Implementation of the Alamouti OSTBC to a Distributed Set of Single-Antenna Wireless Nodes

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Implementation of the Alamouti OSTBC to a
Distributed Set of Single-Antenna Wireless Nodes
Richard E. Cagley Brad T. Weals Scott A. McNally Toyon Research Corp. 6800 Cortona Drive Goleta, CA 93117 E-mail rcagley_at_toyon.com Ronald A. Iltis Shahnam Mirzaei Ryan Kastner University of California Santa Barbara, CA 93106-9560
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Remote Data Collection for Wireless Sensor
Networks (WSNs)

• We address the specific problem of range
  extension of wireless sensor nodes that may have
  to communicate to a remote collection center
• Due to the significant range, such sensors do not
  have line-of-sight to the collector and,
  furthermore, the collector may be mobile
• This results in fast fading

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Use of Space-Time Coding to Provide Resistance to
Fast-Fading in Non LOS

• We seek a MIMO architecture that can provide
  diversity without feedback from a collection
  point
• This allows us to operate in highly mobile
  scenarios
• Orthogonal space-time block codes (OSTBCs) do not
  require channel state information (CSI) to be
  sent back from the collector
• We seek full diversity codes with possible
  reductions in rate, e.g., Tarokh
• For the Alamouti code, consider two transmit and
  one receive antenna with the received signals at
  subsequent time periods being

• Detector outputs use combinations of both
  channels
• As additional channels are added there is reduced
  probability of outage

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Motivation Diversity Increases Probability of
Packet Success

• Packet success as a function of range for
  different numbers of sensor nodes
• Collector is assumed to have one antenna element
• Node transmit power of 20 dBm
• Receiver sensitivity of -105 dBm
• Background noise of -114 dBm/MHz
• Free-space loss exponent of 2.8
• Binary-phase shift-keying (BPSK) modulation at a
  rate of 500 kbps
• Carrier frequency of 1350 MHz with a packet size
  of one kByte
• Collection platform speed is set at 100
  miles/hour
• Jakes fading model
• There is a significant range extension that can
  be achieved

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Signal Model

• With Nc collector antenna elements, the received
  collector signal rc(t) 2 CNc on the
  uplink is given in continuous-time by
• The term
  represents additive white
  Gaussian noise with individual terms having
  variance ?2
• The symbols sk(m) represent a training sequence
  in the estimation phase, or the m-th row and k-th
  column of an OSTBC matrix
• The pulses p(t) are raised-cosine with minimal
  excess bandwidth to maximize orthogonality

where is the channel from
sensor k to the collector, Es is the symbol
energy ?k is the frequency offset in Hz for
sensor k, and ?k is the corresponding delay
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Illustration of Parameter Estimates

• Challenging parameter estimates are the frequency
  offsets
• Synchronization must happen during transmission
  in order to exploit the OSTBC
• Can be achieved with a start packet sent from
  collector
• High oversampling and real-time processing in
  FPGA allow accurate timing

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Time and Frequency Offset Estimation

• In forming the detector, consider a new set of
  symbols formed by the conjugate pairs of received
  samples (ND is oversampling rate)
• We note that if sampled at the symbol rate, and
  aligned with the peak of the pulse shape q(0),
  the resulting received signal can be simplified
  to
• If proper timing alignment is achieved, the
  conjugate pair becomes

where
are
the conjugate pairs of received symbols and
is the
product of two independent circular Gaussians
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Time and Frequency Offset Estimation (cont.)

• We can collect a set of these homodyne symbols
  corresponding to one less than the length of the
  training sequence
• We see that if the symbols d(n) were known then a
  correlation would result and associated carrier
  offset formed
• For this purpose we create a set of conjugate
  training symbol pairs

where and are
a known set of training symbols.

• In forming the correlation
  , a peak will indicate the time offset
• It is at this point that the carrier offset is
  recorded

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Packet Structure and Associated Receiver Structure
Symbol Period (Time)
Xmtr 1 Training Symbols w/ Interleaved 0s
Xmtr 1 Data Symbols
Carrier Frequency fc1 fc MHz Df1
Compare correlation magnitudes select higher
value to determine timing
Homodyne for Xmtr 1 Training Symbols
Space-time decoding and remaining receiver
functions
UNEQUAL RANDOM CARRIER FREQ OFFSETS Df1 ? Df2
A/D
DDC
Analog Rcvr
Homodyne for Xmtr 2 Training Symbols
Carrier Frequency fc2 fc MHz Df2
Xmtr 2 Data Symbols
Xmtr 2 Training Symbols w/ Interleaved 0s
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Channel Estimation and Residual Carrier Offset
Correction

• After timing estimation and associated
  downsampling, the resulting received signal model
  is given by

where
with individual terms

• The term represents
  the residual carrier offset error
• We note there is both a time varying channel
  (hk(l)), due to mobility, as well as a constant
  effective Doppler shift (ej ? l) due to
  inaccuracies in the carrier offset estimation
  block.
• In order to track the time-varying channel, there
  are several possible approaches
• One of the highest performers is to employ a
  Kalman filter (KF) using a second-order
  autoregressive (AR2) process
• Costly in terms of hardware, particularly for a
  high data rate system

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Least Mean Square (LMS) Channel Tracking

• We seek a channel tracker that offers low
  computational complexity and can be performed
  recursively
• Filters, such as least mean square (LMS), offer
  this utility while still obtaining good
  performance
• For such an solution we consider the cost

• Seeking a recursive implementation that can not
  only estimate the channel with multiple training
  symbols, but also track the channel in
  decision-directed (DD) mode, we can form the LMS
  filter

where
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Variable LMS (vLMS)

• One of the drawbacks of the classic LMS
  implementation is the fact that the step size is
  constant
• In most packet-based systems there will be both a
  training period as well as a data packet period
• Intuitively, one solution would be to have
  different values for ? during each period
• But, there is the additional issue that during
  the first few symbols of the training packet
  there will be a much larger error than at the end
  of the training period
• For this reason, we employ the variable step-size
  LMS (vLMS) algorithm proposed by Aboulnasr and
  Mayyas
• Here, the update expression for the step size is
  given by

where MSE e(l)e(l), ? 2 (0,1 and ? gt 0
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Channel Tracking Simulation Results

• In the simulations we compare the vLMS
  architecture to the AR2-KF channel tracker as
  well as the case where the channel is known
• As can be seen from the figure, vLMS offers worse
  performance than the AR2-KF architecture, but is
  still acceptable
• The vLMS algorithm is able to be readily realized
  in hardware.
• The vLMS parameters are ? .99 and ? .001
• The channels are normalized such that the maximum
  value of the channel response is equal in
  magnitude to the transmitted symbol

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System Generator Architecture for One of the
Receive Paths
Peak search and time/frequency offset estimation
Quadrature downconversion and pulse-shape
filtering
Conjugate symbol formation and correlation
vLMS channel tracking and symbol decoding
ADC input
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Receiver FPGA Resource Use

• The transceiver has been targeted to a Xilinx
  Virtex-4SX35 FPGA
• The clocking frequency of the device is 64 MHz
• As can be seen from the table, functions related
  to time and frequency offset estimation represent
  the highest use of resources
• Buffering for producing the correlator output and
  performing the peak search require a significant
  amount of memory
• We currently use on chip dual-port block RAM in
  order to maximize throughput

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Toyons Modular MIMO (ModMIMO) Testbed

• The RF portion of our testbed is designed to
  provide flexibility over both phase and frequency
  coherency
• A set of common IF/RF mixing signals are
  generated on a base board and feed each RF board
  with coherent signals
• This represents the least challenging arrangement
  in terms of signal processing both for timing
  and frequency estimation
• With the modular design, single antenna nodes can
  be prototyped by having their own VCO-RF board
  pair

• One important element of our design is our choice
  of voltage control oscillator
• We are using a Vectron temperature compensated
  crystal with 1.5 ppm stability over -20 C to 70
  C and 5.0 ppm over -40 C to 85 C
• Frequency offset affects our search space for
  that parameter estimate

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Four-Antenna Capable Testbed

• Designed as a research and development platform
• Operates at 915 MHz
• Leverages an Avnet V4SX35 motherboard
• Variety of interfaces, including UART, USB, and
  Ethernet
• Connector, VCO, and RF translation boards were
  all designed in house
• Fabbed and populated by outside partner
• Individual components representative of fieldable
  hardware and can be readily translated to a final
  design

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Conclusion

• We have presented a distributed OSTBC technique
  that can be used to increase the link reliability
  of wireless nodes, particularly when transmitting
  over long range with NLOS conditions
• While able to reduce the necessary link margin,
  through channel diversity, there are several
  technical challenges
• Nodes no longer share a common crystal - We lose
  synchronization over carrier frequency
• As the medium access control (MAC) layer is not
  synchronized, there are special timing
  considerations that must be made
• Our solution for this problem is to use a high
  oversampling rate and employ training sequences
  to make accurate time/frequency offset estimates
• Accurate time resolution provides good
  synchronization
• A minimum of orthogonalization is lost between
  code pairs
• We note that use of an OSTBC requires the nodes
  to share a common set of data
• Data can be shared if assumed that local wireless
  communication is essentially free Ratio of
  long- to short-range power output high