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Optimization of Radio resources Krishna Chaitanya Kokatla

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Contents Introduction Objective Space Multi objective Optimization: Objective Functions Bit Error Rate (BER) Bandwidth Spectral Efficiency Interference SINR Throughput Power Computational Complexity Multi objective Optimization: A different perspective Multi objective Analysis Utility Functions Population – based Analysis Conclusion Reference

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Introduction In this chapter we explain the concept of radio resource optimization with a particular interest in understanding the physical layer in terms of a set of objective functions. In optimization objective space is the set of all possible solutions to a problem often over a multi dimensional set of objective functions.

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Objective Space Spectrum: Communication Resource which is a reusable resource TDMA, FDMA: allows sharing the spectrum DSA: uses spectrum when its primary occupants are silent Each node in a network can look at a resource allocation as an optimization problem with two potential goals. Greedy Approach Perspective Approach

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Multi objective optimization Objective Functions: It has a long history in mathematics research and economics and this concept is introduced in wireless communication. Multi Objective Decision Making (MODM) Problem min/max y = f(x) =[f1(x),…..,fn(x)] Subject to: x = (x 1, x 2,….., x m ) X y = (y 1, y 2,….y n ) Y The solutions to multi objective problems lie on the Pareto front, which is the set of input parameters, x, that defines the non- dominated solutions, y, in any direction.

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Bit error rate Knobs: transmitter power, Modulation type Meters: Noise power, Channel type, Path loss Objective: bandwidth BER is an important objective for all digital communications needs. BER provides a baseline for the amount of information transferred. Cognitive engine requires knowledge of certain environmental conditions.

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Band width(Hz) Knobs: Modulation type, Symbol rate, Pulse Shape Filter Meters: None Objective: None Band width is an objective used in many other objective calculations. Band width is the direct measurement of how much spectrum is occupied by the radios. The approximate null to null band width is calculated B=R s K(1+r)/2

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Spectral Efficiency Knobs: modulation type, Symbol rate Meters: None Objectives: bandwidth Represents the amount of information transferred in a given channel and is measured in bps/Hz. While measuring it offers to determine how suited the waveform is to a particular need when judged by both bandwidth occupancy and data rates. n=R s K/B (bps/Hz)

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Interference Knobs: Frequency Meters: Interference map Objectives: Bandwidth Interference power is calculated over a given bandwidth I pwr =10log 10 (1 ∫ fc+B/2 I(f)df) (dBm) B fc-B/2 Calculation of I pwr is different than SINR The cognitive engine would not simply try to avoid interference – prone spectrum, but it would be forced not to use the spectrum.

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SINR(Signal to interference plus noise ratio) Knobs: Transmit Power Meters: noise Power, Path loss Objectives: interference, bandwidth SINR an inform the cognitive radio about how the presence of interferes can affect the signal reception. Noise Power is given by N=10log 10 (BN o ) +30 (dBm) SINR=(P T - L) - 10log 10 (i+n) (dBm) Noise power and interference power are summed in the linear domain(mW)

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Throughput Knobs: Modulation type, Symbol rate, number of bits per packet Meters: None Objectives: Bit error rate It is a measure of the amount of good information received. It is different from data rate throughput measures the rate at which data arrives with transmission errors in consideration. The probability of a packet error P p =1-(1-P e ) l L bits are received over a time period of l/R b where R b =kR s.

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Power Knobs: Transmit power Meters: none Objectives: None There are two ways to look at power as a resource How the radio transmitter uses the external power in the spectrum. To analyze power is to measure it in terms of power consumption by a radio

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Computational complexity Knobs: modulation type, Symbol Rate Meters: None Objectives: None Power consumption maps almost directly to the computational complexity of an algorithm. The symbol rate directly defines the sampling rate and therefore the computational power required for a waveform.

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Multi Objective Optimization There is an overlap as well as interactions among certain objectives. When an objective is optimized, it affects the performance Of some other objectives, either positively or negatively. Changing the modulation affects all of these objectives. min/max y = f(x) =[f1(x),…..,fn(x)] Subject to: x = (x 1, x 2,….., x m ) X y = (y 1, y 2,….y n ) Y Provides the basic formula to describe a multi objective optimization problem.

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SINR Bandwidth Interface Computational Complexity BERThroughput Spectral Efficiency Power Dependency Map of Objective Functions

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Utility Functions The most straight forward method of selection is to build a single utility function that combines the objectives in to one number. The most basic utility function is the Weighted Sum approach N U = Ʃ w i f i (x) i = 1 Most significant problem is that this form if utility assumes additivity between each objective, where each objective is independent of the others but they are not. A development slightly beyond the weighted sum is the linear- logarithmic function N ln U = Ʃ ß i ln q i i = 1

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Population Based Analysis This is another method of evaluating performance in a multi objective problem space. This uses population based analysis and Pareto-ranking. The Pareto-ranking analysis takes a set or population of possible solutions to a multi objective problem and looks to see which members are non dominated. In a search or optimization algorithm, the idea is to push for better and better solutions until they lie on optimal Pareto front.

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Conclusion In this chapter we discussed the concept of multi objective optimization, both from the theoretical perspective and regarding the use of this type of analysis to optimize waveforms for a cognitive radio.

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References 1.T. Rappaport, wireless Communications: principles and Practices, upper Saddle River, NJ; Prentice Hall, 2001. 2.B.Fette, Ed., Cognitive radio Technology, New York, Elsevier, 2006 3.L. w. Couch, Digital and Analog Communications System,m 7ed., upper Saddle River, NJ; Prentice Hall, 2007.

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