Material de lectura 9 - Bit-Error-Rate Simulation Using...

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Bit-Error-Rate Simulation Using Matlab James E. Gilley Chief Scientist Transcrypt International, Inc. [email protected] August  ,  Introduction Matlab is an ideal tool for simulating digital communications systems, thanks to its easy scripting language and excellent data visualization capabilities. One of the most frequent simulation tasks in the field of digital communications is bit-error- rate testing of modems. The bit-error-rate performance of a receiver is a figure of merit that allows di ff erent designs to be compared in a fair manner. Performing bit-error-rate testing with Matlab is very simple, but does require some prerequisite knowledge. Properties of Sampled Signals In Matlab, we represent continuous-time signals with a sequence of numbers, or samples, which are generally stored in a vector or an array. Before we can perform a bit-error-rate test, we must precisely understand the meaning of these samples. We must know what aspect of the signal the value of these samples represents. We must also know the time interval between successive samples. For communications simulations, the numeric value of the sample represents the amplitude of the continuous-time signal at a specific instant in time. We as- sume this amplitude is a measurement of voltage, though it could just as easily be a measurement of current. The time between successive samples is, by definition, T s . This tells us how often the continuous-time signal was sampled. Instead of specifying T s , we usually specify the sampling frequency, f s , which is the inverse of T s . For convenience, we will always associate a sample value of 1.0 with a voltage of exactly one volt. Furthermore, we will always assume a resistance of exactly one ohm. This allows us to dispense with the notion of resistance altogether. For our simulations, we will represent a continuous time signal as an array of samples, the numeric value of which is in units of volts, referenced to a resistance of one ohm. Usually, the sampling frequency is KHz, but other sampling frequencies are also in common use, so the sampling frequency should always be specified.
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. Power Suppose we have a signal x ( n ), where n is an index of the sample number. We define the instantaneous power of the signal as: P ins x 2 ( n ). In other words, the instantaneous power of a sample is just the value of that sample squared. Since the units of the sample are volts, the units of the power are watts. A far more useful quantity is the average power, which is simply the average of the instantaneous power of every sample in the signal. For signal x ( n ), of N samples, we have: P ave 1 N N summationdisplay n = 1 x 2 ( n ). ( ) Note that this is simply the sum of the square of all samples, divided by the num- ber of samples. One way to compute the average power, ‘pav’, of signal ‘x’, using Matlab is: pav = sum ( x .^ 2 )/ length ( x ).
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