1. ii-1-PHY Taekyoung Kwon

2. Data vs. signal Digital data vs. analog data Digital signal vs. analog signal Data are symbols like bits that have some info. A signal refers to physical representation of data, electrically or electromagnetically

3. signal A signal is a time-varying value (electric or electromagnetic representation) or event that conveys information from a transmitter to a receiver A function of time and location parameters of periodic signals: period T, frequency f=1/T, amplitude A, phase shift  –E.g., sinewave is expressed as s(t) = A t sin(2  f t t +  t )  : phi [fee]

4. signal Different representations of signals –Amplitude over time (time domain) –frequency spectrum (frequency domain) –phase state diagram (amplitude M and phase  in polar coordinates) f [Hz] A [V]  I= M cos  Q = M sin   A [V] t[s]

5. signal f=1/T

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8. Nyquist bandwidth Ideally, we need only B=n/2 bandwidth to represent the original digital signal of bit rate n In reality, we need more due to noise, interference,… –For bit rate n, n/2 ≤ B ≤ n –B = n/2 * (1 + α)0 ≤ α ≤ 1 The most naïve case will be when B is equal to n  : roll-off factor What is  ?

9. Pulse shaping Original rectangle pulses require infinite BW We need to change the binary inputs to BW- limited signals Nyquist BW makes a binary input into a sinc function

10. Inter symbol interference (ISI) Consecutive bits or symbols interfere each other Sampling instants No ISI Theoretically adjacent pulses go to zero hence no ISI Tb

11. Pulse shaping issues  Two practical difficulties If we use a sinc function, minimum BW is required, but physically unrealizable If clocks are perfectly synchronized, then there is no ISI => which is impossible Timing errors, delay jitters  senstive to timing errors

12. Roll-off How to mitigate ISI despite timing errors and delay jitters? To make a sinc realizable, we begin by smoothing the edges of its squared-off spectrum This process is called “roll-off” We can smooth the sinc spectrum by the smoothing parameter. The cost is increased BW f  =0.5  =0  =1 R b /2 RbRb

13. As  increases The pulse (a function of time) after its symbol time decreases more sharply

14. Baseband signal vs. bandpass signal We use B bandwidth to represent the original digital signal of bit rate n This analog signal occupying 0  B Hz is called baseband signal –Used for PSTN local loop and Ethernet In wireless, we cannot use baseband signal –Shared medium –A long antenna will be required (at least half or quarter of wavelength) –Not suitable for propagation That’s why we need bandpass signals

15. Bandpass signal Using carriers to shift the frequency spectrum –Called (analog) modulation –different radio bands can be used for different communications –wireless communications –multiplexing techniques become applicable –However, it occupies twice bandwidth

16. Bandpass signal: twice BW Consider a single frequency component cos(  m t) from within the baseband spectrum (0 – B Hz) perform the mathematical multiplication with the carrier cos(  c t) The modulated signal becomes: –cos(  c t). cos(  m t) = 0.5 cos (  c -  m )t + 0.5 cos (  c +  m )t –two identical components symmetric about the carrier frequency  = 2  f

17. V ASK (t) =V d (t) * V c (t)

18. Summary of modulation digital modulation is a process of transforming a digital signal (or data) into a baseband signal –A digital signal: a series of bits –A baseband signal: an analog signal of [0  B Hz] bandwidth –n bps corresponds to B bandwidth ( n/2 ≤ B ≤ n ) For wireless communications, we have to use a bandpass signal, which requires 2B bandwidth –A process of changing baseband to bandpass is called analog modulation

19. Modulation and demodulation synchronization decision digital data analog demodulation radio carrier analog baseband signal 101101001 radio receiver digital modulation digital data analog modulation radio carrier analog baseband signal 101101001 radio transmitter

20. Spread Spectrum (SS) and CDMA Basic idea: Use a wider bandwidth than needed to transmit the signal Why?? –Don’t put all your eggs in one basket! –Resistance to jamming and interference If one sub-channel is blocked, you still have the others Good for military Minimize impact of a “bad” frequency –Pseudo-encryption Have to know what frequencies it will use Two techniques for spread spectrum So far, we have assumed that BW is precious and should be minimized. What if we don’t know which portion of frequency spectrum is used by a particular technology. Spread spectrum technology is to address this problem; it uses much wider BW to transmit a signal Spread spectrum distributes the energy of a signal over a wider BW to make the system robust to interference Even if some portion of BW (sub-channel) is erroneous, the other parts may be able to get over that interference. This situation happens in ISM band. 900MHz, 2.4GHz, 5GHz. As it is license-free, there are many technologies crowded in that band

21. Frequency Hopping (FH) SS Pick a set of frequencies within a band At each time slot, pick a new frequency –Each frequency has the bandwidth of the original signal Dwell time is the time spent using one frequency Spreading code determines the hopping sequence –Must be shared by sender and receiver (e.g. standardized) –Usually frequency determined by a pseudorandom generator function with a shared seed Time Frequency In FH technique, there are multiple subchannels, and the TX selects a particular subchannel at each interval by a given hopping sequence The hopping sequence is determined by a seed to pseudorandom generator and the seed should be shared by TX and RX

22. Direct Sequence SS (DSSS) Each bit represented by multiple chips using spreading code Spreading code spreads signal across wider frequency band –In proportion to number of bits used –10 chip spreading code spreads signal across 10 times bandwidth of 1 bit code (of original message) One method: –Combine input with spreading code using XOR –Data rate becomes multiplied by the length of spreading code The 2 nd technique, DSSS is more popular. Here, we have a chip sequence or spreading code. The spreading code is a fixed number of chips (they are similar to bits) We multiply or XOR two streams: original bit stream and spreading code E.g. if the input bit of data is 1, we invert the spreading code and do not invert the spreading code otherwise Suppose the spreading code is a 10 chip sequence. If data rate is n bps, the DSSS transmits 10*n chips per second instead of n bits per sec

23. This illustrates how DSSS works when the spreading code is a 8 chip sequence, -1-1-11-1111 (from right to left in the figure) In the circle, what happens is multiplication, so the 1 st data bit leaves the spreading code intact while the 2 nd bit inverts the spreading code the binary digital signal is often formulated by (1,-1) pair instead of (1,0) pair. However, there is no essential difference and I will explain in terms of (1,-1) in this slide On the receipt of the chip sequence, the RX just again multiplies it with the spreading code again. Then the original bit stream is restored

24. DSSS Properties Since each bit is sent as multiple chips, you need more bps bandwidth to send the signal –Number of chips per bit is called the spreading ratio We need more spectral bandwidth to do this –Spreading the signal over the spectrum Advantage is that transmission is more resilient –DSSS signal will look like noise in a narrow band –Can lose some chips in a word and recover easily Multiple users can share bandwidth (easily) –Use a different chipping sequence –CDMA In the previous slide, the spreading code is a 8 bit chip sequence. If we use X bandwidth for original data of n bps, now we need 8*X BW for 8*n chips per second By spreading its energy over 8*X BW, even if there is some error, we may be able to restore the original bit stream If every user can have a different and orthogonal spreading code, they can transmit individually at the same time over the same frequency band, so-called CDMA

25. SS Discussion Spread spectrum is very widely used –Effectively resilient against noise and multipath –Multiple transmitters can use the same frequency range FCC requires the use of SS in ISM band –If signal is above a certain power level Is also used in some 802.11 versions In FH and DS techniques, we achieve a trade-off between bandwidth and robustness: using more BW and getting over noise and interference SS is especially required for communication environments where TX power should be limited. A number of wireless comm. technologies are sharing the ISM band. To lower the interference level of communications, FCC mandates SS for wireless comm. in ISM band and the maximum TX power.

26. Bit rate vs. BW in 802.11 The original 802.11 has two date rates: 1 and 2 Mbps We will consider 1 Mbps first 1 Mbps bit stream requires a baseband signal of B bandwidth between 0.5 MHz and 1MHz 802.11 adopts a naïve approach: 1MHz Wireless requires a bandpass signal, which occupies 2MHz Then there comes spread spectrum technique –11 chip Barker sequence Eventually, 22MHz bandwidth is needed for each channel for IEEE 802.11 Original 802.11 standardized in 1997 offers two bit rates: 1 and 2 Mbps For simplicity, let’s see how much BW is used for 1Mbps case In 802.11, the baseband signal for 1Mbps uses ample BW, 1MHz There are 11 channels in 802.11, each of which has its own carrier frequency. The bandpass signal for each channel occupies 2MHz Owing to SS technique, we need to transmit 11Mchips per sec instead of 1Mbps, which increases BW 11 times Finally, each channel uses 22MHz

27. 802.11 DSSS: how 1Mbps is spread X = “symbol” “Barker” sequence Result of multiplication Symbol time t s “1”“0” Chip time t c Due to the multiplication of a symbol with Barker code, the “rate-of-change” increases with a factor 11 This means that cycle rate increases from 1 MHz to 11 MHz In terms of spectrum, this means that after RF modulation the signal is spread from 2 MHz bandwidth to 22 MHz bandwidth 2 Mhz 22 Mhz This slide how a symbol (which is 1 bit with BPSK) is spread by 11 chip Barker sequence. Note that all the stations use the same Barker code, not CDMA The rate of change (BW) is multiplied 11 times due to DSSS Note that the power distribution around carrier freq. is quite flattened *Barker Code: 10110111000

28. Channel Allocation There are 11 channels in USA, which are depicted in the slide Each channel occupies 22MHz BW, and there are three non-overlapping channels: 1, 6, 11

29. Symbol in communications The original 802.11 has two date rates: 1 and 2 Mbps What about 2Mbps? There is another notion of symbol between a bit and BW If there are M kinds of symbols, a symbol can represent log 2 M bits Chips were transmitted using BPSK modulation. –Data rate was 1 Mbps (i.e. 11 Mchips/sec) –Extended to 2 Mbps by using a QPSK modulation Requires the detection of a ¼ phase shift What I have explained so far has one missing part: the concept of symbol. The bit rate in the earlier slides is actually the symbol rate. So if the symbol rate is n symbols per sec, the baseband signal requires from n/2 to n BW depending on the roll-off factor One symbol can represent multiple bits. BPSK has two symbols; so one symbol represents one bit, which is the 1Mbps in the previous slide QPSK has 4 symbols; so one symbol represents two bits, which is the 2Mbps case. It requires the same 22 MHz

30. Source Encoder Channel Encoder Mod- ulator User Source Decoder Channel Decoder Demod- ulator Message Signal Channel codeword Estimate of Message signal Estimate of channel codeword Received Signal Wireless Channel A Big Picture of wireless TX, RX

31. Source coding Purpose of source coding: to transform the information in the source into a digital form best suited for transmission Often, seeks to minimize the number of bits required to convey information –compression Voice, audio, video are primary targets What is source coding? If the original data is digital, we don’t need source coding However, as voice and video data are inherently analog, we have to digitize the original analog data, which is called source coding Typically, how to reduce the number of bits for the same analog data is of primary concern

32. Channel coding Forward error correction (FEC) add redundancy into the original info to protect them from bit errors due to interference and noise in transmission Input k bits  Output n bits –k/n code rate or (n,k) code rate Interleaving E.g. Reed-solomon (RS) coding, convolutional coding Source coding is important, but channel coding is even more important since it affects the effective bit rate of the wireless link Channel coding is also called FEC since it adds redundant info to original info to make the signal more robust to errors Normally, FEC is denoted by two parameters Sometimes FEC is done in conjunction with interleaving since bit errors are often happening in a burst

33. Example of 802.11a bit rate OFDM, 48 data subcarriers 1 subcarrier: 250K symbol rate 64QAM for each symbol in each subcarrier –One symbol: 6 bits 3/4 convolutional coding (FEC) 48 * 250K * 6 * 3/4 = 54Mbps Let’s analyze the highest bit rate of 802.11a, 54Mbps It employs OFDM, which uses multiple subcarriers Multiple bit streams are TXed in parallel, each of which TXs 250K symbols per sec Using 64QAM modulation, one symbol represents 6 bits Also, it uses ¾ FEC

34. Radio propagation vs Frequency Surface wave –Less than 3MHz Sky wave (ionospheric refraction) –3 and 30 MHz Direct wave (line-of-sight) –Greater than 30Mhz –reflection is important Our main focus is on direct wave –UHF and SHF are subject to direct wave –Ultra High Frequency 300–3000 MHz –Super High Frequency 3–30 GHz 34 c=λf c: speed of light λ: wavelength f: frequency

35. Radio propagation mechanisms: when direct wave is dominant Free space propagation Reflection - occurs when signal encounters a surface that is large relative to the wavelength of the signal Diffraction - occurs at the edge of an impenetrable body that is large compared to wavelength of radio wave Scattering – occurs when incoming signal hits an object whose size in the order of the wavelength of the signal or less 35 reflection scattering diffraction

36. Those lead to multi-path propagation 4 mechanisms –Free space propagation –Reflections –Scattering –Diffraction At receiver (RX) –These components arrive with different delays –These components are combined at RX –Sometimes they add up constructively or destructively 36

37. At RX What happens is… 37

38. General propagation model Path-loss + slow fading + fast fading In free space, received power attenuates like 1/d 2 38

39. Large scale fading A large obstruction such as a hill or large building obscures the main signal path between the transmitter and the receiver Aka, slow fading, shadowing Relatively slow change in signal power 39

40. Small scale fading caused by the superposition or cancellation of multipath propagation Aka, fast fading, multipath fading factors –Multipath propagation. –Speed of the mobile. –Speed of the surrounding objects. –Transmission bandwidth of the signal 40

41. Two main options in fast fading Rician fading –Dominant signal over the line-of-sight (LOS) path –K-factor is defined as the ratio of signal power in dominant component over the (local-mean) scattered power Rayleigh fading –Most representative of fast fading –No dominant signal 41

42. More simplified model Received signal strength is proportional to 1/d n n: path-loss exponent –Normally n is between 2 and 8 –Often, n = 4 in simulation 42 Rapapport, “wireless communications: principles and practice”

43. 43 Signal Propagation Ranges Distance from transmitter sender transmission detection interference Transmission range –communication possible –low error rate Detection range –detection of the signal possible, but communication may not be possible due to high error rate Interference range –signal may not be detected –signal adds to the background noise

44. Antennas Electrical conductor (or system of..) used to radiate electromagnetic energy or collect electromagnetic energy Transmission –RF signal energy from transmitter –Converted to electromagnetic (EM) energy –By antenna –Radiated into surrounding environment Reception –Electromagnetic energy impinging on antenna –Converted to radio frequency electrical energy –Fed to receiver In wireless communications, an antenna is a key player At TX, electric signal energy is transformed into EM energy At RX, the reverse process is performed 44

45. antennas electromagnetic (EM) fields –Tend to propagate –As waves –At speed of light EM waves can travel in empty space or can be confined (guided) by structures A transition structure between guided EM fields and free waves As a circuit: a transformer between terminals & free space radiation To fully understand an antenna, we need to know EM field theory When it is confined, there is an electric current in the circuit-type structure 45

46. At 2.4GHz, λ = 12.5cm by c=fλ So half-wave dipole antenna is 6.25cm Dielectric constant can be a factor Quarter-wave antennas are also popular, which requires ¼ length of wavelength. Dipole antenna 46

47. Radiation Pattern Power radiated in all directions Not same performance in all directions Isotropic antenna is (theoretical) point in space –Radiates in all directions equally –Gives spherical radiation pattern Let’s see how EM waves are radiated from the antenna In real antennas, the radiation pattern is not same for all directions Suppose there is an ideal antenna, isotropic antenna. An EM wave is radiated to all the possible directions of the sphere. The isotropic antenna is often used as a reference. 47

48. Antenna’s directivity Isotropic Omni-directional –Radiation in every direction on azimuth/horizontal plane Directional –Narrower beamwidth, higher gain In reality, every antenna has different level of radiation for each direction To assess the directivity of an antenna, we measure the signal power of an antenna in all 3-D directions and compare with that of the isotropic antenna. The antennas in most of the low cost wireless devices are omni- directional 48

49. Omni vs directional 49

50. Antenna (directed or sectorized) E.g. 3 sectors per BS in cellular networks side view (xy-plane) x y side view (yz-plane) z y top view (xz-plane) x z top view, 3 sector x z top view, 6 sector x z directional antenna sectorized antenna 50