Noncoherent Capacity of Underspread Fading Channels

We derive bounds on the noncoherent capacity of wide-sense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel's delay spread and Doppler spread is small. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel's scattering function, are accurate for a large range of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a function of the peak power and the channel's scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of large bandwidth, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinite-bandwidth capacity and find cases when the bounds coincide and the infinite-bandwidth capacity is characterized exactly. Our lower bound is closely related to a result by Viterbi (1967). The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time- and frequency-selective channels. This discretization explicitly takes into account the underspread property, which is satisfied by virtually all wireless communication channels.Comment: Submitted to the IEEE Transactions on Information Theor

The Noncoherent Rician Fading Channel -- Part II : Spectral Efficiency in the Low-Power Regime

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients. The spectral-efficiency/bit-energy tradeoff in the low-power regime is examined when the input has limited peakedness. It is shown that if a fourth moment input constraint is imposed or the input peak-to-average power ratio is limited, then in contrast to the behavior observed in average power limited channels, the minimum bit energy is not always achieved at zero spectral efficiency. The low-power performance is also characterized when there is a fixed peak limit that does not vary with the average power. A new signaling scheme that overlays phase-shift keying on on-off keying is proposed and shown to be optimally efficient in the low-power regime.Comment: To appear in the IEEE Transactions on Wireless Communication

On the Sensitivity of Noncoherent Capacity to the Channel Model

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the set of harmonics where the power spectral density of the fading process is nonzero determines if capacity grows logarithmically in SNR or slower than logarithmically. An engineering-relevant problem is to characterize the SNR value at which this sensitivity starts to matter. In this paper, we consider the general class of continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread. For this class of channels, we show that the noncoherent capacity is close to the AWGN capacity for all SNR values of practical interest, independently of whether the scattering function is compactly supported or not. As a byproduct of our analysis, we obtain an information-theoretic pulse-design criterion for orthogonal frequency-division multiplexing systems.Comment: To be presented at IEEE Int. Symp. Inf. Theory 2009, Seoul, Kore

Efficient optical communication in a turbulent atmosphere

Efficient optical communication in atmospheric turbulenc

Atmospheric propagation issues relevant to optical communications

Atmospheric propagation issues relevant to space-to-ground optical communications for near-earth applications are studied. Propagation effects, current optical communication activities, potential applications, and communication techniques are surveyed. It is concluded that a direct-detection space-to-ground link using redundant receiver sites and temporal encoding is likely to be employed to transmit earth-sensing satellite data to the ground some time in the future. Low-level, long-term studies of link availability, fading statistics, and turbulence climatology are recommended to support this type of application

Information Theory of underspread WSSUS channels

The chapter focuses on the ultimate limit on the rate of reliable communication through Rayleigh-fading channels that satisfy the wide-sense stationary (WSS) and uncorrelated scattering (US) assumptions and are underspread. Therefore, the natural setting is an information-theoretic one, and the performance metric is channel capacity. The family of Rayleigh-fading underspread WSSUS channels constitutes a good model for real-world wireless channels: their stochastic properties, like amplitude and phase distributions match channel measurement results. The Rayleigh-fading and the WSSUS assumptions imply that the stochastic properties of the channel are fully described by a two-dimensional power spectral density (PSD) function, often referred to as scattering function. The underspread assumption implies that the scattering function is highly concentrated in the delay-Doppler plane. Two important aspects need to be accounted for by a model that aims at being realistic: neither the transmitter nor the receiver knows the realization of the channel; and the peak power of the transmit signal is limited. Based on these two aspects the chapter provides an information-theoretic analysis of Rayleigh-fading underspread WSSUS channels in the noncoherent setting, under the additional assumption that the transmit signal is peak-constrained

Writing on Fading Paper and Causal Transmitter CSI

A wideband fading channel is considered with causal channel state information (CSI) at the transmitter and no receiver CSI. A simple orthogonal code with energy detection rule at the receiver (similar to [6]) is shown to achieve the capacity of this channel in the limit of large bandwidth. This code transmits energy only when the channel gain is large enough. In this limit, this capacity without any receiver CSI is the same as the capacity with full receiver CSI--a phenomenon also true for dirty paper coding. For Rayleigh fading, this capacity (per unit time) is proportional to the logarithm of the bandwidth. Our coding scheme is motivated from the Gel'fand-Pinsker [2,3] coding and dirty paper coding [4]. Nonetheless, for our case, only causal CSI is required at the transmitter in contrast with dirty-paper coding and Gel'fand-Pinsker coding, where non-causal CSI is required. Then we consider a general discrete channel with i.i.d. states. Each input has an associated cost and a zero cost input "0" exists. The channel state is assumed be to be known at the transmitter in a causal manner. Capacity per unit cost is found for this channel and a simple orthogonal code is shown to achieve this capacity. Later, a novel orthogonal coding scheme is proposed for the case of causal transmitter CSI and a condition for equivalence of capacity per unit cost for causal and non-causal transmitter CSI is derived. Finally, some connections are made to the case of non-causal transmitter CSI in [8]

Efficient optical communication in a turbulent atmosphere.

Also issued as a Ph.D. thesis in the Dept. of Electrical Engineering, 1969.Bibliography: p.113-117

Capacity, coding and interference cancellation in multiuser multicarrier wireless communications systems

Multicarrier modulation and multiuser systems have generated a great deal of research during the last decade. Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation generated with the inverse Discrete Fourier Transform, which has been adopted for standards in wireless and wire-line communications. Multiuser wireless systems using multicarrier modulation suffer from the effects of dispersive fading channels, which create multi-access, inter-symbol, and inter-carrier interference (MAI, ISI, ICI). Nevertheless, channel dispersion also provides diversity, which can be exploited and has the potential to increase robustness against fading. Multiuser multi-carrier systems can be implemented using Orthogonal Frequency Division Multiple Access (OFDMA), a flexible orthogonal multiplexing scheme that can implement time and frequency division multiplexing, and using multicarrier code division multiple access (MC-CDMA). Coding, interference cancellation, and resource sharing schemes to improve the performance of multiuser multicarrier systems on wireless channels were addressed in this dissertation. Performance of multiple access schemes applied to a downlink multiuser wireless system was studied from an information theory perspective and from a more practical perspective. For time, frequency, and code division, implemented using OFDMA and MC-CDMA, the system outage capacity region was calculated for a correlated fading channel. It was found that receiver complexity determines which scheme offers larger capacity regions, and that OFDMA results in a better compromise between complexity and performance than MC-CDMA. From the more practical perspective of bit error rate, the effects of channel coding and interleaving were investigated. Results in terms of coding bounds as well as simulation were obtained, showing that OFDMAbased orthogonal multiple access schemes are more sensitive to the effectiveness of the code to provide diversity than non-orthogonal, MC-CDMA-based schemes. While cellular multiuser schemes suffer mainly from MAI, OFDM-based broadcasting systems suffer from ICI, in particular when operating as a single frequency network (SFN). It was found that for SFN the performance of a conventional OFDM receiver rapidly degrades when transmitters have frequency synchronization errors. Several methods based on linear and decision-feedback ICI cancellation were proposed and evaluated, showing improved robustness against ICI. System function characterization of time-variant dispersive channels is important for understanding their effects on single carrier and multicarrier modulation. Using time-frequency duality it was shown that MC-CDMA and DS-CDMA are strictly dual on dispersive channels. This property was used to derive optimal matched filter structures, and to determine a criterion for the selection of spreading sequences for both DS and MC CDMA. The analysis of multiple antenna systems provided a unified framework for the study of DS-CDMA and MC-CDMA on time and frequency dispersive channels, which can also be used to compare their performance