VTechWorks staff will be away for the winter holidays starting Tuesday, December 24, 2024, through Wednesday, January 1, 2025, and will not be replying to requests during this time. Thank you for your patience, and happy holidays!

Browsing by Author "Teotia, Seemant"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Influence of the Number of Degrees of Freedom on the Capacity of Incoherent Optical Fiber Communication Systems
    Teotia, Seemant (Virginia Tech, 2006-05-01)
    The purpose of this dissertation is to find the channel capacity in optical fiber communication systems when incoherent detection is used with single (polarization filtering) and two-polarizations (no polarization filtering). Optical fiber systems employ photodetectors that convert optical intensity to electrical current. Bandpass vector fields may be represented by four orthogonal baseband components corresponding to two quadrature phases and two orthogonal polarizations. Intensity is proportional to the sum of the squares of these four components. In the case of a coherent receiver, a strong optical local oscillator (in phase and with same polarization as the signal) is added to the signal prior to the photodetector. This results in the removal of the quadrature phase and polarization components, and reduces to the one degree of freedom (DOF) case of signal plus local oscillator shot noise for which the Shannon channel capacity formula applies. Electrical noise following the photodetector may also be neglected if there is an optical amplifier before the photodetector in the receiver. The amplifier introduces amplified spontaneous emission noise containing both quadrature phase components and both polarizations (4 DOFs), but the 2 DOF case would result if a polarization filter were used. Although the 1 and 2 DOF cases are of less practical interest than the 4 DOF case, they provide useful benchmarks for comparing performance limits. We evaluate both spectral efficiency limits (bps/Hz) in the limit of high and low SNR for the 1,2 and 4 DOF cases and also find the power efficiency (minimum number of photons per bit) for each of these cases. It is shown that for high SNR the spectral efficiency is the same independent of the number of DOFs and that the half-Gaussian distribution is the optimum distribution. We are able to thus obtain a compact equation for spectral efficiency which behaves in a similar way to the Shannon capacity formula but with the SNR scaled by a constant. We also show that for low SNR the half-Gaussian distribution is not the optimum distribution as the slope of the mutual information changes with the square of SNR which would lead to the number of photons per bit becoming infinite in the limit of SNR going to zero. We use a modified half-Gaussian distribution which has a discrete component (an impulse function at the origin) and provide a simple proof that this distribution results in a mutual information that goes to zero linearly with SNR resulting in a minimum number of photons per bit. Furthermore, by increasing the magnitude of the discrete component at the origin, it is shown that the minimum number of photons per bit for the incoherent channel approaches that of the coherent channel.
  • Thumbnail Image
    Saddlepoint Approximation for Calculating Performance of Spectrum-Sliced WDM Systems
    Teotia, Seemant (Virginia Tech, 1999-07-12)
    Spectrum slicing is a novel technique for the implementation of wavelength-division multiplexing (WDM). While conventional WDM systems employ laser diodes operating at discrete wavelengths as carriers for the different data channels that are to be multiplexed, spectrum-sliced systems make use of spectral slices of a broadband noise source for the different data channels, thus being economically attractive. In spectrum-sliced WDM systems with an optical preamplifier receiver there is an optimum m=BoT (Bo = optical channel bandwidth, T = bit duration) to minimize the average number of photons-per-bit (Np) required at the receiver for a given error probability (Pe). Both the optimum m and the minimum increase as interchannel interference increases. This has been analyzed previously by using the Gaussian approximation, or by assuming that the signals at the decision point are chi-square distributed. Although the chi-square distribution is valid in the case where there is no interference, it is not valid in the presence of interference, since the interference from the neighboring channel has a smaller bandwidth than the signal. In this thesis, a different method is used to analyze this problem. This method is called the Saddlepoint Approximation, and while the exact analysis required determination of the probability density function (pdf) of the received signal, the saddlepoint method makes use of moment generating functions (MGFs) which have a much simpler form and don't require the convolution operations the pdfs require. The saddlepoint method is validated by comparing results obtained with the chi-square analysis for the no interchannel interference case when a rectangular shaped filter is used. The effect of non-rectangular spectra on receiver sensitivity with the use of the Saddlepoint Approximation is also investigated. After verifying its validity, the method is applied to the interchannel interference case caused by filter overlap. It is shown that for small filter overlap, use of an equivalent chi-square distribution is valid, but when the overlap becomes larger, the performance approaches that calculated using the Gaussian distribution. It is shown that there is an optimum filter overlap to maximize the total system throughput when total bandwidth is constrained. Operating at this optimum, the total system throughput is 135 Gbits/s when the total system bandwidth is 4.4 THz (35 nm) for a Bit Error Rate (BER) of 10e-9.