ECSE 6592 Wireless Ad Hoc and Sensor Networks Spatial Diversity in Wireless Networks Hsin-Yi Shen Nov 3, 2005

Introduction Main characteristic in wireless channels- randomness in users’ transmission channels and randomness in users’ geographical locations Diversity- Convey information through multiple independent instantiations of random attenuations Spatial diversity- through multiple antennas or multiple users

Wireless Channel Characteristics Three kind of attenuations-path loss, shadowing loss, fading loss Path loss: Signals attenuate due to distance Shadowing loss : absorption of radio waves by scattering structures Fading loss :constructive and destructive interference of multiple reflected radio wave paths

Attenuation in Wireless Channels

Wireless Channel Characteristics Key parameters of wireless channels-coherence time, coherence bandwidth If symbol period>coherence time, the channel is time selective If symbol period< channel delay spread, the channel is frequency selective

MIMO Channel Model H(k;l) is the lth tap of the Mr x Mt channel response matrix, z is noise vector

Theoretical Consideration Information-Theoretic results for multiple-antenna channels Information-Theoretic results for multi-user channels Diversity order Design consideration

Information-Theoretic results for multiple antenna channels (1)

Information-Theoretic results for multiple antenna channels (2) Assume the receiver had access to perfect channel state information through training or other methods

Information-Theoretic results for multiple antenna channels (3) At high SNR the outage probability is the same as frame error probability in terms of SNR exponent For given rate, we can compare performance through an outage analysis

Information-Theoretic results for multi-user channels Two types of topology- multiple access channel and broadcast channel

Information-Theoretic results for multi-user channels

Diversity Order and multiplexing gain

Relation between Diversity Order and Multiplexing Gain

Relation between rate and SNR

Design Consideration Space time code with low decoding complexity and achieving maximum diversity order Trade-off between diversity order and rate If system is delay-constrained, design with high diversity order and lower data rate Fairness for resource sharing between users Cross layer design

Signal transmission Transmitter Techniques- spatial multiplexing, space-time trellis code and block codes Receiver techniques- joint equalization with channel estimation, space-time code decoding

Spatial Multiplexing (Bell Labs Layered Space-Time Architecture, BLAST) Multiple transmitted data streams are separated and detected successfully using a combination of array processing (nulling) and multi-user detection (interference cancellation) techniques A broadband channel scenario using a MIMO generalization of classical decision feedback equalizer (DFE) The nulling operation is performed as “feed-forward filter” and the interference cancellation operation is performed by the “feedback filter”

Spatial Multiplexing-continued May have error propagation The presence of antenna correlation and the lack of scattering richness in the propagation environment reduce the achievable rates of spatial multiplexing techniques Enhancement: Use MMSE interference cancellation, perform ML detection for first few streams

Space time coding Improve downlink performance without requiring multiple receive antennas Easily combined with channel coding Do not require channel state information at the transmitter Robust against non-ideal operating conditions

Space-time Trellis codes Maps information bit stream into Mt streams of symbols Decoding complexity increases exponentially as a function of the diversity level and transmission rate Example:

Space time block codes

Cons and pros of space time block codes Achieve full diversity at full transmission rate for any signal constellation Does not require CSI at the transmitter ML decoding involves only linear processing at the receiver Does not provide coding gain A rate-1 STBC cannot be constructed for any complex signal constellation with more than two transmit antennas Simple decoding rule valid only for flat-fading channel where channel gain is const over two consecutive symbols

Tradeoff between diversity and throughput BLAST achieves max spatial multiplexing with small diversity gain Space time codes achieves max diversity gain with no multiplexing gain Linear dispersion codes (LDC): achieve higher rate with polynomial decoding complexity for a wide SNR range Build in the diversity into the modulation

Build Diversity into modulation

Receiver techniques Coherent and non-coherent techniques Coherent technique require channel state information by channel estimation or training sequences and feed this to joint equalization/decoding algorithm Non-coherent techniques does not require CSI and more suitable for rapidly time-varying channels

Joint Equalization/Decoding techniques M-BCJR algorithm: at each trellis step, only M active states associated with the highest metrics are retained Significant reduction in the number of equalizer/decoder states

Sphere decoder Suitable for codes with lattice structures Perform ML search with low computation complexity

Joint Equalization/Decoding of space time Block codes Eliminate inter-antenna interference using a low complexity linear combiner Single-carrier frequency domain equalizer (SC-FDE)

Performance of SC-FDE

Non-coherent techniques Does not require channel estimation Include blind identification and detection schemes Exploit channel structure (finite impulse response), input constellation (finite alphabet), output (cyclostationarity) to eliminate training symbols Use ML receiver which assumes statistics about channel state but not knowledge of the state itself

Summary in signal transmission Mitigate fading effect by using space diversity Use MIMO to realize spatial rate multiplexing gains Use equalization techniques (ex: M-BCJR, SC-FDE) to mitigate channel frequency selectivity Use channel estimation and tracking, adaptive filtering, differential transmission/detection to mitigate time selectivity

Networking issues Medium sharing resource allocation Mobility and routing Hybrid networks

Resource allocation Allocation criteria: rate-based criteria and job-based criteria Rate-based criteria provide average data rates to users which satisfy certain properties Job-based criteria schedule data delivery in order to optimize various QoS guarantees based on the job requests

Resource allocation-Rate-Based QoS criteria Utilize the multi-user diversity inherently available in wireless channels Schedule users when their channel state is close to peak rate it can support => inherent unfairness Keep track of the average throughput Tk(t) and rate Rk(t), transmit the user with the largest Rk(t)/ Tk(t) among the active users If channel is slow time-varying, introduce random phase rotations between the antennas to simulate fast fading

Impact of spatial diversity Multi-antenna diversity provide greater reliability by smoothening channel variations Multi-user diversity utilize the channel variability across users to increase throughput Choose diversity techniques according to channel conditions, mobility and application constraints For example, low delay-applications with high reliability requirement may use multi-antenna diversity with space time codes

Hybrid Networks Two approaches to increasing TCP efficiency in hybrid networks Reduce error rate in wireless channel by using more sophisticated coding schemes, such as space-time codes Use explicit loss notification (ELN) to inform the sender that the packet loss occurred due to wireless link failure rather than congestion in wired part

Space time code and TCP throughput STBC-enhanced 802.11a achieves a particular throughput value at a much lower SNR value than the standard 802.11a STBC modify the SNR region under which a particular transmission rate should be chosen STBC increase the transmission range and improve robustness of WLANs

STBC-enhanced 802.11a The difference between STBC 802.11a and 802.11a becomes smaller when channel quality is sufficiently good STBC-802.11a can switch to faster transmission mode at much lower SNR values

Conclusion In wireless networks, power and spectral bandwidth are limited Limitation on signal processing at terminal and requirement of sophisticated resource allocation techniques due to variation in capacity Spatial diversity improves data rates and reliability of individual links Space time codes improves link capacity and system capacity through resource allocation

Future works Space time code design Implementation issues-low-cost multiple RF chains and low-power parallelizable implementation of STC receiver signal processing algorithm Receiver signal processing-the development of practical adaptive algorithm that can track rapid variation of large number of taps in MIMO channel and/or equalizer Standardization activities

Reference [1]S. N. Diggavi, N. Al-Dhahir, A. Stamoulis, and A.R. Calderbank, “Great Expectations: The Value of Spatial Diversity in Wireless Networks,” Proceeding of The IEEE, Vol. 92, No. 2, pp219-270, Feb 2004 [2] Sergio Verdu, “Multiuser Detection,” Cambridge University Press, 1998