EC 723 Satellite Communication Systems

1. EC 723 Satellite Communication Systems Mohamed Khedr http://webmail.aast.edu/~khedr

2. Syllabus • Tentatively

3. Frequency Shift Keying • Two signals are used to convey information • In principle, the transmitted signal appears as 2 sinx/x functions at carrier frequencies • Each of the two states representsa single bit of information • Each state persists for a single bit period and then may be replaced either state • BER is: 2x BPSK BER for coherent for non-coherent Constant Modulus =>

4. Frequency Shift Keying

5. Other Modulations (cont.) • M-ary PSK • PSK with 2n states where n>2 • Incr. spectral eff. - (More bits per Hertz) • Degraded BER compared to BPSK or QPSK • QAM - Quadrature Amplitude Modulation • Not constant envelope • Allows higher spectral eff. • Degraded BER compared to BPSK or QPSK

6. M-ary PSK

7. M-ary QAM

8. Other Modulations • OQPSK • QPSK • One of the bit streams delayed by Tb/2 • Same BER performance as QPSK • MSK • QPSK - also constant envelope, continuous phase FSK • 1/2-cycle sine symbol rather than rectangular • Same BER performance as QPSK

9. Noncoherent receivers. (a) Quadrature receiver using correlators. (b) Quadrature receiver using matched filters. (c) Noncoherent matched filter.

10. Output of matched filter for a rectangular RF wave: (a) q 0, and (b) q 180 degrees.

11. Noncoherent receiver for the detection of binary FSK signals.

12. Factors that Influence Choice of Digital Modulation Techniques • A desired modulation scheme • Provides low bit-error rates at low SNRs • Power efficiency • Performs well in multipath and fading conditions • Occupies minimum RF channel bandwidth • Bandwidth efficiency • Is easy and cost-effective to implement • Depending on the demands of a particular system or application, tradeoffs are made when selecting a digital modulation scheme.

13. Power Efficiency of Modulation • Power efficiency is the ability of the modulation technique to preserve fidelity of the message at low power levels. • Usually in order to obtain good fidelity, the signal power needs to be increased. • Tradeoff between fidelity and signal power • Power efficiency describes how efficient this tradeoff is made Eb: signal energy per bit N0: noise power spectral density PER: probability of error

14. Bandwidth Efficiency of Modulation • Ability of a modulation scheme to accommodate data within a limited bandwidth. • Bandwidth efficiency reflect how efficiently the allocated bandwidth is utilized R: the data rate (bps) B: bandwidth occupied by the modulated RF signal

15. Shannon’s Bound There is a fundamental upper bound on achievable bandwidth efficiency. Shannon’s theorem gives the relationship between the channel bandwidth and the maximum data rate that can be transmitted over this channel considering also the noise present in the channel. Shannon’s Theorem C: channel capacity (maximum data-rate) (bps) B: RF bandwidthS/N: signal-to-noise ratio (no unit)

16. Shannon Bound • 1948 Shannon demonstrated that, with proper coding a channel capacity of Required channel quality for error free communications =>we’re doing much worse

17. Tradeoff between BW Efficiency and Power Efficiency • There is a tradeoff between bandwidth efficiency and power efficiency • Adding error control codes • Improves the power efficiency • Reduces the requires received power for a particular bit error rate • Decreases the bandwidth efficiency • Increases the bandwidth occupancy • M-ary keying modulation • Increases the bandwidth efficiency • Decreases the power efficiency • More power is requires at the receiver

18. Example: • SNR for a wireless channel is 30dB and RF bandwidth is 200kHz. Compute the theoretical maximum data rate that can be transmitted over this channel? • Answer:

19. Modulation Schemes Error Performance

20. M-ary PSK Error Performance

21. Operation Point Comparison

22. Union bound Union bound The probability of a finite union of events is upper bounded by the sum of the probabilities of the individual events. • Let denote that the observation vector is closer to the symbol vector than , when is transmitted. • depends only on and . • Applying Union bounds yields Lecture 5

23. Example of union bound • Union bound: Lecture 5

24. Upper bound based on minimum distance Minimum distance in the signal space: Lecture 5

25. Example of upper bound on av. Symbol error prob. based on union bound Lecture 5

26. Summary of Useful Formulas

27. Summary of Digital Communications -1 Legend of variables mentioned in this section: M = modulation size. (Ex: 2, 4, 16, 64) Bw = Bandwidth in Hertz  = Roll-off factor (from 0 to 1) Gc = Coding Gain (convert from dB to linear to use in formulas) Ov = Channel Overhead (convert from % to fraction : 0 to1) BER = Bit Error Rate

28. Summary of Digital Communications - 2 • Bits per Symbol: • Symbol Rate [symbol/second]: • Gross Bit Rate [bps]: • Net Data Rate [bps]:

29. BER Calculation as a Function of Modulation Scheme and Eb/No Available • Equations given on next slide are used to calculate the bit error rate (BER) given the bit energy by spectral noise ratio (Eb/No) as input. • These functions are used in their direct form for the bit error rate calculations. Excel and some scientific calculators provide the solution for the “erfc” function. • The formulas provided can be inverted by numerical methods to obtain the Eb/No required as a function of the BER. • Also possible to draw the graphic and obtain the “inverse” by graphical inspection.

30. BER Calculation as a Function of Modulation Scheme and Eb/No Available - 2

31. Maximum Likelihood (ML) Detection: Concepts

32. Likelihood Principle • Experiment: • Pick Urn A or Urn B at random • Select a ball from that Urn. • The ball is black. • What is the probability that the selected Urn is A?

33. Likelihood Principle (Contd) • Write out what you know! • P(Black | UrnA) = 1/3 • P(Black | UrnB) = 2/3 • P(Urn A) = P(Urn B) = 1/2 • We want P(Urn A | Black). • Gut feeling: Urn B is more likely than Urn A (given that the ball is black). But by how much? • This is an inverse probability problem. • Make sure you understand the inverse nature of the conditional probabilities! • Solution technique: Use Bayes Theorem.

34. Likelihood Principle (Contd) • Bayes manipulations: • P(Urn A | Black) = • P(Urn A and Black) /P(Black) • Decompose the numerator and denomenator in terms of the probabilities we know. • P(Urn A and Black) = P(Black | UrnA)*P(Urn A) • P(Black) = P(Black| Urn A)*P(Urn A) + P(Black| UrnB)*P(UrnB) • We know all these values Plug in and crank. • P(Urn A and Black) = 1/3 * 1/2 • P(Black) = 1/3 * 1/2 + 2/3 * 1/2 = 1/2 • P(Urn A and Black) /P(Black) = 1/3 = 0.333 • Notice that it matches our gut feeling that Urn A is less likely, once we have seen black. • The information that the ball is black has CHANGED ! • From P(Urn A) = 0.5 to P(Urn A | Black) = 0.333

35. Likelihood Principle • Way of thinking… • Hypotheses: Urn A or Urn B ? • Observation: “Black” • Prior probabilities: P(Urn A) and P(Urn B) • Likelihood of Black given choice of Urn: {aka forward probability} • P(Black | Urn A) and P(Black | Urn B) • Posterior Probability: of each hypothesis given evidence • P(Urn A | Black) {aka inverse probability} • Likelihood Principle (informal): All inferences depend ONLY on • The likelihoods P(Black | Urn A) and P(Black | Urn B), and • The priors P(Urn A) and P(Urn B) • Result is a probability (or distribution) model over the space of possible hypotheses.

36. Maximum Likelihood (intuition) • Recall: • P(Urn A | Black) = P(Urn A and Black) /P(Black) = P(Black | UrnA)*P(Urn A) / P(Black) • P(Urn? | Black) is maximized when P(Black | Urn?) is maximized. • Maximization over the hypotheses space (Urn A or Urn B) • P(Black | Urn?) = “likelihood” • => “Maximum Likelihood” approach to maximizing posterior probability

37. P Maximum Likelihood (ML): mechanics • Independent Observations (like Black): X1, …, Xn • Hypothesis  • Likelihood Function: L() = P(X1, …, Xn | ) = i P(Xi | ) • {Independence => multiply individual likelihoods} • Log Likelihood LL() = i log P(Xi | ) • Maximum likelihood: by taking derivative and setting to zero and solving for  • Maximum A Posteriori (MAP): if non-uniform prior probabilities/distributions • Optimization function

38. OFDM

39. Motivation • High bit-rate wireless applications in a multipath radio • environment. • OFDM can enable such applications without a high • complexity receiver. • OFDM is part of WLAN, DVB, and BWA standards • and is a strong candidate for some of the 4G wireless • technologies.

40. PSD PSD f f * -fc fc Radio- channel e.g. Audio 0110 01101101 Receiver: Source decoding Decoding / deinter-leaving OFDM de-modulation Down-converter, I/Q-demod. Info Sink I/Q RF What is OFDM? • Modulation technique • Requires channel coding • Solves multipath problems Transmitter: I/Q RF OFDM modulation Source coding Channel coding / interleaving I/Q-mod., up- converter Info Source

41. Multipath Transmission • Fading due to constructive and destructive addition of • multipath signals. • Channel delay spread can cause ISI. • Flat fading occurs when the symbol period is large compared • to the delay spread. • Frequency selective fading and ISI go together.

42. Reflections from walls, etc. Time dispersive channel Impulse response: Problem with high rate data transmission: inter-symbol-interference t p ( ) (PDP) t [ns] Multipath Propagation Multipath Radio Channel

43. Delay Spread • Power delay profile conveys the multipath delay spread • effects of the channel. • RMS delay spread quantifies the severity of the ISI • phenomenon. • The ratio of RMS delay spread to the data symbol period • determines the severity of the ISI.

44. Transmitted signal: Received Signals: Line-of-sight: Reflected: The symbols add up on the channel Inter-Symbol-Interference Delays  Distortion! Multipath Radio Channel

45. Time 1 Channel (serial) Channels are transmitted at different frequencies (sub-carriers) 2 Channels 8 Channels In practice: 50 … 8000 Channels (sub-carriers) Concept of parallel transmission (1) Channel impulse response OFDM Technology

46. Power response [dB] 20 15 10 5 0 -5 -10 Frequency The Frequency-Selective Radio Channel • Interference of reflected (and LOS) radio waves • Frequency-dependent fading Multipath Radio Channel

47. Signal is “broadband” 2 Channels Frequency 8 Channels Frequency Channels are “narrowband” Concept of parallel transmission (2) Channel transfer function Channel impulse response Frequency Time 1 Channel (serial) Frequency OFDM Technology

48. Concept of an OFDM signal Ch.1 Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10 Conventional multicarrier techniques frequency Ch.2 Ch.4 Ch.6 Ch.8 Ch.10 Ch.1 Ch.3 Ch.5 Ch.7 Ch.9 Saving of bandwidth 50% bandwidth saving Orthogonal multicarrier techniques frequency Implementation and System Model

49. A Solution for ISI channels • Conversion of a high-data rate stream into several low-rate • streams. • Parallel streams are modulated onto orthogonal carriers. • Data symbols modulated on these carriers can be recovered • without mutual interference. • Overlap of the modulated carriers in the frequency domain - • different from FDM.

50. OFDM • OFDM is a multicarrier block transmission system. • Block of ‘N’ symbols are grouped and sent parallely. • No interference among the data symbols • sent in a block.