Title: Implementation of the Alamouti OSTBC to a Distributed Set of Single-Antenna Wireless Nodes
1Implementation 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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2Remote 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
3Use 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
4Motivation 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
5Signal 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
6Illustration 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
7Time 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
8Time 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
9Packet 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
10Channel 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
11Least 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
12Variable 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
13Channel 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
14System 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
15Receiver 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
16Toyons 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
17Four-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
18Conclusion
- 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