Modelling of Path Arrival Rate for In-Room Radio Channels with Directive Antennas

We analyze the path arrival rate for an inroom radio channel with directive antennas. The impulse response of this channel exhibits a transition from early separate components followed by a diffuse reverberation tail. Under the assumption that the transmitter's (or receiver's) position and orientation are picked uniformly at random we derive an exact expression of the mean arrival rate for a rectangular room predicted by the mirror source theory. The rate is quadratic in delay, inversely proportional to the room volume, and proportional to the product of beam coverage fractions of the transmitter and receiver antennas. Making use of the exact formula, we characterize the onset of the diffuse tail by defining a "mixing time" as the point in time where the arrival rate exceeds one component per transmit pulse duration. We also give an approximation for the power-delay spectrum. It turns out that the power-delay spectrum is unaffected by the antenna directivity. However, Monte Carlo simulations show that antenna directivity does indeed play an important role for the distribution of instantaneous mean delay and rms delay spreadComment: Submitted to IEEE Trans. Antennas and Propagatio

Stochastic Multipath Model for the In-Room Radio Channel based on Room Electromagnetics

We propose a stochastic multipath model for the received signal for the case where the transmitter and receiver, both with directive antennas, are situated in the same rectangular room. This scenario is known to produce channel impulse responses with a gradual specular-to-diffused transition in delay. Mirror source theory predicts the arrival rate to be quadratic in delay, inversely proportional to room volume and proportional to the product of the antenna beam coverage fractions. We approximate the mirror source positions by a homogeneous spatial Poisson point process and their gain as complex random variables with the same second moment. The multipath delays in the resulting model form an inhomogeneous Poisson point process which enables derivation of the characteristic functional, power/kurtosis delay spectra, and the distribution of order statistics of the arrival delays in closed form. We find that the proposed model matches the mirror source model well in terms of power delay spectrum, kurtosis delay spectrum, order statistics, and prediction of mean delay and rms delay spread. The constant rate model, assumed in e.g. the Saleh-Valenzuela model, is unable to reproduce the same effects.Comment: 14 pages, Manuscript Submitted to IEEE Transaction on Antennas and Propagatio

Analysis and Design of Binary Message-Passing Decoders

Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the L-value domain. A hard decision channel results in the well-know Gallager B algorithm, and increasing the output alphabet from hard decisions to two bits yields a gain of more than 1.0 dB in the required signal to noise ratio when using optimized codes. The code optimization requires adapting the mixing property of EXIT functions to the case of binary message-passing decoders. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.Comment: 8 pages, 6 figures, submitted to the IEEE Transactions on Communication