Project Type:
Master/Diploma Thesis
Student:
Erik Leitinger
Mentor: Bernhard Geiger

Noncoherent receiver structures, which include the energy detector, have great importance for ultrawideband systems due to their low complexity. The channel capacity, i.e. the maximum amount of information that can be transmitted at a particular signaltonoise ratio SNR represents a fundamental concept in information theory. In order to achieve the channel capacity, the input alphabet has to satisfy certain statistical properties. For a nonlinear channel like the energy detector, such an alphabet shows a discrete amplitude distribution and can be represented by onoff keying for low SNR or amplitudeshiftkeying for higher SNR. The difficulty lies in providing a solution for the underlying nonlinear optimization problem for the continuous channel (energy detector). This master thesis presents a numerical algorithm to compute the channel capacity and the corresponding capacityachieving input distribution over a wide range of SNR. Furthermore, it will be demonstrated that the input distribution has to be discrete with a finite number of mass points. A detailed literature research supports these conclusions.
The energy detector, as depicted below, is a receiver architecture often used in ultra wideband (UWB) communications due to its simplicity. It is a nonlinear channel, but we believe that for suffciently large integration times it can be modeled as an AWGN channel with signaldependent noise variance.
The capacity of a channel is the maximum amount of information that can be transmitted at a particular SNR. To achieve this capacity, the input has to satisfy certain statistical properties. For nonlinear channels  and many linear channels  it is known that the input has to be a discrete random variable. Corresponding modulation schemes are, e.g., onoff keying for low SNR, amplitude shift keying for higher SNR, etc.
In [1] a numerical procedure to compute the capacity of a channel together with its capacityachieving distribution is described. In this work, this procedure shall be used to obtain the capacity of the energy detector for a wide range of SNR and to verify the modeling assumption. In addition to that, the results for the input statistics shall be compared to standardized UWB signal models.
[1] J. Dauwels, "Numerical computation of the capacity of continuous memoryless channels," in Sym. on Information Theory in the BENELUX, 2005
The full thesis can be downloaded here.
Attachment  Size 

Leitinger12_DA.pdf  3.8 MB 