Maßkonzentration, Derandomisierung und Compressed-Sensing: Effiziente Spitzenwertreduktionsverfahren für MIMO-OFDM-Systeme der nächsten Generation
Final Report Abstract
An essential enabling technology in physical layer of wireless communication systems is multicarrier waveforms. Orthogonal Frequency Division Multiplexing with Cyclic Prefix (CP-OFDM) was the first multicarrier waveform to be widely used in cellular systems that were and are being used throughout the world. Research has been on-going on this type of waveform to meet the new requirements of the future cellular systems. The next generation, 5G, has especially introduced several challenging research problems to the field of waveform design. However, one thing is inherently common to all multicarrier waveform: high fluctuations in instantaneous signal power, a characteristic most commonly referred to as the Peak-To-Average Power Ratio (PAPR) problem. Any non-linear component in the transceiver chain adds distortion to a signal with high dynamic range, i.e., PAPR. The most important one is the power amplifier before the antenna in the transmitter. Briefly speaking, low PAPR is essential to energy-efficient operation of the power amplifier and consequently the transmission system. This DFG project focused on exploring some novel approaches to reduction of PAPR. The main difficulty in dealing with the problem is the mathematical definition of PAPR itself. It is a random variable defined as peak value of instantaneous power of consecutive segments of a signal normalized by its average power. The implied maximum operator causes the difficulty of both analysis of the metric and proposal of solutions. The main track of research in this project is “alternative metrics”. That is, finding metrics that replace PAPR with the following properties 1. The metric has mathematically tractable structure. 2. Reduction of the metric by a chosen algorithm at the cost of some reserved degrees of freedom (rate loss) leads to acceptable “indirect PAPR reduction” 3. Eventually the metric lends itself well to low complexity reduction methods, possibly involving approximations and simplifications. Far from its current state of development, such problem solving paradigm can ultimately reverse the path: degrees of freedom, desired algorithm and target order of computational complexity are chosen first and then a metric is invented to achieve the desired indirect PAPR reduction. The method of Conditional Expectations (CE) for sign selection, which belongs to category of derandomized algorithms and probabilistic tools, is applied to the Cubic Metric (CM). Similar to PAPR, CM directly captures a physical property which is reported to be able to better predict the required adjustments in signal power level or power amplifier. However, in this work the CM was chosen merely as an alternative metric with the desired properties as listed above. It is observed that the indirect PAPR reduction performance is only slightly lower than that of directly applying the algorithm to PAPR. For simplicity here we report effective PAPR, the value that the random PAPR does not exceed for 0.999 of the cases/time. The direct PAPR reduction for a wide range of subcarriers N = 64, 512, 1024 and 2048 results in effective PAPRs of roughly 6.1, 6.3, 6.4, 6.5 dB, respectively. That is, reduction gains of about 4.2, 5.2, 5.3, 5.5 dB. Notice the remarkable gains and the fact that effective PAPR is kept to a small range about 6.5 dB for a wide range of N . Then the indirect PAPR reduction observed from application of CE method to CM is only slightly degraded: effective PAPRs that fall between 6.7 dB and 7.1 dB for N ranging from 64 to 2048. It is observed that the computational complexity of applying the method of CE method to CM is of a lower order than that of applying it directly to PAPR. Following the initial research, exploration of alternative metrics is an interesting path to follow. The reverse path described above requires not only such exploration but also a fundamental investigation into a framework that can connect the metrics in general or in context of the applied algorithm.
