1. EE682L: Lectures 2 and 3 1 Digital Communications Source Encoder Channel Encoder Digital Modulator Channel Digital Demodulator Channel Decoder Source Decoder Sink

2. EE682L: Lectures 2 and 3 2 Digital Comm Functional Blocks Source coding converts message to bits; compression –Remove redundancy from data source –E.g., Huffman codes; Limpel-Ziv; RAR; gzip; winzip –Trade-off: improve data transfer rate with increased complexity Channel coding provides error protection –Insert structured redundancy to allow for “spell-checking” –E.g., BCH block codes; trellis codes –Trade-off: reduce data bit rate for improved error rate Modulation maps bits to waveform suitable for the channel –Baseband symbols may represent one or more bits –Modulate symbols to IF and RF frequencies –Choice affects complexity required at the receiver –Can use SNR to increase data rate

3. EE682L: Lectures 2 and 3 3 EE682L Modem Sourcetext data on PC: file or typed Channel915 MHz wireless, …and… Sinkdisplay of text data on PC To be determined: Given: Source coding?Need/Cost/benefit of compression Channel coding?Need/Cost/benefit of FEC Modulation?Waveform to antenna Affects receiver complexity

4. EE682L: Lectures 2 and 3 4 Communication Resources 1.Channel Bandwidth –Spectral efficiency: bits/second/Hz 2.Transmit Power –Watts –Received signal-to-noise ratio 3.Complexity –Hardware cost –Processing cycles –Delay

5. EE682L: Lectures 2 and 3 5 Shannon Capacity: Example Telephone lines: signals bandlimited to 3300 Hz Typical SNR: ITU Modem at 33.6 kbps Approximately 11 bits per Hz ITU standards, V.34 etc, adjust data rate to adapt to the channel (i.e., the phone line SNR)

6. EE682L: Lectures 2 and 3 6 Channel Model Typical stationary channel model –Additive noise –Time-invariant, linear filtering Flat channel: Gain and phase Frequency selective channel: frequency varying gain and phase h(t) r(t) s(t) n(t) +

7. EE682L: Lectures 2 and 3 7 Channel Measurements Frequency response Impulse response –Shows delay spread and effect of symbols on neighbors –Transmit broadband signal whose autocorrelation approximates the delta function (Kassami sequences) –Measure signal to noise ratio –Send and receive pairs of tones to measure non-linearities

8. EE682L: Lectures 2 and 3 8 Channel: example timefrequency

9. EE682L: Lectures 2 and 3 9 Example: Channel

10. EE682L: Lectures 2 and 3 10 Source Encoding Convert source to bits –Transducer, quantizer –Compression Entropy (a measure of randomness) of source gives limit to compression [Shannon, 1948] Example codes –Huffman (1949 OSU alumnus) –Limpel-Ziv: gzip, RAR, winzip –Morse code Matlab: relevant commands –Double, dec2bin, reshape, char, bin2dec

11. EE682L: Lectures 2 and 3 11 Matlab Conversions: Example message = 'ab c'; mdec = double(message); mbin = dec2bin(message,7) mbin = 1100001a 1100010 b 0100000[space] 1100011c ASCII printable characters: 32-38, 40-126

12. EE682L: Lectures 2 and 3 12 Example, continued message = 'ab c';N=4; mdec = double(message); mbin = dec2bin(message,7); mbin = reshape(mbin',1,7*N)'; %convert array row-by-row to one long string recbin=reshape(mbin,7,N)'; % received binary; convert back to array, 7 bits each row recdec=bin2dec(recbin); % convert binary to decimal receive = char(recdec)‘ %convert decimal ASCII to charater receive = ab c Round trip

13. EE682L: Lectures 2 and 3 13 Channel Codes Forward error correction (FEC) codes insert structured redundancy to allow for ‘spell-checking’ English example: –We havk nothong to fexr but flar itsslf. (n,k) Block codes –Map k source bits to block of n bits (“rate” k/n) –Reduces data rate by k/n –Easy to implement and decode [Proakis, pp. 447-450] –Longer blocks (larger n,k) allow higher rate and better error correction at cost of delay and computational complexity

14. EE682L: Lectures 2 and 3 14 Example: (7,4) block code 00000000000 10001000110 01000100101 11001100011 00100010011 10101010101 01100110110 11101110000 00010001111 10011001001 01010101010 11011101100 00110011100 10111011010 01110111001 11111111111 Information bitsCode word Only 2^k valid code words among 2^n words of length n (here, 16 of 128). Generator matrix

15. EE682L: Lectures 2 and 3 15 Example: (7,4) block code 000000000003 100010001102 010001001014 110011000111 001000100112 101010101013 011001101105 111011100004 000100011113 100110010012 010101010104 110111011005 001100111006 101110110103 011101110015 111111111114 1000011 received Information bitsCode worddistance Closest among 2^k valid code words This (7,4,1) code has minimum distance 3 and can correct 1 error.

16. EE682L: Lectures 2 and 3 16 FEC: further information To randomize the occurrences of multiple errors (“burst”), shuffle, or “interleave”, the bits before coding and transmission. Two basic classes of codes –Block codes –Trellis codes Starting points for more information and free-ware –Proakis textbook, on reserve SEL –Web links available at EE682 course web page http://www.eleceng.ohio-state.edu/~potter/EE682/

17. EE682L: Lectures 2 and 3 17 Memoryless Modulation Quadrature Amplitude Modulation (QAM)

18. EE682L: Lectures 2 and 3 18 QAM Special Cases Pulse Amplitude Modulation: use amplitude only –Example:

19. EE682L: Lectures 2 and 3 19 QAM Special Cases Phase Shift Keying (PSK): use phase only –Example: BPSK

20. EE682L: Lectures 2 and 3 20 QAM Special Cases Phase Shift Keying (PSK): use phase only –Example: QPSK

21. EE682L: Lectures 2 and 3 21 Symbol Constellations Represent symbols by polar plot of BPSK 8QPSK 16QAM

22. EE682L: Lectures 2 and 3 22 Frequency Shift Keying (FSK) Represent symbols by different frequencies –Choose integer number of cycles per symbol 110 4/T 2/T

23. EE682L: Lectures 2 and 3 23 Pulse Shaping, g(t) Chosen to control the transmit power spectrum –Rectangular pulse: sinc function in frequency –Root raised cosine: suppressed frequency side lobes –May have pulse extend beyond symbol duration

24. EE682L: Lectures 2 and 3 24 Example Matlab Code %list of complex QAM constellation points x = symbols; %symbol period of N samples x_up = reshape([x;zeros(N-1,length(x))],1,N*length(x)); %convolve symbols with pulse shape trans = conv(x_up,pulse_shape); % sample index (time) n=[0:length(trans)-1]; % upcovert to carrier frequency trans_mod = real(exp(j*2*pi*fc*n).*trans);