MITP 413: Wireless Technologies Week 4

MITP 413: Wireless Technologies Week 4
Michael L. Honig Department of EECS Northwestern University January 2007

Channel Characterizations: Time vs. Frequency
Frequency-domain description Time-domain description Multipath channel Amplitude attenuation, Delay (phase shift) input s(t) is a sinusoid “narrowband” signal The impulse response is analogous to echoes heard when clapping your hands in an auditorium. r(t) s(t) Multipath channel time t time t multipath components input s(t) is an impulse (very short pulse) “wideband” signal (Note: an impulse has zero duration and infinite bandwidth!)

Two-Ray Impulse Response
reflection (path 2) direct path (path 1) s(t) reflection is attenuated r(t)  time t time t  = [(length of path 2) – (length of path 1)]/c

Pulse Width vs. Bandwidth
Power signal pulse bandwidth = 1/T Narrowband frequency time T signal pulse What happens to the signal as the bandwidth goes to zero? To infinity? Power bandwidth = 1/T Wideband time frequency T

Bandwidth and Multipath Resolution
reflection (path 2) direct path (path 1) multipath components are resolvable signal pulse  (delay spread) signal pulse T >   T <  T Wide bandwidth  high resolution Receiver can clearly distinguish two paths. Narrow bandwidth  low resolution Receiver cannot distinguish the two paths.

Bandwidth and Multipath Resolution
reflection (path 2) direct path (path 1) multipath components are resolvable signal pulse The receiver can easily distinguish the two paths provided that they are separated by much more than the pulse width T. Since the signal bandwidth B ≈ 1/T, this implies B >> 1/, or B >> Bc . . What are the advantages of having a wideband signal with resolvable multipath?  Wide bandwidth  high resolution Receiver can clearly distinguish two paths.

Multipath Resolution and Diversity
reflection (path 2) direct path (path 1) multipath components are resolvable signal pulse Each path may undergo independent fading (i.e., due to Doppler). If one path is faded, the receiver may be able to detect the other path. In the frequency domain, this corresponds to independent fading in different coherence bands.  Wide bandwidth  high resolution Receiver can clearly distinguish two paths.

Bandwidth and Geolocation
reflection delay  = 2 x distance/c delay  s(t) s(t) r(t) r(t) time t Narrow bandwidth pulse time t High bandwidth pulse

Bandwidth and Geolocation
reflection delay  = 2 x distance/c s(t) The resolution of the delay measurement is roughly the width of the pulse. Low bandwidth  wide pulse  low resolution High bandwidth  narrow pulse  high resolution r(t) time t Ex: If the delay measurement changes by 1 microsec, the distance error Is c x 10-6 = 300 meters!

Power-Delay Profile Received power vs. time in response to a transmitted short pulse. delay spread  For cellular systems (outdoors), the delay spread is typically a few microseconds.

Two-Ray Impulse Response
reflection (path 2) direct path (path 1) s(t) reflection is attenuated r(t)  time t time t

Urban Multipath s(t) r(t) time t time t r(t) different location for receiver time t Spacing and attenuation of multipath components depend on location and environment.

Delay Spread and Intersymbol Interference
s(t) r(t) Multipath channel time t time t Time between pulses is >> delay spread, therefore the received pulses do not interfere. r(t) s(t) Multipath channel time t Time between pulses is < delay spread, which causes intersymbol interference. The rate at which symbols can be transmitted without intersymbol interference is 1 / delay spread.

Coherence Bandwidth channel gain frequency f1 f2
coherence bandwidth Bc channel gain Frequencies far outside the coherence bandwidth are affected differently by multipath. frequency f1 f2 The channel gain is approximately constant within a coherence bandwidth Bc. Frequencies f1 and f2 fade independently if | f1 – f2 | >> Bc. If the signal bandwidth < coherence bandwidth Bc, then the channel is called flat fading, and the transmitted signal is regarded as narrowband. If the signal bandwidth > Bc, then the channel is called frequency-selective and the signal is regarded as wideband.

Coherence Bandwidth and Diversity
signal power (wideband) coherence bandwidth Bc channel gain Frequencies far outside the coherence bandwidth are affected differently by multipath. frequency f1 f2 Frequency-selective fading: different parts of the signal (in frequency) are affected differently by fading. What are advantages and disadvantages of frequency-selective fading?

Coherence Bandwidth and Diversity
signal power (wideband) coherence bandwidth Bc channel gain Frequencies far outside the coherence bandwidth are affected differently by multipath. frequency f1 f2 Frequency-selective fading: different parts of the signal (in frequency) are affected differently by fading. Wideband signals exploit frequency diversity. Spreading power across many coherence bands reduces the chances of severe fading. Wideband signals are distorted by the channel fading (distortion causes Intersymbol interference). What are advantages and disadvantages of frequency-selective fading?

Narrowband Signal signal power channel (narrowband) gain frequency f1
coherence bandwidth Bc channel gain Frequencies far outside the coherence bandwidth are affected differently by multipath. frequency f1 f2 Flat fading: the narrowband signal fades uniformly, hence does not benefit from frequency diversity. For the cellular band, Bc is around 100 to 300 kHz. How does this compare with the bandwidth of cellular systems?

Coherence Bandwidth and Delay Spread
frequency channel gain coherence bandwidth Bc delay spread  channel gain delay spread  In general, the shape of the frequency response depends on the timing and position of the multipath. coherence bandwidth Bc frequency Coherence bandwidth is inversely proportional to delay spread: Bc ≈ 1/.

Fading Experienced by Wireless Systems
Standard Flat/Freq.-Sel. Fast/Slow AMPS Flat Fast IS Flat Fast GSM F-S Slow IS-95 (CDMA) F-S Fast 3G F-S Slow to Fast (depends on rate) F-S Slow Bluetooth F-S Slow

Propagation and Handoff
Received Signal Strength (RSS) from right BST from left BST unacceptable (call is dropped) time

Received Signal Strength (RSS) from right BST with handoff handoff threshold from left BST unacceptable (call is dropped) time

Received Signal Strength (RSS) from right BST with handoff handoff threshold from left BST RSS margin unacceptable (call is dropped) time time needed for handoff

Received Signal Strength (RSS) from right BST handoff threshold from left BST RSS margin unacceptable (call is dropped) time time needed for handoff

Handoff Threshold Received Signal Strength (RSS) time
from right BST handoff threshold from left BST RSS margin unacceptable (call is dropped) time time needed for handoff What can cause a call to be dropped during handoff? Handoff threshold too high  too many handoffs (ping pong) Handoff threshold too low  dropped calls are likely Threshold should depend on slope on vehicle speed (Doppler).

Handoff Measurements (3G)
Mobile maintains a list of neighbor cells to monitor. Mobile periodically measures signal strength from BST pilot signals. Mobile sends measurements to network to request handoff. Handoff decision is made by network. Depends on available resources (e.g., channels/time slots/codes). Handoffs take priority over new requests (why?). Hysteresis needed to avoid handoffs due to rapid variations in signal strength.

Handoff Decision Depends on RSS, time to execute handoff, hysteresis, and dwell (duration of RSS) Proprietary methods Handoff may also be initiated for balancing traffic. 1G (AMPS): Network Controlled Handoff (NCHO) Handoff is based on measurements at BS, supervised by MSC. 2G, GPRS: Mobile Assisted Handoff (MAHO) Handoff relies on measurements at mobile Enables faster handoff Mobile data, WLANs (802.11): Mobile Controlled Handoff (MCHO) Handoff controlled by mobile

Soft Handoff (CDMA) ”Make before break”
DURING AFTER MSC MSC MSC BSC BSC BSC BSC BSC BSC Hard Handoff (TDMA) MSC MSC MSC BSC BSC BSC BSC BSC BSC

SINR Measurements: 1xEV-DO
drive test plots

Why Digital Communications?
1G (analog)  2G (digital)  3G (digital) Digitized voice requires about 64 kbps, therefore the required bandwidth is >> the bandwidth of the voice signal (3—4 kHz)!

Why Digital Communications?
1G (analog)  2G (digital)  3G (digital) Digitized voice requires about 64 kbps, therefore the required bandwidth is >> the bandwidth of the voice signal (3—4 kHz)! Can combine with sophisticated signal processing (voice compression) and error protection. Greater immunity to noise/channel impairments. Can multiplex different traffic (voice, data, video). Security through digital encryption. Flexible design possible (software radio). VLSI + special purpose digital signal processing  digital is more cost-effective than analog!

Binary Frequency-Shift Keying (FSK)
Bits:

Quadrature Phase Shift Keying (QPSK)
Bits:

Binary Phase Shift Keying (BPSK)
Bits: Baseband signal

Amplitude Shift Keying (4-Level ASK)
Bits: Baseband signal symbol duration

Baseband  RF Conversion
Passband (RF) signal Baseband signal sin 2fct time X T fc is the carrier frequency Why not transmit the baseband signal? Power signal bandwidth is roughly 1/T Power frequency frequency  0 fc

Why Modulate?

Why Modulate? The baseband spectrum is centered around f=0. Without modulation all signals would occupy low frequencies and interfere with each other. It is difficult to build effective antennas at low frequencies since the dimension should be on the order of a wavelength. Low frequencies propagate further, causing more interference.

Selection Criteria How do we decide on which modulation technique to use? Which of these criteria are especially important for wireless channels (as opposed to wired channels)?

Selection Criteria How do we decide on which modulation technique to use? Performance: probability of error Pe. Probability that a 0 (1) is transmitted and the receiver decodes as a 1 (0). Complexity: how difficult is it for the receiver to recover the bits (demodulate)? FSK was used in early voiceband modems because it is simple to implement. Bandwidth or spectral efficiency: bandwidth (B) needed to accommodate data rate R bps, i.e., R/B measured in bits per second per Hz. Power efficiency: energy needed per bit to achieve a satisfactory Pe. Performance in the presence of fading, multipath, and interference. Which of these criteria are especially important for wireless channels (as opposed to wired channels)?

Example: Binary vs. 4-Level ASK
Rate = 1/T symbols/sec Bandwidth is roughly 1/T Hz Bandwidth efficiency = 1 bps/Hz Rate = 2/T symbols/sec Bandwidth is roughly 1/T Bandwidth efficiency = 2 bps/Hz What about power efficiency?

Noisy Baseband Signals
Rate = 1/T symbols/sec Bandwidth is roughly 1/T Hz Bandwidth efficiency = 1 bps/Hz Power =A2 (amplitude squared). Rate = 2/T symbols/sec Bandwidth is roughly 1/T Bandwidth efficiency = 2 bps/Hz Power = (A2 + 9A2)/2 = 5A2 What about probability of error vs transmitted power?

Probability of Error 4-ASK BPSK 7 dB (factor of 5)
Signal-to-Noise Ratio (dB)

How to Increase Bandwidth Efficiency?

How to Increase Bandwidth Efficiency?
Increase number of signal levels. Use more bandwidth efficient modulation scheme (e.g., PSK). Apply coding techniques: protect against errors by adding redundant bits. Note that reducing T increases the symbol rate, but also increases the signal bandwidth. There is a fundamental tradeoff between power efficiency and bandwidth efficiency.

The Fundamental Question
Given: B Hz of bandwidth S Watts of transmitted signal power N Watts per Hz of background noise (or interference) power What is the maximum achievable data rate? (Note: depends on Pe.)

Claude Shannon (1916-2001) Father of “Information Theory”
His 1948 paper “A Mathematical Theory of Communications” laid the foundations for modern communications and networking. “Shannon was the person who saw that the binary digit was the fundamental element in all of communication. That was really his discovery, and from it the whole communications revolution has sprung.” -- R. Gallager (MIT) Other contributions and interests: digital circuits, genetics, cryptography, investing, chess-playing computer, roulette prediction, maze-solving, unicycle designs, juggling

Shannon’s Channel Coding Theorem (1948)
noise Information Source Encoder Channel Decoder bits input x(t) output y(t) Estimated bits Information rate: R bits/second Channel capacity: C bits/second R < C  There exists an encoder/decoder combination that achieves arbitrarily low error probability. R > C  The error probability cannot be made small.

Shannon Capacity Channel capacity: C = B log(1+S/N) bits/second
noise Information Source Encoder Channel Decoder bits input x(t) output y(t) Estimated bits Channel capacity: C = B log(1+S/N) bits/second B= Bandwidth, S= Signal Power, N= Noise Power No fading

Observations “There exists” does not address complexity issues.
As the rate approaches Shannon capacity, to achieve small error rates, the transmitter and (especially) the receiver are required to do more and more computations. The theorem does not say anything about delay. To achieve Shannon capacity the length of the transmitted code words must tend to infinity! The previous formula does not apply with fading, multipath, frequency-selective attenuation. It has taken communications engineers more than 50 years to find practical coding and decoding techniques, which can achieve information rates close to the Shannon capacity.

Example: GSM Bandwidth = 200 kHz, S/I = 9 dB = 7.943
C = 200,000 x log(8.943) ≈ 632 kbps This is what would be achievable in the absence of fading, multipath, etc. Currently, the rate is about 270 kbps. Is the Shannon formula relevant?

Data Rates for Deep Space Applications
Mariner: 1969 (Mars) Pioneer 10/11: 1972/3 (Jupiter/Saturn fly-by) Voyager: (Jupiter and Saturn) Planetary Standard: 1980’s (military satellite) BVD: “Big Viterbi Decoder” Galileo: 1992 (Jupiter) (uses BVD) Turbo Code: 1993

TYPES ALL PSK (PSK Type Summary Slide)

1000 Symbols Per Second x 1 Bit Per Symbol = 1000 Bits Per Second
BPSK Bitream 0 1000 Bits Per Second 1000 Symbols (Phases) Per Second Now in an actual radio system, the modulator may transmit thousands of symbols each second. 1000 Symbols Per Second x 1 Bit Per Symbol = 1000 Bits Per Second

1000 Symbols Per Second x 1 Bit Per Symbol = 1000 Bits Per Second
BPSK Bitream 1 1000 Bits Per Second 1000 Symbols (Phases) Per Second For example, if the modulator transmits 1000 symbols, or phases, each second, then with Binary PSK, since each symbol represents 1 bit, the data rate is 1000 bits per second. 1000 Symbols Per Second x 1 Bit Per Symbol = 1000 Bits Per Second

1000 Symbols Per Second x 2 Bits Per Symbol = 2000 Bits Per Second
QPSK Bitream 00 2000 Bits Per Second 1000 Symbols (Phases) Per Second But if we use 4-PSK, or QPSK, then each symbol represents 2 bits, and the data rate is 2000 bits per second. 1000 Symbols Per Second x 2 Bits Per Symbol = 2000 Bits Per Second

QPSK Bitream 10 2000 Bits Per Second 1000 Symbols (Phases) Per Second (3-bit bitstream animation continues at random) 1000 Symbols Per Second x 2 Bits Per Symbol = 2000 Bits Per Second

8PSK Bitstream 000 3000 Bits Per Second 1000 Symbols (Phases) Per Second And if we use 8-PSK, which conveys 3 bits for each symbol, then the data rate would be 3000 bits per second. 1000 Symbols Per Second x 3 Bits Per Symbol = 3000 Bits Per Second

8PSK Bitstream 001 3000 Bits Per Second 1000 Symbols (Phases) Per Second (3-bit bitstream animation continues at random) 1000 Symbols Per Second x 3 Bits Per Symbol = 3000 Bits Per Second

8PSK Bitstream 111 3000 Bits Per Second 1000 Symbols (Phases) Per Second (3-bit bitstream animation conlcudes) 1000 Symbols Per Second x 3 Bits Per Symbol = 3000 Bits Per Second

Colored Balls 2 The width of the funnel tube is analogous to the available bandwidth. Now the narrower the funnel, the longer it takes to get the jellybeans through the funnel. So, the less bandwidth we have, the longer it takes to transmit our symbols.

Binary Phase Shift Keying (BPSK)
Bits: Baseband signal

Minimum Bandwidth (Nyquist) Pulse Shape
This pulse has the minimum bandwidth for a given symbol rate. Given bandwidth B, the maximum symbol rate without intersymbol interference (ISI) is B, the “Nyquist rate”.

Power signal pulse bandwidth B = 1/T Narrowband frequency time 2T signal pulse Power bandwidth B = 1/T Wideband time frequency 2T

Shifted Nyquist Pulses
Bits:

Baseband Waveform (Nyquist Signaling)
. . . Bits: . . .

Baseband  RF Conversion
Passband (RF) signal Baseband signal sin 2fct X T time fc is the carrier frequency Why not transmit the baseband signal? Power signal bandwidth is roughly 1/T Power frequency  0 fc frequency

Passband Signal with Different Carrier Frequencies

time Perfect synchronization T time Offset causes severe ISI!

Raised Cosine Pulses Minimum BW frequency time

Raised Cosine Pulses frequency time
Minimum BW 50% excess BW 100% excess BW frequency time Excess bandwidth= (Total bandwidth – Nyquist bandwidth)/Nyquist bandwidth

Circle Vocoder And for voice communications, this data rate depends on the data rate generated by the vocoder.

Blocks Transition (Transitional Slide)

Blocks Stretched 8000 Bits Per Second
The vocoder selected by the Hughes engineers used the same technology that was selected for the North American digital cell phone standard IS54. That vocoder generates 8000 bits per second. But we actually need to transmit significantly more than this because...

Additional Bits Additional Bits Error Correction Control Information
... we need to insert additional bits to guard against errors and to provide overhead control information. The control information tells the transmitter and receiver operational information like which ground station to use, how much power to use, the identity of the person using the service, billing information, and so forth. So, in reality, the system needs to support a data rate significantly larger than 8,000 bits per second – something in the range of approximately bits per second. Channel Ground Station Power Identity Billing

6000 Hz Available Bandwidth
In our case, the FCC has given us 6000 Hz. We can estimate the maximum number of symbols, which we can transmit every second, by applying one of the basic principles of digital communications, sometimes referred to as Nyquist's Theorem. Nyquist's Theorem says that, roughly speaking, we can count on being able to send about 4000 symbols per second over a 6000 Hz channel. Nyquist’s Theorem: Can transmit 4000 symbols per second through a 6000 Hz channel

Colored Balls 2 5000 symbols per second would be quite difficult, and 4000 symbols per second is relatively easy. Nyquist’s Theorem: Can transmit 4000 symbols per second through a 6000 Hz channel

4000 bps < 8000 bps (Vocoder rate)
BPSK 4000 < 8000 BPSK: 1 Bit Per Symbol 4000 Bits Per Second (bps) 4000 bps < 8000 bps (Vocoder rate) BPSK So, let's assume that we are sending 4000 symbols per second. If we use Binary PSK, then we are transmitting 1 bit for each symbol, so the data rate in that case is 4000 bits per second. This is far below the 8000 bits per second generated by the vocoder, which means that we cannot use BPSK to transmit our voice signal.

QPSK 8000 BPS QPSK: 2 Bits Per Symbol
2 X 4000 = 8000 Bits Per Second (bps) 8000 bps = Vocoder rate Need more bits for error correction and control! QPSK So now let's consider 4-PSK, or QPSK. In that case we are transmitting 2 bits per symbol, and with 4000 symbols per second, that gives a data rate of 2 times 4000, or 8000 bits per second. Recall that we need more than this, because on top of the vocoder rate of 8000 bits per second, we need to add additional bits to correct errors, and for control. This means that we cannot use QPSK either.

8PSK 12000 BPS 8PSK: 3 Bits Per Symbol
3 X 4000 = 12,000 Bits Per Second (bps) 8000 bps bps Vocoder rate + Error Correction and Control 8PSK Moving then to 8-PSK, this gives us 3 bits per symbol, and with 4000 symbols per second, that gives a data rate of 3 times 4000, or 12,000 bits per second. This will give us the 8000 bits per second from the vocoder, plus 4000 bits per second for correcting and detecting errors, and for control. For this type of application, an additional 4000 bits per second beyond the vocoder rate gives us a reasonable margin for errors and control, so that we conclude that a voice service over this 6000 Hz channel can be supported with 8-PSK.

16 phases: 4 Bits Per Symbol 4 x 4000 = 16,000 bps
16 PSK BPS 16 phases: 4 Bits Per Symbol 4 x 4000 = 16,000 bps More than enough for vocoder rate + overhead But couldn't we also transmit more than 8 phases, or equivalently, more than 3 bits for every symbol? For example, suppose that we transmit 4 bits per symbol. This would give us a bit rate of 4 times 4000, or 16,000 bits per second, which is more than we need to support a voice service with our 8000 bit per second vocoder. We could do this, but it would make the system more complicated.

MOTION BLUR As explained in the last video, the problem with increasing the number of bits per symbol is that we have to increase the number of phases or symbols to transmit, and these become harder to distinguish at the receiver. Namely, 4 bits per symbol means that we have to choose from among 16 possible phases, and to avoid confusing these symbols at the receiver, we need to transmit with more power.

90˚ QPSK w/Bit Labels 0˚ 180˚ 270˚ Because we can choose from one of four phases, each phase can be used to represent two bits, instead of one as before. This is shown in the figure by labeling each phase with two bits. Namely, zero phase corresponds to transmitting 00, shown in green, 90 degrees corresponds to transmitting 11, shown in purple, 180 degrees corresponds to 10, shown in orange, and 270 degrees corresponds to 01, shown in red. (Bit labels fade-in one at a time)

90˚ 8PSK 45˚ 135˚ 0˚ 180˚ 225˚ 270˚ 315˚ Notice that the angle of each flag position again corresponds directly to the starting phase of the radio wave. (Each pair of colored dots connected by a line wipe down successively)

QPSK Signal Constellation
amplitude = 1 x 1 x x x

“Rotated” QPSK Signal Constellation
amplitude = 1 x x 1 x x

In-Phase/Quadrature Components
x (a,b)  a sin 2fct + b cos 2fct 1 x x b is the “in-phase” signal component a is the “quadrature” signal component x

In-Phase/Quadrature Components
x x 1 x x

Example Constellations
quadrature QPSK BPSK in-phase x x x x x x 16-QAM quadrature 8-PSK x x x x For the 16-QAM signal constellation, what signal does a particular point represent? x x x x x x x x x x x x x x x in-phase x x x x x

Quadrature Modulation
in-phase signal even bits Baseband Signal X Split: Even/Odd source bits transmitted (RF) signal + Baseband Signal X odd bits quadrature signal

Modulation for Fading Channels
Problems: 1. Amplitude variations (shadowing, distance, multipath) 2. Phase variations 3. Frequency variations (Doppler) Solution to 1: Avoid amplitude modulation Power control Solution to 2 & 3: Avoid phase modulation (use FSK) “Noncoherent” demodulation: does not use phase reference Differential coding/decoding “Coherent” demodulation: Estimate phase shifts caused by channel. Increase data rate/Doppler shift ratio

Binary Frequency-Shift Keying (FSK)
Bits:

Minimum Shift Keying (MSK)
Bits: Frequencies differ by ½ cycle Used in GSM

Binary Differential Modulation
(i+1)st bit = 0: 0o phase shift waveform for ith symbol (i+1)st bit = 1: 180o phase shift

Binary Differential Modulation
(i+1)st bit = 0: 0o phase shift waveform for ith symbol (i+1)st bit = 1: 180o phase shift Drawback: a detection error for the ith bit propagates to the (i+1)st bit.

Example: DQPSK x x x x x x x x constellation for ith symbol
bits: 00 x 10 x x 01 x x x 11 x x constellation for ith symbol constellation for (i+1)st symbol Used in IS-136

Coherent Phase Modulation
Receiver estimates phase offset More complicated than noncoherent (e.g., differential) modulation. Receiver requires a pilot signal. Transmit known symbols, measure phase. Pilot symbols are overhead (not information bits).

Probability of Error

Probability of Error with Fading

Orthogonal Frequency Division Multiplexing (OFDM)
Modulate Carrier f1 substream 1 Split into M substreams Modulate Carrier f2 substream 2 source bits substream M OFDM Signal + Modulate Carrier fM

OFDM Spectrum … … f1 f2 f3 f4 f5 f6  0
Total available bandwidth Data spectrum for a single carrier Power … … f1 f2 f3 f4 f5 f6 frequency  0 subchannels M “subcarriers, or subchannels, or tones” “Orthogonal” subcarriers  no cross-channel interference.

OFDM Example: 802.11a 20 MHz bandwidth, M=64 (48 for data payload)
Subchannel bandwidth = 20 MHz / 64 = kHz Symbol rate / subchannel = 250 kilosymbols/sec Total symbol rate = 64 x 250 x 103 = 16 Msymbols/sec Bit rate? 16 QAM/subchannel  4 bits/symbol x 250 x 103 = 1 Mbps/subchannel, or 64 Mbps total 64 QAM/subchannel  6 bits/symbol x 250 x 10^3 = 1.5 Mbps/subchannel, or 96 Mbps total Includes overhead (synchronization, error correction, control) Actual data rate: 36 / 54 Mbps

Why OFDM? Single-carrier transmission also possible: 250 x 10^3 symbols/sec in kHz means 16 Msymbols/sec would be transmitted in 20 MHz.

Why OFDM? Exploits frequency diversity channel gain
Flat fading on each subchannel simplifies receiver (no multipath/ISI) Frequency agility: can avoid “bad” parts of channel (requires feedback). Drawback: high peak-to-average power. subcarrier bandwidth < coherence bandwidth Bc signal power (wideband) channel gain Frequencies far outside the coherence bandwidth are affected differently by multipath. f1 frequency f2 bits are coded across subcarriers Single-carrier transmission also possible: 250 x 10^3 symbols/sec in kHz means 16 Msymbols/sec would be transmitted in 20 MHz.

MITP 413: Wireless Technologies Week 4

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