lect 16 ofdm - sonoma state university · ofdm divides each channel into many narrower subcarriers....
TRANSCRIPT
OFDM Notes
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EE 442 – Spring 2017 Lecture 16
Orthogonal Frequency Division MulAplexing (OFDM) is a digital mulA-‐carrier modulaAon technique extending the concept of single subcarrier modulaAon by using mulAple sub-‐carriers over the channel. Rather than transmit a high-‐rate stream of data with a single carrier, OFDM makes use of a large number of closely spaced orthogonal sub-‐carriers that are transmiAed in parallel. Each sub-‐carrier is modulated with a convenEonal digital modulaEon scheme (such as QPSK, 16QAM, etc.) at a lower symbol rate. However, the combinaEon of many sub-‐carriers enables data rates similar to convenEonal single-‐carrier modulaEon schemes using equivalent bandwidths.
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OFDM Benefits
Q: What are the benefits of using OFDM? A: The first reason is spectral efficiency, also called bandwidth efficiency. What that term really means is that you can transmit more data faster in a given bandwidth in the presence of noise. The measure of spectral efficiency is bits per second per Hertz, or bps/Hz. For a given chunk of spectrum space, different modulaEon methods will give you widely varying maximum data rates for a given bit error rate (BER) and noise level. Simple digital modulaEon methods like amplitude shiX keying (ASK) and frequency shiX keying (FSK) are simple but don’t give the best BER performance. BPSK and QPSK do much beAer. QAM is very good but more suscepEble to noise and low signal levels issues. Code division mulEple access (CDMA) methods are even beAer performance. But none is beAer than OFDM with respect to aAaining the maximum data capacity out of a given channel bandwidth. It approaches the Shannon limit defining channel capacity C in bits per second (bps).
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MulAcarrier CommunicaAon Systems (Uses MulAple Oscillators)
Answer: It is nearly impossible to keep mulAple oscillators in synchronizaAon with each other. And it is difficult to have hundreds of oscillators in a pracAcal system.
What is the problem with this architecture?
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Discrete MulAtone (aka Frequency Division MulAplexing)
POTS
The basic idea of Discrete MulAtone (DMT) is to split the available bandwidth into a large number of sub-‐channels. ADSL2 is an example applicaAon of DMT.
DMT uses available frequencies on the telephone line and splits them into 256/512 equal sized frequency bins of 4.3125 kHz each.
ADSL2
hAp://educypedia.karadimov.info/computer/modemadsl.htm
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Can we get rid of the guard-‐bands in DMT?
Recall from Fourier Transform:
OFDM Spectrum
YES
Spectrum of one OFDM Sub-‐channel
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OFDM Packs Sub-‐channels Closer Together
OFDM divides each channel into many narrower subcarriers. The spacing is such that these subcarriers are orthogonal so they don’t interfere with one another in spite of the lack of guard bands between them. This results from the subcarrier spacing equal to the reciprocal of symbol time. All subcarriers have a complete number of sine wave cycles that sum to zero upon demodulation.
Four sub-‐channels shown
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Spectrum of OFDM Signal Transmission
8 sub-‐carriers
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In OFDM the Sub-‐Carriers are Or_hogonal
Parallel data streams (all at lower data rates) ⇒ large number of subcarriers without guard bands
Data coding based upon amplitude modulaEon
MulEple subcarriers are mulEplexed into one symbol
Subcarriers are computed using IFFT (i.e., Inverse Fast Fourier Transform)
They are spaced at precise frequencies and phases This spacing selecEon provides orthogonality
Orthogonality Principle results in close packing of subcarriers
Provides for mulA-‐user diversity
SynchronizaEon using pilot signals
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OFDM Summary
Serial Data Source
Serial to
Parallel Encode IFFT
Parallel to
Serial
Cyclic Prefix
OFDM Signal
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What Makes OFDM Possible?
Q: How is OFDM implemented in the real world? A: OFDM is accomplished using digital signal processing (DSP). You can program IFFT and FFT math funcEons on any fast PC, but it is usually done using a special DSP IC, or an appropriately programmed FPGA, or hardwired digital logic. With today’s super-‐fast chips, even complex math rouEnes like the FFT are relaEvely easy to implement. In brief, you can put it all on a single IC chip.
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What Does Orthogonality Mean?
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Subcarrier Orthogonality
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Example: OFDM Subcarriers in 802.11a/g Wi-‐Fi Each 20 MHz channel, whether it's 802.11a/g/n/ac, is composed of 64 sub-‐carriers spaced 312.5 KHz apart. This spacing is chosen because we use 64-‐point FFT sampling. 802.11a/g use 48 subcarriers for data, 4 for pilot, and 12 as null subcarriers. 802.11n/ac use 52 subcarriers for data, 4 for pilot, and 8 as null.
A standard Wi-Fi symbol is 4µs, composed of a 3.2µs IFFT useful symbol duration plus 0.8µs guard interval. (When using a shorter guard interval of 0.4µs then the total symbol time is reduced to 3.6µs).
Wi-‐Fi channels
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OFDM Sub-‐Carriers with Guard-‐bands & Pilot Signals
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The MulApath Problem in Wireless
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Path Losses and Fading In wireless telecommunicaEons, mulApath is the propagaEon phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of mulEpath include atmospheric ducEng, ionospheric reflecEon and refracEon, and reflecEon from water bodies and terrestrial objects such as mountains and buildings. Path losses generally vary inversely with distance, namely, ∼ 1/dn, where n is approximately 2, but can be as high as n = 4. MulApath causes mulApath interference including construcAve and destrucAve interference, and phase shieing of the signal. DestrucAve interference causes fading.
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OFDM Performs To Reduce the Problem of Fading MulEpath destroys orthogonality. The figure below shows two copies of the signal (direct path and reflected path with Eme difference).
Time delay is evident
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Adding a Cyclic Prefix
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Cyclic Prefix
Copy
A guard-‐Eme interval is used to increase the robustness of OFDM. A cyclic prefix is formed by part of the OFDM symbol which is copied to the beginning of the symbol period.
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Thus, OFDM is Resistant to MulApath Signal Fading
Q: What else is good about OFDM? A: OFDM is resistant to the mulApath problem in high-‐frequency wireless. Very short-‐wavelength signals normally travel in a straight line (line of sight) from the transmit antenna to the receive antenna. Yet trees, buildings, cars, planes, hills, water towers, and even people will reflect some of the radiated signal. These reflecEons are copies of the original signal that also go to the receive antenna. If the Eme delays of the reflecEons are in the same range as the bit or symbol periods of the data signal, then the reflected signals will add to the most direct signal and create cancellaEons or other anomalies. MulEpath fading is also called Raleigh fading.
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Antenna Diversity
Antenna diversity, also known as space diversity or spaAal diversity, is any one of several wireless diversity schemes that uses two or more antennas to improve the quality and reliability of a wireless link.
Antenna diversity is especially effecEve at miEgaEng these mulEpath situaEons. This is because mulEple antennas offer a receiver several observaEons of the same signal. Each antenna will experience a different interference environment. Thus, if one antenna is experiencing a deep fade, it is likely that another has a sufficient signal. CollecEvely such a system can provide a robust link.
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MulAple Input MulAple Output (MIMO)
Antenna Diversity
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Single-‐Input Single-‐Output (SISO)
TransmiAer Receiver
ConvenAonal communicaAon systems use one transmit antenna and on receive antenna.
This is Single Input Single Output (SISO) . Shannon-‐Hartley:
2log 1S
C BN
⎛ ⎞⎡ ⎤= +⎜ ⎟⎢ ⎥⎣ ⎦⎝ ⎠
1 1
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We have a nine-‐element transmission matrix [H] Note: Antenna spacing is important in using MIMO.
MulAple Input MulAple Output (MIMO) 3 x 3 MIMO
3 transmit antennas
3 receive antennas
TransmiAer Receiver
h11
h22
h33
h31
h32
h21
h23
h12
1
2
3
1
2
3
h13
&
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TransmiAer Receiver
h11
h22
h33
h31
h32
h13
h23 h31
h12
Data to be transmiAed is divided into individual data streams. Three transmit antennas mean three data streams. If m transmiAers is not equal to n receiver antennas, then the number of data streams is the smaller of integers m and n. The capacity can increase directly with the number of data streams.
⎛ ⎞⎡ ⎤= ⋅ +⎜ ⎟⎢ ⎥⎣ ⎦⎝ ⎠=
2log 1
number of data streams
D
D
SC N B
NN
MulAple Input MulAple Output (MIMO)
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Single User MIMO (SU-‐MIMO)
TransmiAer Receiver
h11
h22
h21 h12
This configuraEon doubles the data rate under ideal condiEons.
Why?
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MulA-‐User MIMO (MU-‐MIMO)
When individual data streams are assigned to individual users we have mulE-‐user MIMO. This mode is very useful for cellular uplinks because of the power limitaEons of the UE (cell phone) – it must be kept to a minimum in complexity. The base staEon has mulEple antennas to enhance recepEon of the UE’s signal.
TransmiAer Receiver
h11
h22
h21 h12
1
2
1
2
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SpaAal Diversity
The purpose of spaAal diversity is to make the transmission more robust. In the case shown there is no increase in the data rate. When does it make transmission more robust?
TransmiAer Receiver
h11
h22
h21 h12
1
2
1
2
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Receiver Diversity
TransmiAer
Receiver
h11
h21
1 1
2
Receiver diversity uses more antennas on the receiver than the transmiAer. A 1 x 2 MIMO configuraEon is the simplest version of receiver diversity. Redundant data is transmiAed to the receiver.
Receiver 1 x 2 diversity is simple to implement and requires no special coding.
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Example of Receiver Diversity
( )C A B= +max( , )C A B=
Receiver C
A
B
andA B
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Transmi_er Diversity
The simplest transmi_er diversity configuraAon is shown here. The same data is redundantly transmi_ed to the receiver. Space-‐Ame codes are used in transmi_er diversity.
TransmiAer
Receiver
h11
h12
1
2
1
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MIMO in Wi-‐Fi (802.11n) Some ApplicaAons Using MIMO
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MIMO in 4G LTE-‐Advanced
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hAps://www.researchgate.net/figure/272623859_fig1_Figure-‐1-‐Block-‐Diagram-‐of-‐OFDM-‐Transmission-‐System
Digital Processing in OFDM Transmission System
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