(2003). Comparison Methods for Stochastic Models and Risks. Technometrics: Vol. 45, No. 4, pp. 370-371.

Comparison Methods for Stochastic Models and Risks

Orthogonal frequency-division multiplexing (OFDM) is a modulation technology that has been widely adopted in many new and emerging broadband wireless and wireline communication systems. Due to its capability to transmit a high-speed data stream using multiple spectral-overlapped lower-speed subcarriers, OFDM technology offers superior advantages of high spectrum efficiency, robustness against inter-carrier and inter-symbol interference, adaptability to server channel conditions, etc. In recent years, there have been intensive studies on optical OFDM (O-OFDM) transmission technologies, and it is considered a promising technology for future ultra-high-speed optical transmission. Based on O-OFDM technology, a novel elastic optical network architecture with immense flexibility and scalability in spectrum allocation and data rate accommodation could be built to support diverse services and the rapid growth of Internet traffic in the future. In this paper, we present a comprehensive survey on OFDM-based elastic optical network technologies, including basic principles of OFDM, O-OFDM technologies, the architectures of OFDM-based elastic core optical networks, and related key enabling technologies. The main advantages and issues of OFDM-based elastic core optical networks that are under research are also discussed.

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A Survey on OFDM-Based Elastic Core Optical Networking

Transmit antenna selection technology has been adopted for the uplink by the next generation Long Term Evolution wireless standard in order to harness the spatial diversity offered by multiple antennas at the mobile transmitter, while keeping the hardware complexity and cost of a mobile low. In TAS, the number of RF chains for processing/up-conversion is smaller than the number of available antenna elements, so at any time the signals can only be transmitted from a (dynamically optimized) subset of antenna elements. As a result, the training procedure for AS needs to be carefully engineered. In LTE, this is accomplished by reusing the wideband sounding reference signal for the purpose of AS training. Furthermore, new mechanisms are required to facilitate feedback from the receiver (the base station) to the transmitter about which subset is optimal and should thus be used by the mobile. In LTE, this is accomplished by employing a unique masking technique on the downlink control channel that eliminates the feedback overhead at the expense of a minor increase in complexity at the mobile. This article provides an in-depth and systematic overview of all physical and higher layer features in the LTE standard that enable TAS. Also highlighted are the variety of technical and standardization challenges that drove the specification of AS in LTE, and the aspects of the LTE standard that are impacted by AS.

Antenna selection in LTE: from motivation to specification

In this paper, we consider distributed estimation of an unknown random vector by using wireless sensors and a fusion center (FC). We adopt a linear model for distributed estimation of a vector source where both observation models and sensor operations are linear and the multiple access channel (MAC) is coherent. Two cases are considered: Noiseless fusion center and Noisy fusion center. In the case of a Noiseless fusion center (where there is no noise at the fusion center), the sensor precoders are designed to minimize the mean square error (MSE) at the fusion center. A closed form solution is found and it is shown that the system performance approaches the benchmark as long as the number of messages transmitted by each sensor is equal to the length of the vector source. Subsequently, if there is noise at the fusion center and one is interested in a closed form solution, a filter is designed to cancel out the effect of noise at the fusion center. This separate design will come at the expense of losing performance. An alternative iterative solution can be found when considering noise at the fusion center where sensor precoders are designed to minimize the MSE at the fusion center subject to transmit power constraints at each sensor. It is shown that the proposed scheme always converges. Finally, simulations are provided to verify the analysis and present the performance of the proposed schemes.

Linear Decentralized Estimation of Correlated Data for Power-Constrained Wireless Sensor Networks

Antenna selection in multiple-input-multipleoutput (MIMO) systems preserves diversity gain while significantly reducing hardware complexity. However, imperfect channel state information (CSI) affects performance. In this paper, we first analyze the performance of a MIMO system employing antenna selection at the transmitter and maximal ratio combining (MRC) at the receiver in the presence of feedback delay and channel estimation errors. Then, we determine whether channel prediction can compensate for the effect of feedback delay. Outage probability is analyzed as a function of ?, the correlation coefficient between the CSI used at the receiver for decoding (CSIR) and the CSI used at the transmitter for selection (CSIT). Analytical results show that the effect of feedback delay is more significant than the effect of estimation error. In order to overcome the effect of delay, ? should increase with SNR. For a given SNR, the length of the linear minimum mean square error (LMMSE) prediction filter required is calculated and shown to increase with SNR. Finally, we determine the asymptotic diversity order as a function of the feedback quality. Results show that if 1 - ? ? SNR-1, the diversity order with imperfect CSI is same as that with perfect CSI.

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Using delayed feedback for antenna selection in MIMO systems

We study space-time-frequency coded multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexed (OFDM) systems employing receiver antenna selection (AS), where training has been utilized to perform linear minimum mean square error (LMMSE)-based channel estimation. To minimize the mean square error (MSE) of this estimator, equispaced and equipowered training symbols are used, with the number of training symbols per OFDM symbol equal to the channel length. The maximum received signal power AS rule is proposed, which decouples the AS process from the channel estimation process. By upper bounding the pairwise error probability (PEP) expression, we show that the system with a channel-estimation error (CEE) still achieves maximum spatial and multipath diversity. The performance of the system for the special case of square unitary and orthogonal codes has been analyzed. For the case of orthogonal codes using constant modulus symbols, we also derive the exact bit-error-rate (BER) expression. The degradation in performance, due to the presence of the CEE, is captured by the loss-in-coding-gain (LCG) and loss-in-performance (LP) expressions. To minimize the loss due to the CEE, an optimal power-allocation scheme that distributes the total available power between training symbols and data symbols is defined. Compared with the perfect channel knowledge case, equal power training for the CEE case performs at least 3 dB worse, whereas optimal power training for the CEE case suffers a loss less than 3 dB always. Analytical and simulation results are presented to validate our analysis and results.

Antenna Selection for MIMO-OFDM Systems With Channel Estimation Error

Orthogonal Frequency Division Multiplexing (OFDM) systems are widely used in the standards for digital audio/video broadcasting, WiFi and WiMax. Being a frequency-domain approach to communications, OFDM has important advantages in dealing with the frequency-selective nature of high data rate wireless communication channels. As the needs for operating with higher data rates become more pressing, OFDM systems have emerged as an effective physical-layer solution. This short monograph is intended as a tutorial which highlights the deleterious aspects of the wireless channel and presents why OFDM is a good choice as a modulation that can transmit at high data rates. The system-level approach we shall pursue will also point out the disadvantages of OFDM systems especially in the context of peak to average ratio, and carrier frequency synchronization. Finally, simulation of OFDM systems will be given due prominence. Simple MATLAB programs are provided for bit error rate simulation using a discrete-time OFDM representation. Software is also provided to simulate the effects of inter-block-interference, inter-carrier-interference and signal clipping on the error rate performance. Different components of the OFDM system are described, and detailed implementation notes are provided for the programs. The program can be downloaded here. Table of Contents: Introduction / Modeling Wireless Channels / Baseband OFDM System / Carrier Frequency Offset / Peak to Average Power Ratio / Simulation of the Performance of OFDM Systems / Conclusions

Ofdm Systems for Wireless Communications

Multi-user diversity (MUD) is considered when the number of users in the system is random. Average throughput of a MUD system is shown to have a completely monotone derivative with respect to (deterministic) number of users. Following this, randomization of number of users is shown to give degraded throughput averaged across the number of users distribution. Using stochastic ordering theory, a framework for comparison of performance for different user distributions is provided. For Poisson distributed number of users communicating over Rayleigh faded channels, long-term average throughput is shown to scale as a double logarithmic function of average number of users.

Multi-User Diversity with Random Number of Users

A distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered. The proposed estimator is shown to be strongly consistent for any sensing noise distribution in the i.i.d. case both for a per-sensor power constraint, and a total power constraint. When the distributions of the sensing noise are not identical, a bound on their variances is shown to establish strong consistency. The estimator is shown to be asymptotically normal with a variance ( AsV) that depends on the characteristic function of the sensing noise. Optimization of the AsV is considered with respect to a transmission phase parameter for a variety of noise distributions exhibiting differing levels of impulsive behavior. The robustness of the estimator in the sense of degrading gracefully when the sensing noise deviates from the Gaussian distribution to impulsive sensing noise distributions such as those with positive excess kurtosis, or those that do not have finite moments is shown. The proposed estimator is favorably compared with the amplify and forward scheme under an impulsive noise scenario. The effect of fading and phase error at the sensors are shown to not affect the consistency of the estimator, but to degrade the asymptotic variance by terms that depend on the fading and phase error distributions. Simulations corroborate our analytical results.

Universal Distributed Estimation Over Multiple Access Channels With Constant Modulus Signaling

We study space-time-frequency coded multiple- input-multiple-output (MIMO) orthogonal frequency-division multiplexed (OFDM) systems employing antenna selection at the receiver where optimal training has been utilized for performing linear minimum mean square error (LMMSE) based channel estimation. The maximum signal power antenna selection rule is introduced. By upper bounding the pairwise error probability (PEP) expression, we show that the system with channel estimation error (CEE) still achieves full diversity. The loss in coding gain (LCG) and the loss in performance (LP) expressions are derived. It is shown that while equal power training performs about 3 dB worse than the perfect CSI case, the optimal power training performs between the two depending on the number of subcarriers assigned per OFDM word. Simulation results are presented to validate our analysis.

Adarsh B. Narasimhamurthy

Papers

Antenna Selection for MIMO-OFDM Systems With Channel Estimation Error

Ofdm Systems for Wireless Communications

Multi-User Diversity with Random Number of Users

Universal Distributed Estimation Over Multiple Access Channels With Constant Modulus Signaling

Antenna Selection for MIMO OFDM Systems with Channel Estimation Error