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**Wireless Communications Professor Andrea Goldsmith**

Short Course: Wireless Communications Professor Andrea Goldsmith UCSD March 22-23 La Jolla, CA

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**Course Outline Overview of Wireless Communications**

Path Loss, Shadowing, and WB/NB Fading Capacity of Wireless Channels Digital Modulation and its Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications Wireless Networks Future Wireless Systems Lecture 1 Lecture 2 Lecture 3

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**Wireless History Ancient Systems: Smoke Signals, Carrier Pigeons, …**

Radio invented in the 1880s by Marconi Many sophisticated military radio systems were developed during and after WW2 Cellular has enjoyed exponential growth since the mid 1980s, with billions of users worldwide today Ignited the wireless revolution Voice, data, and multimedia becoming ubiquitous Use in third world countries growing rapidly Wifi also enjoying tremendous success and growth Wide area networks (e.g. Wimax) and short-range systems other than Bluetooth (e.g. UWB) less successful

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**Future Wireless Networks**

Ubiquitous Communication Among People and Devices Next-generation Cellular Wireless Internet Access Wireless Multimedia Sensor Networks Smart Homes/Spaces Automated Highways In-Body Networks All this and more …

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Future Cell Phones Burden for this performance is on the backbone network Everything wireless in one device BS Phone System San Francisco New York Nth-Gen Cellular Internet Much better performance and reliability than today - Gbps rates, low latency, 99% coverage indoors and out

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**Future Wifi: Multimedia Everywhere, Without Wires**

Performance burden also on the (mesh) network 802.11n++ Streaming video Gbps data rates High reliability Coverage in every room Wireless HDTV and Gaming

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**Challenges Network Challenges Device Challenges**

Scarce difficult spectrum Interference Demanding applications Reliability Ubiquitous coverage Indoor to outdoor operation Device Challenges Size, Power, Cost Multiple Antennas in Silicon Multiradio Integration Coexistance Cellular Apps Processor BT Media GPS WLAN Wimax DVB-H FM/XM

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**Software-Defined (SD) Radio:**

Is this the solution to the device challenges? BT A/D FM/XM Cellular GPS A/D DVB-H DSP Apps Processor A/D WLAN Media Processor Wimax A/D Wideband antennas and A/Ds span BW of desired signals DSP programmed to process desired signal: no specialized HW Today, this is not cost, size, or power efficient Compressed sensing may be a solution for sparse signals

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Compressed Sensing Basic premise is that signals with some sparse structure can be sampled below their Nyquist rate Signal can be perfectly reconstructed from these samples by exploiting signal sparsity This significantly reduces the burden on the front-end A/D converter, as well as the DSP and storage Might be key enabler for SD and low-energy radios Only for incoming signals “sparse” in time, freq., space, …

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**Evolution of Current Systems**

Wireless systems today 3G Cellular: ~ Kbps. WLANs: n; 600 Mbps (and growing). Next Generation is in the works 4G Cellular: LTE ; R>100Mbps 4G WLANs: ac, ad; R>1Gbps Technology Enhancements Hardware: Better circuits/processors. Link: More bandwidth, more antennas, better modulation and coding, adaptivity, cognition. Network: MU MIMO, cooperation, relaying, femtocells. Application: Soft and adaptive QoS.

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**Evolution of Tradeoffs**

Other Tradeoffs: Rate vs. Coverage Rate vs. Delay Rate vs. Cost Rate vs. Energy 4G LTE 802.11ac,ad Rate 3G 802.11n Wimax/3G 2G 802.11b WLAN 2G Cellular -Diminishing returns by beating on the same areas for optimization -Other network tradeoffs not even considered -Fundamental breakthroughs both in the way wireless networks are designed and in the design tradeoffs that are considered. Mobility Other tradeoffs becoming more important

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**Multimedia Requirements**

Voice Data Video Delay <100ms - <100ms Packet Loss <1% <1% BER 10-3 10-6 10-6 Data Rate 8-32 Kbps 1-100 Mbps 1-20 Mbps Traffic Continuous Bursty Continuous One-size-fits-all protocols and design do not work well Wired networks use this approach, with poor results

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**Quality-of-Service (QoS)**

QoS refers to the requirements associated with a given application, typically rate and delay requirements. It is hard to make a one-size-fits all network that supports requirements of different applications. Wired networks often use this approach with poor results, and they have much higher data rates and better reliability than wireless. QoS for all applications requires a cross-layer design approach.

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**Crosslayer Design Application Network Access Link Hardware**

Delay Constraints Rate Constraints Energy Constraints Adapt across design layers Reduce uncertainty through scheduling Provide robustness via diversity

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**Current Wireless Systems**

Cellular Systems Wireless LANs Wimax Satellite Systems Paging Systems Bluetooth Zigbee radios

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**Cellular Phones Everything Wireless in One Device**

Burden for this performance is on the backbone network BS Phone System San Francisco New York Nth-Gen Cellular Internet Much better performance and reliability than today - Gbps rates, low latency, 99% coverage indoors and out

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**3G Cellular Design: Voice and Data**

Data is bursty, whereas voice is continuous Typically require different access and routing strategies 3G “widens the data pipe”: 384 Kbps (802.11n has 100s of Mbps). Standard based on wideband CDMA Packet-based switching for both voice and data 3G cellular popular in Asia and Europe Evolution of existing systems in US (2.5G++) GSM+EDGE, IS-95(CDMA)+HDR 100 Kbps Dual phone (2/3G+Wifi) use (iPhone, Android) 3G insufficient for smart phone requirements

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**4G/LTE/IMT Advanced Much higher peak data rates (50-100 Mbps)**

Greater spectral efficiency (bits/s/Hz) Flexible use of up to 100 MHz of spectrum Low packet latency (<5ms). Increased system capacity Reduced cost-per-bit Support for multimedia

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**Wifi Networks Multimedia Everywhere, Without Wires**

Streaming video Gbps data rates High reliability Coverage in every room Wireless HDTV and Gaming

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**Wireless Local Area Networks (WLANs)**

1011 0101 Internet Access Point WLANs connect “local” computers (100m range) Breaks data into packets Channel access is shared (random access) Backbone Internet provides best-effort service Poor performance in some apps (e.g. video)

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**Wireless LAN Standards**

802.11b (Old – 1990s) Standard for 2.4GHz ISM band (80 MHz) Direct sequence spread spectrum (DSSS) Speeds of 11 Mbps, approx. 500 ft range 802.11a/g (Middle Age– mid-late 1990s) Standard for 5GHz band (300 MHz)/also 2.4GHz OFDM in 20 MHz with adaptive rate/codes Speeds of 54 Mbps, approx ft range 802.11n (New – since Fall’09) Standard in 2.4 GHz and 5 GHz band Adaptive OFDM /MIMO in 20/40 MHz (2-4 antennas) Speeds up to 600Mbps, approx. 200 ft range Other advances in packetization, antenna use, etc. Many WLAN cards have all 4 (a/b/g/n) What’s next? 802.11ac/ad

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**Wimax (802.16) Wide area wireless network standard**

System architecture similar to cellular Called “3.xG” (e.g. Sprint EVO), evolving into 4G OFDM/MIMO is core link technology Operates in 2.5 and 3.5 GHz bands Different for different countries, 5.8 also used. Bandwidth is MHz Fixed (802.16d) vs. Mobile (802.16e) Wimax Fixed: 75 Mbps max, up to 50 mile cell radius Mobile: 15 Mbps max, up to 1-2 mile cell radius

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**WiGig and Wireless HD New standards operating in 60 GHz band**

Data rates of 7-25 Gbps Bandwidth of around 10 GHz (unregulated) Range of around 10m (can be extended) Uses/extends MAC Layer Applications include PC peripherals and displays for HDTVs, monitors & projectors

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**Satellite Systems Cover very large areas Different orbit heights**

GEOs (39000 Km) versus LEOs (2000 Km) Optimized for one-way transmission Radio (XM, Sirius) and movie (SatTV, DVB/S) broadcasts Most two-way systems struggling or bankrupt Global Positioning System (GPS) use growing Satellite signals used to pinpoint location Popular in cell phones, PDAs, and navigation devices

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**Paging Systems Broad coverage for short messaging**

Message broadcast from all base stations Simple terminals Optimized for 1-way transmission Answer-back hard Overtaken by cellular

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**Bluetooth Cable replacement RF technology (low cost)**

Short range (10m, extendable to 100m) 2.4 GHz band (crowded) 1 Data (700 Kbps) and 3 voice channels, up to 3 Mbps Widely supported by telecommunications, PC, and consumer electronics companies Few applications beyond cable replacement 8C Cimini-7/98

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**IEEE 802.15.4/ZigBee Radios Low-Rate WPAN**

Data rates of 20, 40, 250 Kbps Support for large mesh networking or star clusters Support for low latency devices CSMA-CA channel access Very low power consumption Frequency of operation in ISM bands Focus is primarily on low power sensor networks

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**Tradeoffs 802.11n 3G Rate 802.11g/a Power 802.11b UWB Bluetooth ZigBee**

Range

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**Scarce Wireless Spectrum**

$$$ and Expensive

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**Spectrum Regulation Spectrum a scarce public resource, hence allocated**

Spectral allocation in US controlled by FCC (commercial) or OSM (defense) FCC auctions spectral blocks for set applications. Some spectrum set aside for universal use Worldwide spectrum controlled by ITU-R Regulation is a necessary evil. Innovations in regulation being considered worldwide, including underlays, overlays, and cognitive radios

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**Spectral Reuse Due to its scarcity, spectrum is reused**

BS In licensed bands and unlicensed bands Wifi, BT, UWB,… Cellular, Wimax Reuse introduces interference

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**Need Better Coexistence Many devices use the same radio band**

Technical Solutions: Interference Cancellation Smart/Cognitive Radios

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**Standards Interacting systems require standardization**

Companies want their systems adopted as standard Alternatively try for de-facto standards Standards determined by TIA/CTIA in US IEEE standards often adopted Process fraught with inefficiencies and conflicts Worldwide standards determined by ITU-T In Europe, ETSI is equivalent of IEEE

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**Emerging Systems 4th generation cellular (LTE)**

OFDMA is the PHY layer Other new features Ad hoc/mesh wireless networks Cognitive radios Sensor networks Distributed control networks Biomedical networks

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Ad-Hoc/Mesh Networks ce Outdoor Mesh Indoor Mesh

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Design Issues Ad-hoc networks provide a flexible network infrastructure for many emerging applications. The capacity of such networks is generally unknown. Transmission, access, and routing strategies for ad-hoc networks are generally ad-hoc. Crosslayer design critical and very challenging. Energy constraints impose interesting design tradeoffs for communication and networking.

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Cognitive Radios Cognitive radios can support new wireless users in existing crowded spectrum Without degrading performance of existing users Utilize advanced communication and signal processing techniques Coupled with novel spectrum allocation policies Technology could Revolutionize the way spectrum is allocated worldwide Provide sufficient bandwidth to support higher quality and higher data rate products and services

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**Cognitive Radio Paradigms**

Underlay Cognitive radios constrained to cause minimal interference to noncognitive radios Interweave Cognitive radios find and exploit spectral holes to avoid interfering with noncognitive radios Overlay Cognitive radios overhear and enhance noncognitive radio transmissions Knowledge and Complexity

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**Wireless Sensor Networks**

Data Collection and Distributed Control Smart homes/buildings Smart structures Search and rescue Homeland security Event detection Battlefield surveillance Energy (transmit and processing) is the driving constraint Data flows to centralized location (joint compression) Low per-node rates but tens to thousands of nodes Intelligence is in the network rather than in the devices

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**Energy-Constrained Nodes**

Each node can only send a finite number of bits. Transmit energy minimized by maximizing bit time Circuit energy consumption increases with bit time Introduces a delay versus energy tradeoff for each bit Short-range networks must consider transmit, circuit, and processing energy. Sophisticated techniques not necessarily energy-efficient. Sleep modes save energy but complicate networking. Changes everything about the network design: Bit allocation must be optimized across all protocols. Delay vs. throughput vs. node/network lifetime tradeoffs. Optimization of node cooperation. All the sophisticated high-performance communication techniques developed since WW2 may need to be thrown out the window. By cooperating, nodes can save energy

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**Distributed Control over Wireless**

Automated Vehicles - Cars - Airplanes/UAVs - Insect flyers Interdisciplinary design approach Control requires fast, accurate, and reliable feedback. Wireless networks introduce delay and loss Need reliable networks and robust controllers Mostly open problems : Many design challenges

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**Wireless and Health, Biomedicine and Neuroscience**

The brain as a wireless network EKG signal reception/modeling Signal encoding and decoding Nerve network (re)configuration Body-Area Networks Doctor-on-a-chip Cell phone info repository Monitoring, remote intervention and services Cloud

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Main Points The wireless vision encompasses many exciting systems and applications Technical challenges transcend across all layers of the system design. Cross-layer design emerging as a key theme in wireless. Existing and emerging systems provide excellent quality for certain applications but poor interoperability. Standards and spectral allocation heavily impact the evolution of wireless technology

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**Course Outline Overview of Wireless Communications**

Path Loss, Shadowing, and Fading Models Capacity of Wireless Channels Digital Modulation and its Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications & Wireless Networks Future Wireless Systems

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**Propagation Characteristics**

Path Loss (includes average shadowing) Shadowing (due to obstructions) Multipath Fading Slow Very slow Pr/Pt Fast Pt Pr v d=vt d=vt

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**Path Loss Modeling Maxwell’s equations Free space path loss model**

Complex and impractical Free space path loss model Too simple Ray tracing models Requires site-specific information Empirical Models Don’t always generalize to other environments Simplified power falloff models Main characteristics: good for high-level analysis

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**Free Space (LOS) Model Path loss for unobstructed LOS path**

d=vt Path loss for unobstructed LOS path Power falls off : Proportional to 1/d2 Proportional to l2 (inversely proportional to f2)

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**Ray Tracing Approximation**

Represent wavefronts as simple particles Geometry determines received signal from each signal component Typically includes reflected rays, can also include scattered and defracted rays. Requires site parameters Geometry Dielectric properties

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Two Path Model Path loss for one LOS path and 1 ground (or reflected) bounce Ground bounce approximately cancels LOS path above critical distance Power falls off Proportional to d2 (small d) Proportional to d4 (d>dc) Independent of l (f)

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**General Ray Tracing Models all signal components**

Reflections Scattering Diffraction Requires detailed geometry and dielectric properties of site Similar to Maxwell, but easier math. Computer packages often used

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**Simplified Path Loss Model**

Used when path loss dominated by reflections. Most important parameter is the path loss exponent g, determined empirically.

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**Empirical Models Okumura model Hata model Cost 231 Model:**

Empirically based (site/freq specific) Awkward (uses graphs) Hata model Analytical approximation to Okumura model Cost 231 Model: Extends Hata model to higher frequency (2 GHz) Walfish/Bertoni: Cost 231 extension to include diffraction from rooftops Commonly used in cellular system simulations

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**Main Points Path loss models simplify Maxwell’s equations**

Models vary in complexity and accuracy Power falloff with distance is proportional to d2 in free space, d4 in two path model Empirical models used in 2G simulations Main characteristics of path loss captured in simple model Pr=PtK[d0/d]g

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**Shadowing Models attenuation from obstructions**

Xc Models attenuation from obstructions Random due to random # and type of obstructions Typically follows a log-normal distribution dB value of power is normally distributed m=0 (mean captured in path loss), 4<s<12 (empirical) LLN used to explain this model Decorrelated over decorrelation distance Xc

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**Combined Path Loss and Shadowing**

Linear Model: y lognormal dB Model 10logK Slow Pr/Pt (dB) Very slow -10g log d

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**Outage Probability and Cell Coverage Area**

Path loss: circular cells Path loss+shadowing: amoeba cells Tradeoff between coverage and interference Outage probability Probability received power below given minimum Cell coverage area % of cell locations at desired power Increases as shadowing variance decreases Large % indicates interference to other cells

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**Model Parameters from Empirical Measurements**

K (dB) log(d0) sy 2 Fit model to data Path loss (K,g), d0 known: “Best fit” line through dB data K obtained from measurements at d0. Exponent is MMSE estimate based on data Captures mean due to shadowing Shadowing variance Variance of data relative to path loss model (straight line) with MMSE estimate for g Pr(dB) 10g log(d)

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Main Points Random attenuation due to shadowing modeled as log-normal (empirical parameters) Shadowing decorrelates over decorrelation distance Combined path loss and shadowing leads to outage and amoeba-like cell shapes Cellular coverage area dictates the percentage of locations within a cell that are not in outage Path loss and shadowing parameters are obtained from empirical measurements

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**Statistical Multipath Model**

Random # of multipath components, each with Random amplitude Random phase Random Doppler shift Random delay Random components change with time Leads to time-varying channel impulse response

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**Time Varying Impulse Response**

Response of channel at t to impulse at t-t: t is time when impulse response is observed t-t is time when impulse put into the channel t is how long ago impulse was put into the channel for the current observation path delay for MP component currently observed Received Signal

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**Received Signal Characteristics**

Received signal consists of many multipath components Amplitudes change slowly Phases change rapidly Constructive and destructive addition of signal components Amplitude fading of received signal (both wideband and narrowband signals)

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**Narrowband Model Assume delay spread maxm,n|tn(t)-tm(t)|<<1/B**

Then u(t)u(t-t). Received signal given by No signal distortion (spreading in time) Multipath affects complex scale factor in brackets. Characterize scale factor by setting u(t)=d(t)

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**In-Phase and Quadrature under CLT Approximation**

In phase and quadrature signal components: For N(t) large, rI(t) and rQ(t) jointly Gaussian (sum of large # of random vars). Received signal characterized by its mean, autocorrelation, and cross correlation. If jn(t) uniform, the in-phase/quad components are mean zero, indep., and stationary.

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**Auto and Cross Correlation**

Assume fn~U[0,2p] Recall that qn is the multipath arrival angle Autocorrelation of inphase/quad signal is Cross Correlation of inphase/quad signal is Autocorrelation of received signal is

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Uniform AOAs Under uniform scattering, in phase and quad comps have no cross correlation and autocorrelation is The PSD of received signal is Decorrelates over roughly half a wavelength Sr(f) Used to generate simulation values fc fc-fD fc+fD

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**Signal Envelope Distribution**

CLT approx. leads to Rayleigh distribution (power is exponential) When LOS component present, Ricean distribution is used Measurements support Nakagami distribution in some environments Similar to Ricean, but models “worse than Rayleigh” Lends itself better to closed form BER expressions

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**Level crossing rate and Average Fade Duration**

LCR: rate at which the signal crosses a fade value AFD: How long a signal stays below target R/SNR Derived from LCR For Rayleigh fading Depends on ratio of target to average level (r) Inversely proportional to Doppler frequency t1 t2 t3 R

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**Markov Models for Fading**

Model for fading dynamics Simplifies performance analysis Divides range of fading power into discrete regions Rj={g: Aj g < Aj+1} Aj s and # of regions are functions of model Transition probabilities (Lj is LCR at Aj): A2 R1 A1 R0 A0

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Main Points Narrowband model has in-phase and quad. comps that are zero-mean stationary Gaussian processes Auto and cross correlation depends on AOAs of multipath Uniform scattering makes autocorrelation of inphase and quad follow Bessel function Signal components decorrelate over half wavelength Cross correlation is zero (in-phase/quadrature indep.) The power spectral density of the received signal has a bowl shape centered at carrier frequency PSD useful in simulating fading channels

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**Main Points Narrowband fading distribution depends on environment**

Rayleigh, Ricean, and Nakagami all common Average fade duration determines how long a user is in continuous outage (e.g. for coding design) Markov model approximates fading dynamics.

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**Wideband Channels Individual multipath components resolvable**

True when time difference between components exceeds signal bandwidth t t Narrowband Wideband

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**Scattering Function Fourier transform of c(t,t) relative to t**

Typically characterize its statistics, since c(t,t) is different in different environments Underlying process WSS and Gaussian, so only characterize mean (0) and correlation Autocorrelation is Ac(t1,t2,Dt)=Ac(t,Dt) Statistical scattering function: r s(t,r)=FDt[Ac(t,Dt)] t

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**Multipath Intensity Profile**

Ac(t) TM Defined as Ac(t,Dt=0)= Ac(t) Determines average (TM ) and rms (st) delay spread Approximate max delay of significant m.p. Coherence bandwidth Bc=1/TM Maximum frequency over which Ac(Df)=F[Ac(t)]>0 Ac(Df)=0 implies signals separated in frequency by Df will be uncorrelated after passing through channel t Ac(f) t Bc f

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**Doppler Power Spectrum**

Sc(r) r Sc(r)=F[Ac(t=0,Dt)]= F[Ac(Dt)] Doppler spread Bd is maximum doppler for which Sc (r)=>0. Coherence time Tc=1/Bd Maximum time over which Ac(Dt)>0 Ac(Dt)=0 implies signals separated in time by Dt will be uncorrelated after passing through channel Bd

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**Summary of Wideband Channel Models**

Scattering Function: Used to characterize c(t,t) statistically Multipath Intensity Profile Determines average (TM ) and rms (st) delay spread Coherence bandwidth Bc=1/TM Doppler Power Spectrum: Sc(r)= F[Ac(Dt)] Power of multipath at given Doppler s(t,r)=FDt[Ac(t,Dt)] t r Ac(f) t f Bc

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Main Points Scattering function characterizes rms delay and Doppler spread. Key parameters for system design. Delay spread defines maximum delay of significant multipath components. Inverse is coherence bandwidth of channel Doppler spread defines maximum nonzero doppler, its inverse is coherence time

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**Course Outline Overview of Wireless Communications**

Path Loss, Shadowing, and Fading Models Capacity of Wireless Channels Digital Modulation and its Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications & Wireless Networks Future Wireless Systems

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**Shannon Capacity Defined as the maximum MI of channel**

Maximum error-free data rate a channel can support. Theoretical limit (not achievable) Channel characteristic Not dependent on design techniques

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**Capacity of Flat-Fading Channels**

Capacity defines theoretical rate limit Maximum error free rate a channel can support Depends on what is known about channel Fading Statistics Known Hard to find capacity Fading Known at Receiver Only

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**Fading Known at Transmitter and Receiver**

For fixed transmit power, same as with only receiver knowledge of fading Transmit power S(g) can also be adapted Leads to optimization problem

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**Optimal Adaptive Scheme**

Power Adaptation Capacity Waterfilling 1 g g0

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**Channel Inversion Fading inverted to maintain constant SNR**

Simplifies design (fixed rate) Greatly reduces capacity Capacity is zero in Rayleigh fading Truncated inversion Invert channel above cutoff fade depth Constant SNR (fixed rate) above cutoff Cutoff greatly increases capacity Close to optimal

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**Capacity in Flat-Fading**

Rayleigh Log-Normal

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**Frequency Selective Fading Channels**

For TI channels, capacity achieved by water-filling in frequency Capacity of time-varying channel unknown Approximate by dividing into subbands Each subband has width Bc (like MCM). Independent fading in each subband Capacity is the sum of subband capacities 1/|H(f)|2 Bc P f

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Main Points Fundamental capacity of flat-fading channels depends on what is known at TX and RX. Capacity when only RX knows fading same as when TX and RX know fading but power fixed. Capacity with TX/RX knowledge: variable-rate variable-power transmission (water filling) optimal Almost same capacity as with RX knowledge only Channel inversion practical, but should truncate Capacity of wideband channel obtained by breaking up channel into subbands Similar to multicarrier modulation

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**Course Outline Overview of Wireless Communications**

Path Loss, Shadowing, and Fading Models Capacity of Wireless Channels Digital Modulation and its Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications & Wireless Networks Future Wireless Systems

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**Passband Modulation Tradeoffs**

Want high rates, high spectral efficiency, high power efficiency, robust to channel, cheap. Amplitude/Phase Modulation (MPSK,MQAM) Information encoded in amplitude/phase More spectrally efficient than frequency modulation Issues: differential encoding, pulse shaping, bit mapping. Frequency Modulation (FSK) Information encoded in frequency Continuous phase (CPFSK) special case of FM Bandwidth determined by Carson’s rule (pulse shaping) More robust to channel and amplifier nonlinearities Our focus

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**Amplitude/Phase Modulation**

Signal over ith symbol period: Pulse shape g(t) typically Nyquist Signal constellation defined by (si1,si2) pairs Can be differentially encoded M values for (si1,si2)log2 M bits per symbol

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**Linear Modulation in AWGN**

ML detection induces decision regions Example: 8PSK Ps depends on # of nearest neighbors aM Minimum distance dmin (depends on gs) Approximate expression dmin

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**Alternate Q Function Representation**

Traditional Q function representation Infinite integrand Argument in integral limits New representation (Craig’93) Leads to closed form solution for Ps in PSK Very useful in fading and diversity analysis

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**Linear Modulation in Fading**

In fading gs and therefore Ps random Performance metrics: Outage probability: p(Ps>Ptarget)=p(g<gtarget) Average Ps , Ps: Combined outage and average Ps

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**Outage Probability Ps t or d Outage**

Ps(target) Outage Ts t or d Probability that Ps is above target Equivalently, probability gs below target Used when Tc>>Ts

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**Average Ps Ps Ps t or d Ts Expected value of random variable Ps**

Used when Tc~Ts Error probability much higher than in AWGN alone Alternate Q function approach: Simplifies calculations (Get a Laplace Xfm)

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**Combined outage and average Ps**

Ps(gs) Ps(gs) Pstarget Ps(gs) Used in combined shadowing and flat-fading Ps varies slowly, locally determined by flat fading Declare outage when Ps above target value

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Doppler Effects High doppler causes channel phase to decorrelate between symbols Leads to an irreducible error floor for differential modulation Increasing power does not reduce error Error floor depends on BdTs

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ISI Effects Delay spread exceeding a symbol time causes ISI (self interference). ISI leads to irreducible error floor Increasing signal power increases ISI power ISI requires that Ts>>Tm (Rs<<Bc) 1 2 3 4 5 Tm Ts

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Main Points In fading Ps is a random variable, characterized by average value, outage, or combined outage/average Outage probability based on target SNR in AWGN. Fading greatly increases average Ps . Alternate Q function approach simplifies Ps calculation, especially its average value in fading (Laplace Xfm). Doppler spread only impacts differential modulation causing an irreducible error floor at low data rates Delay spread causes irreducible error floor or imposes rate limits Need to combat flat and frequency-selective fading Main focus of the remainder of the short course

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Main Points Linear modulation more spectrally efficient but less robust than nonlinear modulation Ps approximation in AWGN: Alternate Q function representation simplifies calculations In fading Ps is a random variable, characterized by average value, outage, or combined outage/average Fading greatly increases average Ps . Doppler spread only impacts differential modulation causing an irreducible error floor at low data rates Delay spread causes irreducible error floor or imposes rate limits

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**Main Takeaway Need to combat flat and frequency-selective fading**

Focus of the next section of the short course

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Lecture 1 Summary

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**Future Wireless Networks**

Ubiquitous Communication Among People and Devices Wireless Internet access Nth generation Cellular Wireless Ad Hoc Networks Sensor Networks Wireless Entertainment Smart Homes/Spaces Automated Highways All this and more… Hard Delay/Energy Constraints Hard Rate Requirements

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Signal Propagation Path Loss Shadowing Multipath d Pr/Pt d=vt

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**Statistical Multipath Model**

Random # of multipath components, each with varying amplitude, phase, doppler, and delay Narrowband channel Signal amplitude varies randomly (complex Gaussian). 2nd order statistics (Bessel function), Fade duration, etc. Wideband channel Characterized by channel scattering function (Bc,Bd)

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**Capacity of Flat Fading Channels**

Three cases Fading statistics known Fade value known at receiver Fade value known at receiver and transmitter Optimal Adaptation Vary rate and power relative to channel Optimal power adaptation is water-filling Exceeds AWGN channel capacity at low SNRs Suboptimal techniques come close to capacity

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**Modulation Considerations**

Want high rates, high spectral efficiency, high power efficiency, robust to channel, cheap. Linear Modulation (MPAM,MPSK,MQAM) Information encoded in amplitude/phase More spectrally efficient than nonlinear Easier to adapt. Issues: differential encoding, pulse shaping, bit mapping. Nonlinear modulation (FSK) Information encoded in frequency More robust to channel and amplifier nonlinearities

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**Linear Modulation in AWGN**

ML detection induces decision regions Example: 8PSK Ps depends on # of nearest neighbors Minimum distance dmin (depends on gs) Approximate expression dmin

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**Linear Modulation in Fading**

In fading gs and therefore Ps random Metrics: outage, average Ps , combined outage and average. Ts Ps Outage Ps(target) Ps Ts

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ISI Effects Delay spread exceeding a symbol time causes ISI (self interference). ISI leads to irreducible error floor Increasing signal power increases ISI power Without compensation, requires Ts>>Tm Severe constraint on data rate (Rs<<Bc) 1 2 3 4 5 Tm Ts

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