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MIMO I: Spatial Diversity

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MIMO I: Spatial Diversity MIMO I: Spatial Diversity COS 463: Wireless Networks Lecture 16 Kyle Jamieson [Parts adapted from D. Halperin et al., T. Rappaport] What is MIMO, and why? • Multiple-Input, Multiple-Output (MIMO) communications – Sends and receive more than one signal on different transmit and receive antennas • We’ve already seen frequency, time, spatial multiplexing in 463: – MIMO is a more powerful way to multiplex wireless medium in space – Transforms multipath propagation from an impediment to an advantage 2 Many Uses of MIMO • At least three different ways to leverage space: 1. Spatial diversity: Send or receive redundant streams of information in parallel along multiple spatial paths – Increases reliability and range (unlikely that all paths will be degraded simultaneously) 2. Spatial multiplexing: Send independent streams of information in parallel along multiple spatial paths – Increases rate, if we can avoid interference 3. Interference alignment: “Align” two streams of interference at a remote receiver, resulting in the impact of just one interference stream MIMO-OFDM (5) QPSK Modulated f subcarriers Symbols (6) Mapped onto Subcarriers as OFDM Symbol Figure 1: A graphical• Multipath view of fading: the OFDM different encoding effects on process different for frequencies the 18 Mbps rate (QPSK, 3/4)of802.11a. The data bits (0) are encoded– OFDM: by Orthogonal a rate-1/2 convolutionalFrequency Domain code Multiplexing (1) and then optionally punctured by dropping certain bits for higher coding rates (here, 3/4) that send fewer redundant bits (2). The remaining bits are in- terleaved (3) to spread– theDifferent redundancy subcarriers across are subcarriers independent and protectof each other against frequency-selective fades. These bits are grouped into symbols (4) based on the modulation (QPSK encodes 2 bits per symbol), modulated (5), and finally mapped• ontoChannel the dimodel↵erent for subcarriers OFDM: y = toh∙x form+ w an OFDM symbol (6). – A single complex number h captures the effect of the channel on data h11 h h11 iny1 a = particular h11 x subcarrier 11 y = (+h11 h21 )x y1 = h11x1+h21x2 x x x1 h12 h21 Tx•h For MIMO: Rx Think about each subcarrier, independentTxof other subcarriers Rx 12 Txh21 Rx x x2 h22 y2 = h12 x y y2 = h12x1+h22x2 (a) Receive diversity (b) Transmit diversity (c) Spatial multiplexing Figure 2: Using some of the transmit/receive antennas in an example 2x2 system to exploit diversity and multiplexing gain. xi and yi represent transmitted and received signals. The channel gain hij is a complex number indicating a signal’s attenuated amplitude and phase shift over the channel between the ith transmit antenna and the jth receive antenna. The received signals yi will additionally include thermal RF noise. modulation sending more bits per symbol and being used volutional code of rate 1/2 adds redundant information. It when there is a higher SNR. There are minor di↵erences be- is then punctured [3] by removing bits as needed to support tween 802.11a/g and 802.11n. In 802.11a/g there are 48 data coding rates of 2/3 and 3/4, plus 5/6 for 802.11n. At a rate subcarriers, 4 pilot tones for control, and 6 unused guard of 3/4, for example, a quarter of the data on the subcarriers subcarriers at each edge of the channel. In 802.11n, there is redundant. An alternative LDPC (Low-Density Parity- are only 4 guard subcarriers at each edge of the channel, and Check) code with slightly better performance can also be two adjacent 20 MHz channels can be merged into a single used for 802.11n. Figure 1 presents a pictorial overview of 40 MHz channel. the OFDM encoding process. The beauty of OFDM is that it divides the channel in a The net e↵ect of OFDM plus coding is to provide consis- way that is both computationally and spectrally efficient. tently good 802.11 performance despite significant variabil- High aggregate data rates can be achieved, while the en- ity in the wireless signal due to multi-path fading. coding and decoding on di↵erent subcarriers can use shared hardware components. More relevant to our point here, how- ever, is that OFDM transforms a single large channel into 3. SPATIAL DIVERSITY many relatively independently faded channels. This is be- In this section we look at spatial diversity techniques that cause multi-path fading is frequency selective, so the di↵er- can be applied at the receiver and at the transmitter. Adding ent subcarriers will experience di↵erent fades. Some adja- multiple antennas to an 802.11n receiver or transmitter pro- cent subcarriers may be faded in a similar way, but the fading vides a new set of independently faded paths, even if the for more distant subcarriers is often uncorrelated. Dividing antennas are separated by only a few centimeters. This the channel also increases the symbol time per channel, since adds spatial diversity to the system, which can be exploited many slow symbols will be sent in parallel instead of many to improve resilience to fades. There is also a power gain fast symbols in sequence. This adds time diversity because from multiple receive antennas because, everything else be- the channel is more likely to average out fades over a longer ing equal, two receive antennas will receive twice the signal. period of time. These factors combine to improve performance at a given 802.11 makes use of the frequency diversity provided by distance, and hence increase range. OFDM by coding across the data carried on the subcarriers. This uses a fraction of them for redundant information that 3.1 Receive Diversity Techniques can later be used to correct errors that occur when fading Consider the arrangement in Figure 2(a). One transmit reduces the SNR on some of the subcarriers. First, a con- antenna at a node is sending to two receive antennas at a Plan 1. Today: Diversity in Space – Receive Diversity – Transmit Diversity 2. Next time: Multiplexing in Space 3. Next time: Interference Alignment 5 Path Diversity: Motivation 1. Multi-Antenna Access Points (APs), especially 802.11n,ac: 2. Multiple APs cooperating with each other: Wired backhaul 3. Distributed Antenna systems, separating antenna from AP: Antenna 2 Antenna 1 AP Coaxial / Fiber backhaul 6 Review: Fast Fading • Typical outdoor multipath propagation environment, channel h • On one link each subcarrier’s power level experiences Rayleigh fading: ! " 7 Uncorrelated Rayleigh Fading • Suppose two antennas, separated by distance d12 • Channels from each to a distant third antenna (h13, h23) can be uncorrelated – Fading happens at different times with no bias for a simultaneous fade # # !" , !# 8 When is Fading Uncorrelated, and Why? ≫ , !"# • Channels from each antenna (h13, h23) to a third antenna – Channels are uncorrelated when !"# > ≈ &. () – Channels correlated, fade together when !"# < ≈ ) • This correlation distance depends on the radio environment around the pair of antennas – Increases, e.g., atop cellular phone tower 9 Plan 1. Today: Diversity in Space – Receive Diversity • Selection Diversity • Maximal Ratio Combining – Transmit Diversity 2. Next time: Multiplexing in Space 3. Next time: Interference Alignment 10 Channel Model for Receive Diversity • One transmit antenna sends a symbol to two receive antennas – Receive diversity, or Single-Input, Multi-Output (SIMO) y =3ei3π/4x 9/p13 h 1 1 Receive antenna 1 rotate, scale by 3/p13 xx n 1 p13 h2 4/p13 ⊕ Receive antenna 2 rotate, scale by 2/p13 n expected 1 n2 -iπ/6 y2=2e x i3⇡/4 i⇡/6 Figure 3: MRC operation on a sample channel. The channel gains are ~h = 3e , 2e− ,withGaussian Figure 1: A graphical view of the OFDM encoding process for the 18h Mbps ratei (QPSK, 3/4)of802.11a. noise ~n = n1,n2 of expected power 1. The antennas have respective SNRs of 9 and 4. To implement MRC, • Each receiveh i antenna gets own copy of transmitted signal via The data bitsthe (0) receiver are encoded multiplies the by received a rate- signal1/2 convolutional~y = ~hx + ~n by the codeunit vector (1) and~h⇤/ ~h then, where optionally~h⇤ denotes the punctured complex by dropping || || certain bits–conjugate forDifferent higher of ~h coding. path This operation rates (here, scales each3/4) antenna’s that send signal fewer by its redundant magnitude, and bits rotates (2). The the signals remaining into bits are in- terleaved (3)–the toPotentially same spread phase the referencedifferent redundancy before channel adding across them. subcarriers (For graphical and clarity, protect we depict against the common frequency-selective phase vertically, fades. These bits are groupedrather into than symbolsat 0). The resulting(4) based sum on has the magnitude modulationp13, and (QPSK expected encodes noise power2 bits1 because per symbol), the scaling is modulated (5), normalized. Thus, by coherently combining received signals from di↵erent antennas, the MRC output has and finally mappedthe expected onto SNR the of 13 di.↵ Inerent systems subcarriers with OFDM, to MRC form is performed an OFDM separately symbol for each (6). subcarrier. h11 y = h x h11 y =0(+h h )x h11 y = h x +h x x second node. This is known1 11 as a 1x2 system. Realx systems 11 21 x 1 11 1 21 2 may have more than two receive antennas, but two will suf- 1 h fice for our explanation. With this setup, each receive an- 12 -5 h21 Txtenna receives a copy of Rx the transmitted signal modified by Tx Rx the channelh12 between the transmitter andTx itself. The chan-h Rx 21 -10 nel gains hij are complex numbers that represent both the x x2 amplitude attenuation over the channel as well as the path- h22 dependent phase shifty (see = h Figurex 3 for a graphical example).
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