On Multipath Fading Channels at High SNR

This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog - defined as the limiting ratio of the capacity to loglog SNR as SNR tends to infinity - is studied. It is shown that, irrespective of the number paths L, the capacity pre-loglog is 1.Comment: To be presented at the 2008 IEEE Symposium on Information Theory (ISIT), Toronto, Canada; replaced with version that appears in the proceeding

On the Non-Coherent Wideband Multipath Fading Relay Channel

We investigate the multipath fading relay channel in the limit of a large bandwidth, and in the non-coherent setting, where the channel state is unknown to all terminals, including the relay and the destination. We propose a hypergraph model of the wideband multipath fading relay channel, and show that its min-cut is achieved by a non-coherent peaky frequency binning scheme. The so-obtained lower bound on the capacity of the wideband multipath fading relay channel turns out to coincide with the block-Markov lower bound on the capacity of the wideband frequency-division Gaussian (FD-AWGN) relay channel. In certain cases, this achievable rate also meets the cut-set upper-bound, and thus reaches the capacity of the non-coherent wideband multipath fading relay channel.Comment: 8 pages, 4 figures, longer version (including proof) of the paper in Proc. of IEEE ISIT 201

Capacity bounds and estimates for the finite scatterers MIMO wireless channel

We consider the limits to the capacity of the multiple-input–multiple-output wireless channel as modeled by the finite scatterers channel model, a generic model of the multipath channel which accounts for each individual multipath component. We assume a normalization that allows for the array gain due to multiple receive antenna elements and, hence, can obtain meaningful limits as the number of elements tends to infinity. We show that the capacity is upper bounded by the capacity of an identity channel of dimension equal to the number of scatterers. Because this bound is not very tight, we also determine an estimate of the capacity as the number of transmit/receive elements tends to infinity which is asymptotically accurate

Channel Uncertainty in Ultra Wideband Communication Systems

Wide band systems operating over multipath channels may spread their power over bandwidth if they use duty cycle. Channel uncertainty limits the achievable data rates of power constrained wide band systems; Duty cycle transmission reduces the channel uncertainty because the receiver has to estimate the channel only when transmission takes place. The optimal choice of the fraction of time used for transmission depends on the spectral efficiency of the signal modulation. The general principle is demonstrated by comparing the channel conditions that allow different modulations to achieve the capacity in the limit. Direct sequence spread spectrum and pulse position modulation systems with duty cycle achieve the channel capacity, if the increase of the number of channel paths with the bandwidth is not too rapid. The higher spectral efficiency of the spread spectrum modulation lets it achieve the channel capacity in the limit, in environments where pulse position modulation with non-vanishing symbol time cannot be used because of the large number of channel paths

The Noncoherent Rician Fading Channel -- Part I : Structure of the Capacity-Achieving Input

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 SNR range when there is only a peak power constraint. The Rician fading with 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 capacity-achieving 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.Comment: To appear in the IEEE Transactions on Wireless Communication