $M$-ary phase shift keying (M-PSK) and differential M-PSK. The estimator is non data aided and is shown to have the following advantages: 1) It does not require prior carrier synchronization; 2) the estimator has a compact fixed-point hardware implementation suitable for field-programmable gate arrays and application-specific integrated circuits; 3) it requires only 1 sample/symbol; 4) accurate estimates can be generated in real time; and 5) the estimator is resistant to imperfections in the automatic gain control circuit. We investigate the proposed estimator theoretically and through simulations. In particular, we investigate the required quantization necessary to achieve a good estimator performance. General formulas are developed for SNR estimation in the presence of frequency-flat slow fading, and specific results are presented for Nakagami- $m$ fading. The proposed estimator is then compared with other SNR estimators, and it is shown that the proposed method requires less hardware resources while, at the same time, providing comparable or superior performance.      

Closed‐form expressions for the average channel capacity of the α– μ fading model under different adaptive transmission protocols

In this paper,we consider a small‐scale multipath fading channel following the α– μ generalized fading model distribution.We first derive an expression for the amount of fading () for this channel model to show the generalization attribute of this fading model recently reported in the literature. Then, we derive closed‐form expressions for the average channel capacity considering this channel distribution under different adaptive transmission protocols, namely the simultaneous power and rate adaptation protocol, the optimal rate adaptation with fixed power protocol, and the channel inversion with fixed‐rate protocol. All the obtained expressions are in closed‐form and general expressions that can reduce to other channel capacity expressions that are well‐known and to some others that are not known for Rayleigh, Nakagami‐m, and Weibull, as special cases. The derived expressions in this paper are new and have not been previously reported in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

A 240-MHz Low-Pass Filter With Variable Gain in 65-nm CMOS for a UWB Radio Receiver

An integrated fifth-order continuous-time low-pass filter for a WiMedia ultrawideband radio receiver is described in this paper. The prototype filter is realized with a passive pole at the filter input and a fourth-order leapfrog filter in which the gm-C technique with pseudodifferential transconductors is used. The transconductors do not include internal nodes, and they are designed to have a nominal 26-dB dc gain, of which process, voltage, and temperature variations are controlled by means of a negative resistance circuit. The losses of the low-dc-gain filter integrators are already taken into account in the filter synthesis. The passband edge frequency of the implemented filter is 240 MHz in order to receive multiband-orthogonal-frequency-division-multiplexing signals using the direct-conversion topology. The voltage gain of the filter can be controlled from 9 to 43 dB in the 1-dB gain steps. The filter achieves a 7.8-$hbox{nV}surdhbox{Hz}$ input-referred noise density, a $-$8-dBV out-of-band third-order intermodulation intercept point, and a $+$ 15-dBV out-of-band second-order intermodulation intercept point. The circuit uses a 1.2-V supply and has been fabricated in a modern 65-nm CMOS technology.      

Notes on Fading-Memory Conditions

In some studies concerning the approximation of nonlinear systems, the concept of a weighting function w plays a central role. This paper, in which attention is focused on continuous-time cases, directs attention to some interesting properties of systems that have R₊ fading memory or fading memory. In particular, we show that half-line input-output maps that have R₊ fading memory with respect to some w in fact have R₊ fading memory with respect to all such ws. And we show that a similar proposition holds in a setting concerning Volterra-series approximations for continuous-time systems with inputs and outputs defined on all of R. We show also that, in that setting, fading memory is equivalent to uniform fading memory. Some related results are also described.     

Performance of unequalized frequency-hopped TDMA with convolutional coding on dispersive fading channels

Increasing demand for wireless personal communications has stimulated research on new digital radio technologies that are optimized for various service applications and environments. This paper discusses the performance of a slow-frequency-hopped time-division multiple-access (SFH-TDMA) technique, which has been proposed as a high-tier extension of a low-complexity TDMA architecture optimized for low-power pedestrian applications. The SFH-TDMA technique considered uses QPSK modulation and rate-1/2 convolutional coding. Numerical results for a wide range of fading rates are obtained through analytical calculation of the effective signal-to-noise ratio combined with a simulation approach which incorporates measured multipath channels and actual frequency correlation among contiguous hopping channels. The results indicate that the SFH-TDMA technique can tolerate root-mean-square (rms) delay spread up to several bit periods without a need for adaptive equalization, but also point to the need for fast power control when the fading is slow and the rms delay spread is much smaller than the bit period. This work is targeted toward understanding the implications to local exchange networks of wireless technology alternatives that could provide access to those networks.     

A 25-MHz Self-Referenced Solid-State Frequency Source Suitable for XO-Replacement

Recent trends in the development of integrated silicon frequency sources are discussed. Within that context, a 25-MHz self-referenced solid-state frequency source is presented and demonstrated where measured performance makes it suitable for replacement of crystal oscillators (XOs) in data interface applications. The frequency source is referenced to a frequency-trimmed and temperature-compensated 800-MHz free-running $LC$ oscillator (LCO) that is implemented in a standard logic CMOS process and with no specialized analog process options. Mechanisms giving rise to frequency drift in integrated LCOs are discussed and supported by analytical expressions. Design objectives and a compensation technique are presented where several implementation challenges are uncovered. Fabricated in a 0.25-$mu$m 1P5M CMOS process, and with no external components, the prototype frequency source dissipates 59.4 mW while maintaining ${pm} 152$ ppm frequency inaccuracy over process, ${pm} 10hbox{%}$ variation in the power supply voltage, and from ${-}$ 10 $^{circ}$ C to 80 $^{circ}$ C. Variation against other environmental factors is also presented. Nominal period jitter and power-on start-up latency are 2.75 ps$_{rm rms}$ and 268 $mu$s, respectively. These performance metrics are compared with an XO at the same frequency.