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Cellular COMMUNICATIONS

Cellular COMMUNICATIONS. MIDTERM REVIEW. Representing Oscillations. w is angular frequency Need two variables to represent a state Use a single 2D variable to represent a state as a vector (a phasor ). Wavelength and propagation velocity. Constructive and Destructive Interference.

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Cellular COMMUNICATIONS

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  1. Cellular COMMUNICATIONS MIDTERM REVIEW

  2. Representing Oscillations • w is angular frequency • Need two variables to represent a state • Use a single 2D variable to represent a state as a vector (a phasor)

  3. Wavelength and propagation velocity

  4. Constructive and Destructive Interference

  5. Doppler Effect When no relative motion When moving @U

  6. Fast fading: Multipath

  7. ISI

  8. Example

  9. Example: Sawtooth Frequency Domain X(k)=1/k

  10. Ambiguity problem

  11. Ambiguity in frequency domain

  12. Nyquist sampling frequency • Signal band • Avoid aliasing • Nyquist sampling frequency • Maximum frequency without aliasing

  13. Time vs. Frequency • Short pulse in time domain->wide spectrum

  14. Power Spectral Density(PSD)

  15. Example:1Hz+3Hz

  16. Nonlinear Example: 1Hz+3Hz f(x1+x2)!=f(x1)+f(x2)

  17. SUI are a basis

  18. Finite Impulse Response • Filter • Impulse response

  19. Convolution

  20. Convolution in Frequency Domain • x(t), y(t) are signals • X(f), Y(f) are their spectrum • What is the spectrum C(f) of • Convolution theorem C=X*Y (multiplication) • Convolution in the time domain===Multiplication in the frequency domain

  21. Amplitude Modulation(AM) • Change amplitude of the signal according to information • Simplest digital form is “on-off keying”(telegraph Morse code)

  22. Audio AM

  23. Frequency Modulation

  24. Phase Modulation • Another form of FM

  25. Circular 16-QAM

  26. Frequency Hopping

  27. Example :DSSS with PN • Transmitter/Receiver should be able to generate same synchronized Pseudo Random Noise sequences

  28. OFDM • Select orthogonal carriers • Reach maximum at different times • Can pack close without much interference • More carriers within the same bandwidth

  29. Hierarchy of speech coders

  30. -Law

  31. Vector quantization • Encode a segment of sampled analog signal (e.g. L samples) • Use codebooks of n vectors • Segment all possible samples of dimension L into areas of equal probability • Very efficient at very low rates( R=0.5 bits per sample)

  32. DPCM and prediction

  33. Sub-band coding • Human ear does not detect error at all frequencies equally well

  34. Human Vocal Tract demo

  35. Voice Generation Model

  36. LPC

  37. Mean Opinion Score Quality Rating

  38. Codec MOS rating

  39. Binary Symmetric Channel • Transmission medium introduce errors • Demodulator produces errors • Model as a channel • Memoryless: probability of error is independent from one symbol to the next • Symmetric: any error is equally probable • Binary Symmetric Channel (BSC)

  40. Error Correcting Codes (ECC) • Redundancy added to information • Encode message of k bits with n (n>k) bits • Example: Systematic Encoding • Redundant symbols are appending to information symbols to obtain a coded sequence • Codeword

  41. Error correction vs. Error Detection • Error-detection • Detect that received sequence contains an error • Request retransmission • ARQ: Automatic Repeat Request/Query (HSDPA) • Error-correction • Detect that received sequence contains an error • Correct the error • Forward Error Correction • “A Code allows correction of up to p errors and detection up to q (q>p) errors”

  42. Block Codes vs. Convolution Codes • Block Codes • Encode information block by block • Each block encoded independently • Encoding/Decoding is a memoryless operation • Convolutional Codes • Next symbol depend on a history of inputs/outputs

  43. Linear Codes • Linear combination of valid codewords is also a codeword • Code distance is a minimum among all nonzero codeword weights (number of 1s) • Linear space spanned by basis:

  44. Syndrome • Syndrome depends only on error pattern • Different errors=>different syndromes except for the addition of codeword • Can identify error patterns of weight w<=t by looking at the syndrome • One-to-one between syndromes and errors w<=t

  45. Convolution Codes

  46. Decoding: Viterbi Algorithm • Errors on the channel • Find path with minimal total errors

  47. Trellis Coded Modulation (TCM) • Combined coding and modulation scheme • Make most similar signals (phases) represent most different/distance codewords

  48. Turbo Codes • Use 2 convolutional codes on the same data • Feed data in different order to the encoders

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