Optical fiber communications can be modeled using the non-linear Schrödinger equation, which is integrable. In this paper we show how integrability can be exploited to communicate using multisoliton pulses. Starting with a white Gaussian input signal, we use the known distributions of eigenvalues and scattering data to derive an analytical expression for a lower bound to the spectral efficiency, taking into account the effects of noise due to amplification explicitly. We show that in the low noise regime, the soliton channel shows two different behaviors, interpolated by a single scalar parameter that controls the nonlinearity of the system. In the linear regime the soliton channel approaches an additive white Gaussian noise channel, while for strongly nonlinear systems the bound declines. The bound reaches a maximum between the two regions.

Linear receivers offer a low complexity option for multiantenna communication systems. Therefore, understanding the outage behavior of the corresponding SINR is important in a fading mobile environment. In this paper, we introduce a large deviation method, valid nominally for a large number M of antennas, which provides the probability density of the SINR of Gaussian channel MIMO minimum mean square error (MMSE) and zero-forcing (ZF) receivers, with arbitrary transmission power profiles and in the presence of receiver antenna correlations. This approach extends the Gaussian approximation of the SINR, valid for large M asymptotically close to the center of the distribution, to obtain the non-Gaussian tails of the distribution. Our methodology allows us to calculate the SINR distribution to next-to-leading order ( O(1/M)) and showcase the deviations from approximations that have appeared in the literature (e.g., the Gaussian or the generalized Gamma distribution). We also analytically evaluate the outage probability, as well as the uncoded bit-error-rate. We find that our approximation is quite accurate even for the smallest antenna arrays (2 × 2).

A large deviations approach is introduced, which calculates the probability density and outage probability of the multiple-input multiple-output (MIMO) mutual information, and is valid for large antenna numbersN. In contrast to previous asymptotic methods that only focused on the distribution close to its most probable value, this methodology obtains the full distribution, including its non-Gaussian tails. The resulting distribution interpolates between the Gaussian approximation for ratesRclose its mean and the asymptotic distribution for large signal-to-noise ratios (SNRs) ρ. For large enoughN, this method provides the outage probability over the whole (R, ρ) parameter space. The presented analytic results agree very well with numerical simulations over a wide range of outage probabilities, even for smallN. In addition, the outage probability thus obtained is more robust over a wide range of ρ andRthan either the Gaussian or the large-ρ approximations, providing an attractive alternative in calculating the probability density of the MIMO mutual information. Interestingly, this method also yields the eigenvalue density constrained in the subset where the mutual information is fixed toRfor given ρ. Quite remarkably, this eigenvalue density has the form of the Marčenko-Pastur distribution with square-root singularities.

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused to the distribution close to its most probable value, thus obtaining an asymptotically Gaussian distribution, we calculate the full distribution including its tails, which behave quite differently from the bulk of the distribution. Our resulting probability distribution seamlessly interpolates between the Gaussian approximation for rates R close to the ergodic value of the mutual information and the approach of Zheng and Tse [1], valid for large signal to noise ratios rho. This provides us with a tool to analytically calculate outage probabilities at any point in the (R, rho,N) parameter space, as long as the number of antennas N is not too small. In addition, this method also yields the probability distribution of eigenvalues constrained in the subspace where the mutual information per antenna is fixed to R for a given rho. Quite remarkably, this eigenvalue density is of the form of the Marcenko-Pastur distribution with square-root singularities.