1
Fixed

Point Modeling in an Ultra Wideband (UWB)
Wireless Communication System
by
Martin Clark
,
Mike Mulligan
,
Dave Jackson
, and
Darel Linebarger
Ultra wideband (UWB) wireless technology is poised to replace high

speed data cables in
homes and offices (Stroh 2003). UWB technology will be capable of transmit
ting hundreds of
megabits per second over distances of several meters. Target applications include connecting
digital cameras to computers and DVD players to HDTV screens. Companies expect to ship
commercial UWB products by the end of 2005.
UWB range is f
undamentally limited by low

power, high

speed transmission, and so there is
little margin for implementation losses. However, the success of UWB in the marketplace also
hinges on low

cost implementation. The difference of a few meters in range, or a few do
llars in
cost, could make or break UWB.
Fixed

point engineering is critical in managing this all

important tradeoff between UWB
range and cost. First, fixed

point word lengths strongly influence hardware size and cost. The
silicon area of a multiply opera
tion, for instance, is roughly proportional to the
square
of word
length. Second, word lengths and scaling strongly influence the signal

to

noise ratio (SNR)
degradation of the communication link. Decreasing the SNR degradation by 1 dB can increase
coverag
e by up to 25%.
Unfortunately, fixed

point engineering is also very challenging and time

consuming,
typically demanding 25%
–
50% of the total design time. In this article, we explore fixed

point
design using Simulink® with a focus on a UWB technology propo
sal. We demonstrate techniques
and offer tips for accelerating the design process.
Simulink Model
—
Overview
We base our Simulink model on the
multiband orthogonal frequency division multiplexing
(
OFDM)
(Heiskala and Terry, 2002) UWB proposal submitted to the
IEEE 802.15.3a
standards
group in September 2003. Subsequent proposals have not changed the essential technology
.
The proposal supports seven data rates in the range 55
–
480 Mb/s. The highest mandatory rate
is 200 Mb/s. OFDM signals are transmitted using a frequency hopping (multiband) scheme. Our
Simulink model captures the end

to

end physical layer (PHY) for the
highest mandatory data rate
and for the mandatory frequency hopping mode.
Key Characteristics of Multiband OFDM PHY
–
200 Mb/s Mode
RF transmission bandwidth
528 MHz
Frequency hopping ("Mode 1 device")
3 sub

bands (3.43, 3.96, 4.49 GHz centers)
Error co
rrection coding
Convolutional with puncturing
Code rate
R=5/8
Modulation
Quaternary Phase Shift Keying (QPSK)
OFDM transmission
128

point IFFT; zero

DC
2
Payload symbols per OFDM symbol
100
Time spreading
2x (across frequency hops)
Multipat
h resistance from cyclic prefix
60 ns
The multiband OFDM proposal is, in many ways, similar to the IEEE 802.11a/g WLAN
PHY standards. Leveraging this similarity, we adapted our
UWB model
(see Figure 1) in just a
few days, from an existing
802.11a model
. Our adapted model also includes th
e UWB channel
MATLAB code
programmed by Intel and used by the IEEE 802.15.3a group.
Figure 1: Top level of Simulink model. Click on image to see enlarged v
iew.
The transmitter and receiver each comprise three sections (Figure 1):
binary data processing (blue)
digital baseband processing (orange)
baseband model of the analog front

end and channel (purple).
We are interested primarily in the fixed

point d
esign of the digital baseband section. You can
think of the rest of the model as a test harness: it enables us to quickly assess the impact of the
fixed

point design on end

to

end link performance.
OFDM Transmitter
The purpose of this subsystem (Figure 2)
is to transform a payload of QPSK symbols into a
large frame of OFDM symbols (165 samples each) to be passed along to the transmitter’s
front

end.
Figure 2: OFDM transmitter. Click on image to see enlarged view.
The blue
Convert block
at the subsystem input converts the incoming signal into a
fixed

point data type. In reality, this operation wouldn't exist; rather, the QPSK modulator would
translate incoming bits directl
y into fixed

point data. The purple block at the subsystem output
converts to double

precision floating point (for our purposes, you can think of it as a D/A
converter).
We highlight (orange) the inverse fast Fourier transform (IFFT) block and gain block
because
3
they perform fixed

point
arithmetic
. All other blocks (white) are simply fixed

point "data
shufflers." The orange highlighting throughout the UWB model helps you quickly identify which
blocks will be involved in the fixed

point design process.
OF
DM Receiver
The OFDM receiver (Figure 3) involves more signal processing
—
and, thus, more fixed

point
arithmetic
—
than the transmitter. The receiver requires arithmetic in four sections:
cyclic processing
FFT
channel estimation/compensation
time despread
ing
Cyclic processing and channel estimation/compensation are necessary to mitigate the effects
of multipath channel dispersion.
Figure 3: OFDM receiver. Click on image to see enlarged view.
Figure 4 shows our channel estimation/compensation subsystem. It implements a simple,
low

cost phase

compensation scheme. (More sophisticated schemes exploit the channel's
frequency coherence, and thus improve noise averaging [2].) It does not compensate for channel
magnitude variations across the OFDM tone set because such schemes are computat
ionally
expensive and also unnecessary for QPSK. Our scheme avoids division with a complex divisor,
and ensures that the magnitude of the division output has a small dynamic range.
Figure 4: Channel estimation and compensation. Click on image to see enlarged view.
Floating

Point Reference
Si
mulink’s
data

type override
feature makes it straightforward to switch between fixed point
and floating point for any subsystem or for the entire model. Our m
odel also automatically runs a
script that highlights (in green) arithmetic subsystems/blocks that use floating

point override.
For our initial floating

point reference, we set the channel SNR to a high value (60 dB),
which helps us isolate the impact of f
ixed

point effects on symbol distortion. Figure 5 shows two
scopes from the UWB simulation: (a) the
power spectrum
of the baseband

equivalent received
signal,
over all three sub

bands, and (b) the
signal constellation
after channel phase estimation and
compensation.
4
Figure 5: UWB simulation scopes. Click on image to see enla
rged view.
The DC null in the power spectrum is from the OFDM transmission, but the rest of the
spectrum approximately follows the frequency

selective fading characteristic of the multipath
channel. The dynamic range over the OFDM tone set is about 30 dB,
which is also evident in the
magnitude

spread of the phase

compensated signal constellation. A clean "X" indicates almost
perfect phase compensation.
Fixed

Point Design Methodology
The next phase is to set word lengths and scaling for
every fixed

point ar
ithmetic block
in the
system. Together, the word length and scaling constrain the dynamic range of a signal. If poorly
engineered, they will introduce overflow or underflow, and degrade link performance. It makes
sense, therefore, that one of the most usef
ul things you can analyze in a fixed

point design is the
dynamic range of signals.
We used the following methodology for the UWB fixed

point design:
1.
Work through the system in the order of signal processing, enabling floating

point
overrides for downstrea
m subsystems.
2.
For a given arithmetic (orange) subsystem or block:
i.
Enable floating

point override and analyze the output signal’s dynamic range
ii.
Adjust word length and scaling to minimize overflow and underflow
iii.
Disable floating

point override, re

examine
dynamic range, and assess the
impact on link performance
This procedure is an iterative process, and the work flow can be tedious and time

consuming.
Fortunately, MATLAB and Simulink provide a number of tools to help accelerate the process. To
analyze dy
namic range, for instance, you can use one or more of the following:
Fixed

point
min/max logging
Model Verification
blocks
Built

in scopes
MATLAB analysis/visualization (via
Signal To Workspace
block or an
M S

function
)
We demonstrate the last approach in the following section.
Example: Transmitter Design
For the UWB model, we built a block that automatically outputs a Simu
link signal to a
histogram, which is an invaluable way to visualize dynamic range. Figure 2 shows this block
(labeled "Fixed

Point Analysis") attached to the transmitter gain’s output. Figure 6 shows the
5
associated histogram for the floating

point referenc
e (both in

phase and quadrature). The base

2
log scale is useful for visualizing dynamic range in terms of number of bits, i.e., word length.
Figure 6: Histogram of OFDM transmitter output; floating

point reference. Click on image to see
enlarged view.
Excluding zero

valued samples (which
are mapped to 2

15
in the plot), the signal magnitude
lies in the range 2

13
to 2
2
for more than 99.9% of the time, and so the signal can be represented
adequately with 16 bits (signed). This large dynamic range
—
90 dB
—
is typical in OFDM, and is
essentiall
y the result of passing a random signal through an IFFT.
The analysis block also automatically estimates that 2

14
might be a reasonable scale factor to
minimize overflow and underflow. The Fixed

Point settings dialog provides a similar estimation
capabil
ity, and can even
automatically set fixed

point scaling
for user

selected blocks.
Based on this analysis, we initially set the word length to 16 bits and the sca
ling factor to 2

14
for
all
arithmetic blocks (orange) in the transmitter. We do this by explicitly setting the fixed

point
parameters of the input gateway block and selecting "Same as input" for the fixed

point
parameters of all other arithmetic blocks in
the transmitter (Figure 7). We maintain floating

point
overrides in the receiver subsystem to isolate and diagnose potential problems in the transmitter
design.
Figure 7: Dialogs for (a) Gateway block at transmitter input and (b) Gain block. Click on image
to see enlarged view.
Figure 8 shows
the resulting histogram and phase

compensated signal constellation. Notice
that the constellation is somewhat distorted compared with our floating

point reference (Figure 5).
The histogram reveals that the highest values are saturated to a value of 2. (The
dashed lines in the
histogram represent the floating

point reference.) While these high

power transmitted values
occur only about 1% of the time, this is enough to cause
—
with high probability
—
significant
distortion at the output of the 128

point
receiver
FFT.
6
Figure 8: Results for 2

14
scaling. Click on image to see enlarged view.
We need to increase the scaling by one or two bits. Such an increase will cause underflow for
the small values at the gain’s output, but the effect should be minimal because transmitted signal
values smaller t
han 2

10
will be buried in the channel noise. Figure 9 shows the improvement with
2

12
scaling.
Figure 9: Improved results for 2

12
scaling. Click on image to see enlarged view.
Favoring the high end of a signal's range is not always the right strategy. Small signal values
sometimes pla
y a significant role, for instance, in channel estimation and compensation algorithms.
The point is that setting fixed

point scaling requires some finesse, particularly when it comes to
engineering for smaller word lengths. Auto

computation tools provide c
oarse estimates. However,
fine tuning often calls for a combination of visualization and insight.
The above example covers the basics of setting word lengths and scaling factors. The next
steps involve analyzing output signal dynamic ranges of individual
blocks in the transmitter,
tuning each block's fixed

point settings, and moving through the receiver using the same design
techniques.
Smaller Word Lengths
Beginning with 16 bits throughout the system lets you approach design issues incrementally
and the
n apply what you learn to smaller word lengths. For instance, when you care more about
overflow than about underflow, as is often the case, the desired
integer length
tends to be similar
for different word lengths.
Using the tools and methodology discussed
here, we were able to get a 10

bit design working
at a bit error rate of 0.1%, with only a 0.5 dB SNR degradation compared with the floating

point
reference.
Figure 10 illustrates how you can capture multiple fixed

point designs in a single model. The
wor
kspace variable
uwb.OFDMDataType
stores the word length. The
fpscaling
function selects
fixed

point scaling (or fraction length) based on the word length. For 16 bits, it uses a fraction
length of 14; for 12 bits, a fraction length of 11; and so on.
7
Figure 10: Capturing multi
ple fixed

point designs in a single model. Click on image to see
enlarged view.
Using variables and selector functions in this way, you can quickly switch between different
fixed

point designs. You can also write simple MATLAB® scripts to run simulations o
ver a range
of word lengths and channel conditions to explore tradeoffs between chip size (or power
consumption) and wireless range.
References
S. Stroh, "Ultra

wideband: multimedia unplugged," IEEE Spectrum, October 2003.
J. Heiskala and J. Terry, "OFDM
wireless LANs: a theoretical and practical guide," SAMS, 2002.
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