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**Wireless Communications: Lecture 2 Professor Andrea Goldsmith**

Short Course: Wireless Communications: Lecture 2 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

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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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Main Takeaway Narrowband wireless channel characterized by random flat-fading (Bu<<Bc) Wideband wireless channel characterized by random frequency-selective fading (ISI) Need to combat flat and frequency-selective fading Focus of this section of short course

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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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**Adaptive Modulation Change modulation relative to fading**

Parameters to adapt: Constellation size Transmit power Instantaneous BER Symbol time Coding rate/scheme Optimization criterion: Maximize throughput Minimize average power Minimize average BER Only 1-2 degrees of freedom needed for good performance

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**Variable-Rate Variable-Power MQAM**

Uncoded Data Bits Delay Point Selector M(g)-QAM Modulator Power: P(g) To Channel g(t) log2 M(g) Bits One of the M(g) Points BSPK 4-QAM 16-QAM Goal: Optimize P(g) and M(g) to maximize R=Elog[M(g)]

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**Optimization Formulation**

Adaptive MQAM: Rate for fixed BER Rate and Power Optimization Same maximization as for capacity, except for K=-1.5/ln(5BER).

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**Optimal Adaptive Scheme**

gk g Power Adaptation Spectral Efficiency g Equals capacity with effective power loss K=-1.5/ln(5BER).

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**Spectral Efficiency Can reduce gap by superimposing a trellis code K2**

K=-1.5/ln(5BER) Can reduce gap by superimposing a trellis code

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**Constellation Restriction**

Restrict MD(g) to {M0=0,…,MN}. Let M(g)=g/gK*, where gK* is later optimized. Set MD(g) to maxj Mj: Mj M(g). Region boundaries are gj=MjgK*, j=0,…,N Power control maintains target BER M3 M(g)=g/gK* MD(g) M3 M2 M2 M1 M1 Outage g0 g1=M1gK* g2 g3 g

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**Power Adaptation and Average Rate**

Fixed BER within each region Es/N0=(Mj-1)/K Channel inversion within a region Requires power increase when increasing M(g) Average Rate

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**Efficiency in Rayleigh Fading**

Spectral Efficiency (bps/Hz) Average SNR (dB)

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**Constellation Restriction**

M3 M(g)=g/gK* MD(g) M3 M2 M2 M1 M1 Outage g0 g1=M1gK* g2 g3 g Power adaptation: Average rate:

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**Efficiency in Rayleigh Fading**

Spectral Efficiency (bps/Hz) Average SNR (dB)

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**Practical Constraints**

Constellation updates: fade region duration Error floor from estimation error Estimation error at RX can cause error in absence of noise (e.g. for MQAM) Estimation error at TX causes mismatch of adaptive power and rate to actual channel Error floor from delay: let r(t,t)=g(t-t)/g(t). Feedback delay causes mismatch of adaptive power and rate to actual channel

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**Detailed Formulas Error floor from delay: let =g[i]/g[i-id].**

Error floor from estimation error () Joint distribution p(,) depends on estimation: hard to obtain. For PSAM the envelope is bi-variate Rayleigh Error floor from delay: let =g[i]/g[i-id]. p(|) known for Nakagami fading ^ ^

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Main Points Adaptive modulation leverages fast fading to improve performance (throughput, BER, etc.) Adaptive MQAM uses capacity-achieving power and rate adaptation, with power penalty K. Comes within 5-6 dB of capacity Discretizing the constellation size results in negligible performance loss. Constellations cannot be updated faster than 10s to 100s of symbol times: OK for most dopplers.

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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

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**Introduction to Diversity**

Basic Idea Send same bits over independent fading paths Independent fading paths obtained by time, space, frequency, or polarization diversity Combine paths to mitigate fading effects Tb t Multiple paths unlikely to fade simultaneously

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**Combining Techniques Selection Combining Maximal Ratio Combining**

Fading path with highest gain used Maximal Ratio Combining All paths cophased and summed with optimal weighting to maximize combiner output SNR Equal Gain Combining All paths cophased and summed with equal weighting Array/Diversity gain Array gain is from noise averaging (AWGN and fading) Diversity gain is change in BER slope (fading)

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**Selection Combining Analysis and Performance**

Selection Combining (SC) Combiner SNR is the maximum of the branch SNRs. CDF easy to obtain, pdf found by differentiating. Diminishing returns with number of antennas. Can get up to about 20 dB of gain. Outage Probability

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**MRC and its Performance**

With MRC, gS=gi for branch SNRs gi Optimal technique to maximize output SNR Yields dB performance gains Distribution of gS hard to obtain Standard average BER calculation Recall Integral hard to obtain in closed form and often diverges

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**g depends on modulation (a,b)**

MGF Approach Use alternate form of Q function Define the MGF of gi as Laplace transform of distribution Often simple closed form expressions Rearranging order of integration, we get g depends on modulation (a,b)

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**EGC and Transmit Diversity**

EGQ simpler than MRC Harder to analyze Performance about 1 dB worse than MRC Transmit diversity With channel knowledge, similar to receiver diversity, same array/diversity gain Without channel knowledge, can obtain diversity gain through Alamouti scheme: works over 2 consecutive symbols

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Main Points Diversity typically entails some penalty in terms of rate, bandwidth, complexity, or size. Techniques trade complexity for performance. MRC yields dB gain, SC around 20 dB. Analysis of MRC simplified using MGF approach EGC easier to implement than MRC: hard to analyze. Performance about 1 dB worse than MRC Transmit diversity can obtain diversity gain even without channel information at transmitter.

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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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**MIMO Systems and their Decomposition**

MIMO (multiple-input multiple-output) systems have multiple transmit and receive antennas Decompose channel through transmit precoding (x=Vx) and receiver shaping (y=UHy) Leads to RHmin(Mt,Mr) independent channels with gain si (ith singular value of H) and AWGN Independent channels lead to simple capacity analysis and modulation/demodulation design ~ ~ ~ y=Hx+n y=S x+n H=USVH ~ ~ ~ yi=six+ni ~ ~

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**Capacity of MIMO Systems**

Depends on what is known at TX and RX and if channel is static or fading For static channel with perfect CSI at TX and RX, power water-filling over space is optimal: In fading waterfill over space (based on short-term power constraint) or space-time (long-term constraint) Without transmitter channel knowledge, capacity metric is based on an outage probability Pout is the probability that the channel capacity given the channel realization is below the transmission rate.

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**Beamforming Scalar codes with transmit precoding y=uHHvx+uHn**

Transforms system into a SISO system with diversity. Array and diversity gain Greatly simplifies encoding and decoding. Channel indicates the best direction to beamform Need “sufficient” knowledge for optimality of beamforming

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**Optimality of Beamforming**

Mean Information Covariance Information

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**Diversity vs. Multiplexing**

Use antennas for multiplexing or diversity Diversity/Multiplexing tradeoffs (Zheng/Tse) Error Prone Best use depends on the application Low Pe

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**How should antennas be used?**

Use antennas for multiplexing: Use antennas for diversity High-Rate Quantizer ST Code High Rate Decoder Error Prone Low Pe Low-Rate Quantizer ST Code High Diversity Decoder Depends on end-to-end metric: Solve by optimizing app. metric

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**MIMO Receiver Design Optimal Receiver: Decision-Feedback receiver**

Maximum likelihood: finds input symbol most likely to have resulted in received vector Exponentially complex # of streams and constellation size Decision-Feedback receiver Uses triangular decomposition of channel matrix Allows sequential detection of symbol at each received antenna, subtracting out previously detected symbols Sphere Decoder: Only considers possibilities within a sphere of received symbol. Space-Time Processing: Encode/decode over time & space

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**Other MIMO Design Issues**

Space-time coding: Map symbols to both space and time via space-time block and convolutional codes. For OFDM systems, codes are also mapped over frequency tones. Adaptive techniques: Fast and accurate channel estimation Adapt the use of transmit/receive antennas Adapting modulation and coding. Limited feedback: Partial CSI introduces interference in parallel decomp: can use interference cancellation at RX TX codebook design for quantized channel

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Main Points MIMO systems exploit multiple antennas at both TX and RX for capacity and/or diversity gain With TX and RX channel knowledge, channel decomposes into independent channels Linear capacity increase with number of TX/RX antennas With TX/RX channel knowledge, capacity vs. outage is the capacity metric Beamforming provides diversity gain in direction of dominent channel eigenvectors Fundamental tradeoff between capacity increase and diversity gain: optimization depends on application

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**Main Points MIMO RX design trades complexity for performance**

ML detector optimal; exponentially complex DF receivers prone to error propagation Sphere decoders allow performance tradeoff via radius Space-time processing (i.e. coding) used in most systems Adaptation requires fast/accurate channel estimation Limited feedback introduces interference between streams: requires codebook design

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**ISI Countermeasures Equalization Multicarrier Modulation**

Signal processing at receiver to eliminate ISI, must balance ISI removal with noise enhancement Can be very complex at high data rates, and performs poorly in fast-changing channels Not that common in state-of-the-art wireless systems Multicarrier Modulation Break data stream into lower-rate substreams modulated onto narrowband flat-fading subchannels Spread spectrum Superimpose a fast (wideband) spreading sequence on top of data sequence, allows resolution for combining or attenuation of multipath components.

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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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**Multicarrier Modulation**

R/N bps QAM Modulator x cos(2pf0t) cos(2pfNt) S R bps Serial To Parallel Converter R/N bps QAM Modulator Breaks data into N substreams Substream modulated onto separate carriers Substream bandwidth is B/N for B total bandwidth B/N<Bc implies flat fading on each subcarrier (no ISI)

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**Overlapping Substreams**

Can have completely separate subchannels Required passband bandwidth is B. OFDM overlaps substreams Substreams (symbol time TN) separated in RX Minimum substream separation is BN/(1+b). Total required bandwidth is B/2 (for TN=1/BN) B/N f0 fN-1

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**Fading Across Subcarriers**

Leads to different BERS Compensation techniques Frequency equalization (noise enhancement) Precoding Coding across subcarriers Adaptive loading (power and rate)

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**FFT Implementation of OFDM**

Use IFFT at TX to modulate symbols on each subcarrier Cyclic prefix makes linear convolution of channel circular, so no interference between FFT blocks in RX processing Reverse structure (with FFT) at receiver x cos(2pfct) R bps QAM Modulator Serial To Parallel Converter IFFT X0 XN-1 x0 xN-1 Add cyclic prefix and To Serial Convert D/A TX x cos(2pfct) R bps QAM Modulator FFT Y0 YN-1 y0 yN-1 Remove cyclic prefix and Serial to Parallel Convert A/D LPF To Serial RX

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**OFDM Design Issues Timing/frequency offset:**

Impacts subcarrier orthogonality; self-interference Peak-to-Average Power Ratio (PAPR) Adding subcarrier signals creates large signal peaks Different fading across subcarriers Same mitigation techniques as in MCM: Precoding to invert fading, coding across subcarriers, and adaptative loading over time most common MIMO/OFDM Apply OFDM across each spatial dimension Can adapt across space, time, and frequency

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**Main Points OFDM efficiently implemented using FFTs**

ISI can be mitigated through equalization, multicarrier modulation (MCM) or spread spectrum Today, equalizers often too complex or can’t track channel. MCM splits channel into NB flat fading subchannels Fading across subcarriers degrades performance. Compensate through coding or adaptation OFDM efficiently implemented using FFTs OFDM challenges are PAPR, timing and frequency offset, and fading across subcarriers

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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

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**Introduction to Spread Spectrum**

Modulation that increases signal BW Mitigates or coherently combines ISI Mitigates narrowband interference/jamming Hides signal below noise (DSSS) or makes it hard to track (FH) Also used as a multiple access technique Two types Frequency Hopping: Narrowband signal hopped over wide bandwidth Direction Sequence: Modulated signal multiplied by faster chip sequence

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**Direct Sequence Spread Spectrum**

Bit sequence modulated by chip sequence Spreads bandwidth by large factor (K) Despread by multiplying by sc(t) again (sc(t)=1) Mitigates ISI and narrowband interference S(f) s(t) sc(t) Sc(f) S(f)*Sc(f) 1/Tb 1/Tc Tc Tb=KTc 2

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**ISI and Interference Rejection**

Narrowband Interference Rejection (1/K) Multipath Rejection (Autocorrelation r(t)) S(f) I(f) S(f)*Sc(f) Info. Signal Receiver Input Despread Signal I(f)*Sc(f) aS(f) S(f) S(f)*Sc(f)[ad(t)+b(t-t)] brS’(f) Info. Signal Receiver Input Despread Signal

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**Pseudorandom Sequences**

Autocorrelation determines ISI rejection Ideally equals delta function Maximal Linear Codes No DC component Large period (2n-1)Tc Linear autocorrelation Recorrelates every period Short code for acquisition, longer for transmission In SS receiver, autocorrelation taken over Tb Poor cross correlation (bad for MAC) 1 -1 2n-1 Tc -Tc

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Synchronization Adjusts delay of sc(t-t) to hit peak value of autocorrelation. Typically synchronize to LOS component Complicated by noise, interference, and MP Synchronization offset of Dt leads to signal attenuation by r(Dt) 1 -1 2n-1 Tc -Tc r(Dt) Dt

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**RAKE Receiver Multibranch receiver**

Branches synchronized to different MP components These components can be coherently combined Use SC, MRC, or EGC x Demod y(t) sc(t) ^ dk Diversity Combiner x Demod sc(t-iTc) x Demod sc(t-NTc)

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**Main Points In DSSS, bit sequence modulated by chip sequence**

Spreads bandwidth by large factor (K) Despread by multiplying by sc(t) again (sc(t)=1) Mitigates ISI and narrowband interference ISI mitigation a function of code autocorrelation Must synchronize to incoming signal RAKE receiver used to combine multiple paths S(f) s(t) sc(t) Sc(f) S(f)*Sc(f) 1/Tb 1/Tc Tc Tb=KTc 2

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