Correlation, Interference. Kalle Ruttik Department of Communications and Networking School of Electrical Engineering Aalto University

Transcription

1 Correlation, Interference Kalle Ruttik Department of Communications and Networking School of Electrical Engineering Aalto University

2 Correlation

3 Correlation Digital communication uses extensively signals correlation properties Used in Synchronization Digital symbol identification Users separation Correlation generates also disturbance Between the symbols Between the users

4 Correlation: definition Statistical dependency between two random variables or sets of data Random variable is a variable whose value is subject to chance Gaussian noise is a random value It does not have single fixed value, but it can have a set of possible values It can have any value from Gaussian distribution Transmitted signal not know at the receiver is a random value In digital communication we know which signals could be transmitted but not which one is transmitted at each moment Receiver estimates which signal is has most likely been transmitted Computes correlation between the received signal and the possible candidates Correlation coefficient measures the level of correlation Most common Pearson correlation coefficient

5 Pearson correlation coefficient cov(x,y) covariance, - mean, - second moment

6 Zero mean random variable For zero mean random variable with normalized second moments,, covariance and correlation are the same For normalized random variables

7 Correlation of ergodic signals The receiver can compute correlation by using ergodicity property For ergodic signals expectation computed over distribution and average over time are the same

8 Correlation for discrete values For discrete values we can use estimate

9 Correlation of stationary discrete random variables Approximation of the integral with discrete values

10 Example: signal in noise x1 signal y1= x1 + n > signal plus noise x2 other signal

11 Correlation example: cos in noise Input signal x1 Correlation x1 vs y1 Noise n Components x1[n]*y1[n] y 1 = x1 + n All plots together

12 Correlation example: cos in noise Input signal s2 Correlation s1 vs y2 Noise n Components s1[n]*y2[n] y2 = s2 + n

13 Correlation example: both correlations - Signals before integration - Intergration averages over the samples correlation between x1 and y1=x1+n: correlation between x1 and y2=x2+n: We can use correlation for separating signals: - separation between different symbols - separation of different users

14 Example: analytical model of a digital receiver Two users signals in a receiver input Processed signal is computed as correlation with reference signal

15 Example: correlation 3) correlation result is sum of three correlations 1) Signals sum in air 2) Receiver correlates with reference signal 4) Other signal Impact is disturbance

16 Example: digital receiver 1) 2 signals sum in the air 3) correlation is computed from discrete samples A/D 2) Receiver converts the continuous signal to discrete samples. Sample rate is higher than symbol rate Symbol sample 4)After correlation the signal is oversampled

17 Example of OFDM signal spectrum Power Spectrum when the samples are taken during the symbol FFT taken from the samples in this interval Spectrum has only one component One peak

18 Example of signal spectrum Spectrum if the samples are taken over random interval FFT taken from the samples in this interval Spectrum resembles sinc function

19 Example: OFDM signal OFDM is generated by multiplying square pulse with the ofdm carriers Information is in the phase of the carriers Example:One carrier Freq f = 1/T Amplitude:1 What is the initial phase?

20 OFDM signal Multiple carriers are send at the same time Carriers separated in frequencies Carrier frequencies selected such that the carriers are uncorrelated Example: two carriers 1/T

21 Correlation function of a sinus Correlation of the carriers is defined by the symbol length The square pulse length T 1/T

22 Interference

23 Orthogonality between signals from different transmitters Communication system uses correlation For identifying which signal was transmitted Most likely signal has highest correlation with received signal Correlation properties help to reduce disturbance from other transmitters Signal design attempts to minimize the disturbance (correlation) between other transmitter signals and and our transmitter signals

24 Reference signal correlation with wanted transmitted signal. This term generates the symbol amplitude Interference (I) Refernece signal correlation with interfering signal. Reference signal correlation with noise

25 Interference model Interference is usually modeled as a zero mean random process Often approximated by Gaussian distribution Mean Variance

26 Interference (II) Interference from other users is correlation between the wanted signal and other users signals Interference is avoided by Using different frequencies Still have to avoid the adjacent channel interference Using distance between transmitters Utilize the signal attenuation Used for avoiding co-channel interference

27 Co-channel interference Interference generated by transmitters using the same frequency Can be reduced by locating transmitters at some distance Frequency reuse Uses the signal attenuation property Spatial filtering

28 Adjacent channel interference (ACI) ACI is generated since usually signal on neighboring channel is not orthogonal to our signals The amount of interference is limited by setting the requirements on out of bandwidth power level spectrum mask Guarantees that the interference is at least at that amount In case of sinus we show that at certain frequencies we can have zero correlation

29 Definitions Adjacent channel interference (ACI) Adjacent channel leakage ratio (ACLI) Interference generated by transmitters using adjacent channels How much transmitter signal power is spilled on adjacent channels Adjacent channel selectivity (ACS) Describes how much the receiving filter is suppressing signal on adjacent channels.

30 ACI Adjancent transmitter f0 f0 f1 Tx2 Tx1 ACLR Rx ACS Own transmitter f0 f1 Always present Can be removed with oversampling and FFT

31 Attenuation

32 Path loss Path loss describes loss of the signal strength due to the signal propagation in space In line of sight the path loss is described by free space path loss model Often the environment creates bigger attenuation than 2 (the free space attenuation factor). That is captured with more complex attenuation model Actual attenuation values for models are derived from measurements

33 Radio channel measurements In channel measurement Transmitter sends known sequence Receiver correlates the received signal with the same sequence Example: Channel attenuation estimation is done by measuring the signal at multiple distance points from the receiver To the measurement points is fit the channel attenuation function Coefficients are computed by optimizing distance (cost function) between the measured point and the fitting function