EECS 380: Wireless Technologies Week 7-8

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1 EECS 380: Wireless Technologies Week 7-8 Michael L. Honig Northwestern University May 2018

2 Outline Diversity, MIMO Multiple Access techniques FDMA, TDMA OFDMA (LTE) CDMA (3G, b, Bluetooth) Random Access

3 Diversity Idea: Obtain multiple independent copies of the received signal. Improves the chances that at least one is not faded. Macroscopic (space): copies of signal are received over distances spanning many wavelengths. Microscopic (space): copies of signal are received over distances spanning a fraction of a wavelength Different types

4 Macroscopic Diversity Copies of signal are separated by many wavelengths.

5 Macroscopic Diversity MSO Copies of signal are separated by many wavelengths.

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

7 Microscopic Space Diversity Antenna 2 s2 Antenna 1 s1 Want signals s1 and s2 to experience independent fading (why?). distance between antennas should be ½ wavelength. Ex: 900 MHz, λ = c/f 1/3 meter 2 GHz, λ 0.15 meter

8 Multiple Antennas: Multi-Input/Multi-Output (MIMO) Channel Transmitted Data Multi-Channel Detector Estimated Data (multiple data streams) Multiple (M) antennas at receiver and transmitter Channel has multiple inputs and multiple outputs. 8

9 Single Transmit Antenna Transmitted Data (single stream) Multi-Channel Detector Estimated Data Multiple receiver antennas provides spatial diversity Lowers error rate Single-Input/Multiple-Output (SIMO) channel 9

10 Multi-Input/Single Output (MISO) Channel Transmitted Data Single-Channel Detector Estimated Data (single or multiple streams) Transmitting the same symbol from all transmitters provides transmit spatial diversity (e.g., select the best antenna, turn the others off). Practical for cellular downlink. 10

11 Downlink Beamforming Narrow beam focused on one user Different beams can use the same frequency! M antennas at the base station (single or multiple antennas at mobiles) Can support up to M data streams. Multi-user MIMO: multiple users on the same channel Introduced in LTE, ac 11

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

13 Multiple Antennas: Multi-Input/Multi-Output (MIMO)Channel Transmitted Data Multi-Channel Detector Estimated Data Multiple (M) antennas at receiver and transmitter. 13

14 Multiple Antennas: Multi-Input/Multi-Output (MIMO)Channel Substream 1 Substream M Multi-Channel Detector Estimated Data Multiple (M) antennas at receiver and transmitter. Transmitted data is divided into M substreams, one for each antenna. Transmit antennas are used to multiplex multiple data streams. 14

15 Multiple Antennas: Multi-Input/Multi-Output (MIMO)Channel Substream 1 Substream M Multi-Channel Detector Estimated Data Multiple (M) antennas at receiver and transmitter. Transmitted data is divided into M substreams, one for each antenna. Transmit antennas are used to multiplex multiple data streams. Multiple receiver antennas (plus signal processing) are used to remove interference from the different antennas. 15

16 Multiple Antennas: Multi-Input/Multi-Output (MIMO)Channel Substream 1 Substream M Multi-Channel Detector Estimated Data Multiple (M) antennas at receiver and transmitter. Transmitted data is divided into M substreams, one for each antenna. Transmit antennas are used to multiplex multiple data streams. Multiple receiver antennas (plus signal processing) are used to remove interference from the different antennas. Data rate (Shannon capacity) is proportional to M! 16

17 WiFi Evolution: n Technology based on OFDM with multiple antennas at the transmitter and receivers Supports data rates up to 540 Mbps 4 spatial streams, 40 MHz bandwidth Can replace USB 2.0 connections. Also important part of ac (multi-user MIMO) 17

18 Frequency Diversity channel gain signal power (wideband) coherence bandwidth B c Frequencies far outside the coherence bandwidth are affected differently by multipath. f 1 f 2 frequency 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). 18

19 Time Diversity

20 Time Diversity: Error Control Coding channel source bits errors noise, fading, interference introduces errors How can we improve reliability (control errors)? According to Shannon, we have to add redundancy: Add redundant bits to the source stream. Retransmit.

21 Time Diversity Transmit multiple copies of the signal in time. Error control coding: add redundant bits Problem: slow fading Combine with power control

22 Path Diversity τ 1 τ 2 received signal adjust phase + Delay τ 2 - τ 1 adjust phase Called a RAKE receiver, since it rakes up (combines) the energy in the different paths. Can substantially increase the S/I. An important component of CDMA receivers. Each branch in the Rake is typically referred to as a finger.

23 Multiuser Diversity

24 Multiuser Diversity d 1 d 2 > d 1 Received power user 1 user 2 transmit to user 2 transmit to user 1 transmit to user 2 transmit to user 1 time The BST can choose to transmit to the user with the best channel. Exploits variations in signal strength across users.

25 Selection Diversity Antenna 2 s2 Antenna 1 s1 Received power antenna 1 antenna 2 select ant. 2 select ant. 1 select ant. 2 select ant. 1 time Choose the best signal (highest instantaneous SNR). Easy to implement (antenna switch).

26 Benefit of Selection Diversity (Example) Suppose that the signal on each antenna experiences independent Rayleigh fading. Determine the probability that the received signal is faded: Recall Rayleigh fading formula: Probability that the signal power is less than a x P 0 (average received power) = 1 e -a Hence the probability that the signals on both antennas are less than a x P 0 = (1 e -a ) 2 Without diversity, probability of a signal fade = 1 e -1 = 0.63 With 2-branch diversity, probability of a signal fade = = 0.39

27 Benefit of Selection Diversity (cont.) Suppose that there are N copies of the signal (e.g., N antennas, paths, coherence bands, etc.) Probability that the signal power is less than a x P 0 (average received power) = 1 e -a Hence the probability that all N signals are less than a x P 0 = (1 e -a ) N Without diversity, probability of a signal fade = 1 e -1 = 0.63 With 4-branch diversity, probability of a signal fade = = 0.16 Without diversity, Prob(signal is faded by more than 10 db) = 1 e With diversity this probability is (1 e -0.1 ) !

28 Coherent Combining S1 (ant. 1) S2 (ant. 2) adjust phase adjust phase + Coherent means that the phases of the two signals are estimated at the receiver and aligned. Performs better than selection combining (why?). Example: RAKE receiver Can weight the combined signals to maximize the received SNR. (How should the weights depend on the signal levels?)

29 Outage Probability Pr{SNR < x (db)}

30 Probability of Error with Fading add diversity Diversity can transform a fading channel back to a non-fading (additive noise) channel. Essential for mobile wireless communications.

31 Error Control Coding channel source bits errors noise, fading, interference introduces errors How can we improve reliability (control errors)?

32 Error Control Coding channel source bits errors noise, fading, interference introduces errors How can we improve reliability (control errors)? According to Shannon, we have to add redundancy: Add redundant bits to the source stream. Retransmit.

33 Transmit each bit 3 times: Example: Repetition Code channel error is undetected error can be corrected. error can be detected, but not corrected Probability of (undetected) errors has decreased. Many errors are detected. Disadvantage?

34 Transmit each bit 3 times: Example: Repetition Code channel error is undetected error can be corrected. error can be detected, but not corrected Probability of (undetected) errors has decreased. Many errors are detected. Disadvantage? Information rate reduced by 1/3!

35 Transmit each bit 3 times: Example: Repetition Code channel error is undetected error can be corrected. error can be detected, but not corrected More repetition è probability of error à 0, but the rate also goes to 0! Can we make probability of error à 0 with positive rate? Yes, that s Shannon s result (channel coding theorem).

36 Block Coding k source bits coder n coded bits Example (k=2, n=4): 00 à à à à 0110 Code rate = k/n (n coded bits per k information bits) In the example, the code rate is ½. The smaller the code rate, in general the better the performance (lower prob of error).

37 Minimum Codeword Distance k source bits coder n coded bits The Hamming distance between two codewords is the number of bits which differ. The Hamming distance between and is 2. The minimum distance of a code is the minimum Hamming distance between any two code words. Examples: 1. Uncoded: 0 à 0, 1 à Repetition code 0 à 000, 1 à Rate ½ block (Hadamard) code: 00 à 0000, 01 à à 0101, 11 à 0110

38 Minimum Codeword Distance k source bits coder n coded bits The Hamming distance between two codewords is the number of bits which differ. The Hamming distance between and is 2. The minimum distance of a code is the minimum Hamming distance between any two code words. Examples: 1. Uncoded: 0 à 0, 1 à 1. Minimum distance = 1 2. Repetition code 0 à 000, 1 à 111. Min distance = 3 3. Rate ½ block (Hadamard) code. Min distance = 2

39 Minimum Distance Decoding repetition code (n=4): 0000 channel 0100 received codeword What if the received codeword is 0110? decoder 0000 à 0 chooses code word closest to received codeword. Error correction and detection capability depends critically on minimum distance. If the minimum distance is d, then the code can correct up to d/2-1 errors, and can detect up to d-1 errors (why?).

40 Examples of Block Codes Parity-check code Example (k=3, n=4): 010 à à 0110 Detects errors, does not correct errors. Can add parity bits to detect more errors. parity bit ensures even number of 1 s Cyclic Redundancy Check (CRC) Code Cyclic code: any cyclic shift of a code word is another code word. (e.g., , , , ) Enables simple coding and decoding. Detects all error bursts of length n-k. (No error correction.) International standards (e.g., CRC-12 with 12 parity bits, CRC-16).

words are there? Is 1011010 a legitimate code word? How about 111011?

41 (7,4) Hamming Code Code word consists of 4 data bits, 3 parity bits: d1, d2, d3, d4, p1, p2, p3 parity bits force even parity within circle How many code words are there? Is a legitimate code word? How about ? What is the minimum distance of the code? How many errors does it correct/detect?

42 (7,4) Hamming Code Code word consists of 4 data bits, 3 parity bits: d1, d2, d3, d4, p1, p2, p3 code word is legitimate code word has one error (correctable) code word has two errors (detectable)

43 Examples of Block Codes (cont.) Hamming codes Family of cyclic block codes where n= 2 m -1, k= 2 m -1-m for integer m. Example: m=3 gives n=7, k=4. This code has minimum distance 3, and correct single errors. Reed-Solomon Codes Block length n=2 m 1 Minimum distance = n-k+1 (maximum possible). Can correct (n-k)/2 errors.

44 Error Probability: Block Codes Shannon limit: -1.6 db about 1 db

45 Error Probability with Convolutional Coding Shannon limit: -1.6 db

46 Coded Error Probability with Fading

47 Turbo Code Code 1 Interleaver Code 2 coded bits source bits Idea: Shannon says that good codes must be very long and look random The interleaver can span 1000 bits or more Concatenating the two codes enables a practical decoder

48 Turbo Decoder estimates, reliabilities received symbols Decoder 2 Deinterleaver Decoder 1 Each decoder provides an independent estimate of the input bits along with an estimated reliability Estimates and reliabilities are passed back and forth through the deinterleaver until the decoders agree on what bits were sent. Can achieve within a fraction of a db of the Shannon bound!

49 Probability of Error with Fading add diversity Diversity can transform a fading channel back to a non-fading (additive noise) channel. Essential for mobile wireless communications.

MSIT 413: Wireless Technologies Week 5

MSIT 413: Wireless Technologies Week 5 Michael L. Honig Department of EECS Northwestern University October 2017 Outline Diversity, MIMO Multiple Access techniques FDMA, TDMA OFDMA (LTE) CDMA (3G, 802.11b,