Abstract not found

The tradeoff of spectral efficiency (b/s/Hz) versus energy -per-information bit is the key measure of channel capacity in the wideband power-limited regime. This paper finds the fundamental bandwidth--power tradeoff of a general class of channels in the wideband regime characterized by low, but nonzero, spectral efficiency and energy per bit close to the minimum value required for reliable communication. A new criterion for optimality of signaling in the wideband regime is proposed, which, in contrast to the traditional criterion, is meaningful for finite-bandwidth communication.

Abstract—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 peakto-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 lowpower 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 (OOK) is proposed and shown to be optimally efficient in the low-power regime. Index Terms—Fading channels, low-power regime, memoryless fading, peak constraints, Rician fading, spectral efficiency. I.

Abstract—Transmission of information over a discrete-time memoryless Rician fading channel is considered, where neither the receiver nor the transmitter knows the fading coefficients. First, the structure of the capacity-achieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacity-achieving input amplitude distribution is discrete with a finite number of mass points in the low-power regime. A similar discrete structure for the optimal amplitude is proven over the entire signal-to-noise ratio (SNR) range when there is only a peak-power constraint. The Rician fading with the phase-noise channel model, where there is phase uncertainty in the specular component, is analyzed. For this model, it is shown that, with only an average power constraint, the capacityachieving input amplitude is discrete with a finite number of levels. For the classical average-power-limited Rician fading channel, it is proven that the optimal input amplitude distribution has bounded support. Index Terms—Capacity-achieving input, channel capacity, fading channels, memoryless fading, peak constraints, phase noise, Rician fading. I.

While capacity in the limit of vanishing SNR per degree of freedom is known to be linear in SNR for fading and non-fading channels, regardless of channel side information at the receiver, such asymptotic results hide the cost of channel variability in terms of performance. In this paper, rather than maintain a fixed channel model with a given coherence and consider a vanishing SNR, we present a model in which coherence, peak energy and SNR are considered jointly. In particular, we show that channel variability, characterized by coherence, when considered in terms of SNR, determines a sublinear term in SNR which reduces the coherent capacity, itself linear in SNR. We explicitly characterize this sublinear term and show how coherence, when considered jointly with SNR, affects the peakiness required in transmissions. We examine how, by using suboptimal training schemes, we may achieve rates that trail coherent capacity by a sublinear term in SNR. 1

A discrete-time single-user channel with correlated Rayleigh fading is analyzed. At low SNR, the capacity of such a channel is known to be achieved by input signals with large peak powers. Since such burstiness in the input signal may not be practically feasible, the possibility of such signals is eliminated in the model by imposing a peak power constraint on every input symbol. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The proof uses an adaptation of the simple formula of Verdu to a channel with memory. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity.

Abstract—Channel uncertainty limits the achievable data rates of certain ultra-wideband systems due to the need to estimate the channel. The use of bursty duty-cycled transmission reduces the channel uncertainty because the receiver has to estimate the channel only when transmission takes place, but the maximum amount of burstiness and hence the possible reduction of channel uncertainty both depend on the spectral efficiency of the modulation scheme used. This general principle is demonstrated by comparing the channel conditions that allow duty-cycled direct-sequence spread spectrum (DSSS) and pulse position modulation (PPM) to achieve the additive white Gaussian noise (AWGN) channel capacity in the wideband limit. We show that duty-cycled DSSS systems achieve the wideband capacity as long as the number of independently faded resolvable paths increases sublinearly with the bandwidth, while duty-cycled PPM systems can achieve the wideband capacity only if the number of paths increases sublogarithmically. The difference is due to the fact that DSSS is spectrally more efficient than PPM and hence allows more bursty transmission. Index Terms—Channel uncertainty, direct sequence spread spectrum, flash signaling, pulse position modulation (PPM), spectral efficiency, wideband communications. I.

Flat-fading channels that are correlated in time are considered under peak and average power constraints. For discrete-time channels, a new upper bound on the capacity per unit time is derived. A low SNR analysis of a fullscattering vector channel is used to derive a complimentary lower bound. Together, these bounds allow us to identify the exact scaling of channel capacity for a fixed peak to average ratio, as the average power converges to zero. The upper bound is also asymptotically tight as the average power converges to zero for a fixed peak power. For a continuous time infinite bandwidth channel, Viterbi identified the capacity for M-FSK modulation. Recently, Zhang and Laneman showed that the capacity can be achieved with non-bursty signaling (QPSK). An additional contribution of this paper is to obtain similar results under peak and average power constraints.

We have previously presented the exponent for an upper bound on the error probability of a "peaky" signaling scheme that achieves the capacity of the Rayleigh fading channel under an average power constraint in the limit of infinite bandwidth. In the present work, we complement this result with a lower bound. We find that the exponents of the upper and lower bounds coincide in the wideband limit and therefore yield the reliability function of the Rayleigh fading channel using peaky signaling. We illustrate the behavior of the reliability function and the upper and lower error probability bounds with some numerical examples.

We present an efficient, low-cost implementation of time-hopping impulse radio that fulfills the spectral mask mandated by the FCC and is suitable for high-data-rate, short-range communications. Key features are: (i) allbaseband implementation that obviates the need for local oscillators and other passband components, (ii) symbolrate (not chip rate) sampling, A/D conversion, and digital signal processing, (iii) fast acquisition due to novel search algorithms, (iv) spectral shaping that can be adapted to accommodate different spectrum regulations and interference environments. Computer simulations show that this system can provide 110Mbit/s at 7-10m distance, as well as higher data rates at shorter distances under FCC emissions limits. Due to the spreading concept of time-hopping impulse radio, the system can sustain multiple simultaneous users, and can suppress narrowband interference effectively.