Rasika R. Perera

Bounds on mutual information of Rayleigh fading channels with Gaussian input

The mutual information of a discrete time Rayleigh fading channel is considered, where neither the transmitter nor the receiver has the knowledge of the channel state information. We specifically derive a lower bound for the mutual information of this channel when the input distribution is Gaussian. The bound is expressed in terms of the capacity of the corresponding non fading channel and the capacity when the perfect channel state information is known at the receiver

Gaussian inputs: performance limits over non-coherent SISO and MIMO channels

Performance limits of information transfer over a discrete time memoryless Rayleigh fading channel with neither the receiver nor the transmitter knowing the fading coefficients except its statistics is an important problem in information theory. We derive closed form expressions for the mutual information of single input single output (SISO) and multiple input multiple output (MIMO) Rayleigh fading channels for any antenna number at any signal to noise ratio (SNR). Using these expressions, we show that the maximum mutual information of non-coherent Rayleigh fading MIMO channels is achieved with a single transmitter and multiple receivers when the input distribution is Gaussian. We show that the addition of transmit antennas for a fixed number of receivers result in a reduction of mutual information. Furthermore, we argue that the mutual information is bounded by the SNR in both SISO and MIMO systems showing the sub-optimality of Gaussian signalling in non-coherent Rayleigh fading channels. Copyright

On Dimensionality for Sparse Multipath

We give a 2WT style result for the degrees of freedom of multipath signals that pass through spatially limited (sparse) scattering environments. The dimensionality scales with the circumference of the scattering region, and the total communications path length. We provide a direct comparison to the time-frequency case, where space replaces time. This is a rigorous wavefield examination of previous heuristic geometric arguments.

Upper bound on non-coherent MIMO channel capacity in Rayleigh fading

Limits of information transfer over a discrete time uncorrelated Rayleigh fading MIMO channel is considered, where neither the transmitter nor the receiver has the knowledge of the channel state information (CSI) except the fading statistics. We show the capacity supremum with the receive antenna number at any SNR using Lagrange optimisation. Furthermore, we show the asymptotic capacity when the input power is large, and compare with the existing capacity results when the receiver is equipped with large number of antennas

On capacity of non-coherent Rayleigh fading MIMO channels

This paper investigates the capacity of discrete time uncorrelated Rayleigh fading multiple input multiple output (MIMO) channels with no channel state information (CSI) at both the transmitter and the receiver. We prove that to achieve the capacity, the amplitude of the multiple input needs to have a discrete distribution with a finite number of mass points with one of them located at the origin. We show how to compute the capacity numerically in multi antenna configuration at any signal to noise ratio (SNR) with the discrete input using the Kuhn-Tucker condition for optimality. Furthermore, we show that at low SNR, the capacity with two mass points is optimal. Since the first mass point is necessarily located at the origin, we argue that at low SNR, on-off keying is optimal for any antenna number. As the number of receiver antennas increases, the maximum SNR at which two mass points are optimal decreases

Performance of Gaussian Distributed Input in Non-Coherent Rayleigh Fading MIMO Channels

The mutual information of a discrete time Rayleigh fading channel is considered, where neither the transmitter nor the receiver has knowledge of the channel state information (CSI). We show the mutual information of uncorrelated multiple input multiple output (MIMO) Rayleigh fading channels in closed form when the input distribution is complex Gaussian for any transmit and receive antenna configuration at any signal to noise ratio (SNR). In addition, we show the maximum mutual information is achieved with a single transmitter and multiple receivers with a reduction in mutual information with additional transmitters. Also, we argue that the mutual information is bounded on the SNR similar to non-coherent SISO systems

Non-coherent Rayleigh fading MIMO channels: Capacity and optimal input

Information transfer over a discrete time uncorrelated Rayleigh fading multiple input multiple output (MIMO) channel is considered, where neither the transmitter nor the receiver has the knowledge of the channel state information (CSI) except the fading statistics. We derive a capacity supremum with the receive antenna number at any signal to noise ratio (SNR) using Lagrange optimisation. We show that the asymptotic capacity is double logarithmic when the input power is large. We prove that to achieve the capacity, the amplitude of the multiple input needs to have a discrete distribution with a finite number of mass points, one of them necessarily located at the origin. We show how to compute the capacity numerically in multi-antenna configuration at any SNR with the discrete input using the Kuhn-Tucker condition for optimality. Furthermore, we show that the capacity with two mass points is optimal at low SNR signifying on-off keying. As the number of receive antennas increases, the maximum SNR at which two mass points are optimal decreases.

Mutual information of non-coherent Rayleigh fading channels with Gaussian input

In this paper, the mutual information of a discrete time Rayleigh fading channel is considered, where neither the transmitter nor the receiver has the knowledge of the channel state information. We derive a closed form expression for the mutual information of single input single output Rayleigh fading channel when the input distribution is complex Gaussian. We compare the channel capacity and the mutual information attained with Gaussian input using the derived closed form expressions. Furthermore, we argue that the mutual information is bounded by the signal to noise ratio with the simulation results showing the sub optimality of Gaussian signalling in non-coherent Rayleigh fading channels.