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Constellation Mapper and
Demapper for WiMAX
May 2007, version 1.1 Application Note 439
Introduction Altera provides building blocks that can be used to accelerate the
development of an IEEE 802.16e-2005 (WiMAX) compliant basestation.
This application note describes a reference design that demonstrates the
suitability of the Altera® tools and devices for implementing the
constellation mapping and demapping functions, which can also be
easily adapted for compatibility with other wireless standards.
WiMAX is an emerging broadband wireless technology that promises
high-speed data services. The IEEE 802.16e-2005 standard enables
mobility. There is significant market potential for this technology and it is
currently being deployed by equipment manufacturers. Altera devices
are the ideal platform for high throughput DSP designs such as those
found on a WiMAX basestation channel card. The devices’ dedicated
multiplier blocks and inherent parallel structure gives a significant cost
and performance advantage over general purpose processors for this
type of design.
f For more information on IEEE 802.16e-2005, refer to the IEEE Standard for
Local and Metropolitan Area Networks, Part 16: Air Interface for Fixed
Broadband Wireless Access Systems, IEEE P802.16e-2005, February 2006.
The reference design has the following features:
■ DSP Builder-based design
■ Parameterizable design optimized for efficient use of Cyclone® III
and Stratix® III FPGA resources
■ Soft-decision demapping for optimal BER performance when used
with the Altera Viterbi Compiler
You can use the reference design can be used as a starting point to
accelerate designs based on WiMAX or 3GPP LTE (third generation
partner project, long-term evolution) protocol
WiMAX Physical Figure 1 on page 2 gives an overview of Altera's reference design blocks
for implementing the IEEE 802.16e-2005 scalable orthogonal frequency-
Layer division multiple-access physical layer in WiMAX basestations. This
application note illustrates the functionality and implementation of the
symbol mapping and symbol demapping blocks. These blocks represent
the interfaces between bit level and symbol level processing.
Altera Corporation 1
AN-439-1.1 Preliminary
Constellation Mapper and Demapper for WiMAX
Figure 1. WiMAX Physical Layer
MAC/PHY Interface
Downlink Randomization Derandomization Uplink
FEC Encoding FEC Decoding
Interleaving Deinterleaving
Symbol Mapping Symbol Demapping
Channel Estimation
and Equalization To MAC
Pilot Insertion Desubchannelization
Pilot Extraction
Cyclic Prefix
Cyclic Prefix
Digital IF From ADC
2 Altera Corporation
WiMAX Physical Layer
WiMAX Modulation Specifications
This reference design provides a constellation mapper and demapper to
use with the IEEE 802.16e-2005 specification. The modes supported are
gray-coded QPSK, 16QAM, and 64QAM modulation schemes. You can
configure the hardware modules at run time, so you can use them in a
multi-user system where each user or subchannel may be operating with
a different modulation scheme.
The symbols are normalized so that each constellation has an equal
average power, as described by the specification. The mapping process
also multiplies each constellation point by a scaling factor. Figure 2 shows
the gray mapping for the three constellation modes and the associated
scaling factor. The demapper performs the complementary operation of
the mapper by extracting the bitstream from the received complex stream.
Figure 2. Gray-Coded Modulation Schemes
b2b1b0 c = 1 / √42
011 7
Q c = 1 / √10
010 5
Q 000 3 000 3
b0 c = 1 / √2
001 1 001 1 001 1
-1 1 I -3 -1 1 3 I -7 -5 -3 -1 1 3 5 7 I
101 -1 101 -1 101 -1
101 001 b1
100 -3 100 -3
100 101 001 000 b3b2
110 -5
111 -7
111 110 100 101 001 000 010 011 b5b4b3
The constellation mapper takes groups of bits and maps them to specific
constellation points. A specific magnitude and phase represents a certain
combination of bits. The operating mode for each user or subchannel is
configured at run time and is determined by assessing the channel
quality. The MAC layer adjusts the modulation scheme of each user, to
maximize throughput while meeting an acceptable error rate.
At the receiver, the phase and magnitude of each carrier is extracted, and
a decision must be made about what combination of bits the transmitter
sent. Because each of the carriers has been subjected to distortion by the
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Constellation Mapper and Demapper for WiMAX
wireless channel, there is an error in the position of each constellation
point. To decide on the combination of bits the design divides the
complex plane into equally sized regions that correspond to each
constellation point and outputs the bit combination of the region that the
received signal appears in—known as hard decision decoding.
You can achieve significantly better coding gain by making soft decisions.
For soft decision decoding each bit is assigned a confidence that it will be
a 0 or a 1. Although this decoding leads to greater hardware complexity,
it is essential to achieve satisfactory bit error performance, especially for
higher order modulation schemes such as 64QAM.
For QPSK, the soft information associated with each bit is calculated by
evaluating the values of the in-phase and quadrature components. The
calculation of soft information is more difficult for higher order
modulation schemes, because the real and imaginary axes carry more
than one bit of information.
This reference design implements a highly efficient, simplified log
likelihood ratio method for calculating the soft information.
f For more information on the theory and performance of the algorithm,
refer to Simplified Soft-Output Demapper for Binary Interleaved COFDM
with Application to HIPERLAN/2, Filippo Tosator & Paola Bisaglia, HPL-
2001-246, October 2001.
Soft Information Calculations
The following equations summarize the calculation of the soft
information for the bits on the I plane. You can calculate the
corresponding soft information associated with the imaginary plane
using the same equations and substituting the imaginary part of the
received symbol into the equations.
D ≈ –y [ i ]
I ,1 I
D ≈ –y [ i ]
I ,1 I
D ≈ –y [ i ] – 2
I ,2 I
D ≈ –y [ i ]
I ,1 I
4 Altera Corporation
Implementation with DSP Builder
D ≈ –y [ i ] – 2
I ,2 I
D ≈ –y [ i ] – 4 – 2
I ,3 I
Viterbi MegaCore Function Design Considerations
The soft decision metrics are ultimately passed on to the Viterbi decoder
MegaCore® function. The precision of the soft decision metrics must be
reduced, to reduce the complexity of the Viterbi decoder. Six bits of
precision exhibits the best balance between performance and complexity.
To make forward error correction (FEC) possible, the WiMAX
specification requires the transmitter to apply redundancy to the data, by
encoding each block of data using a tail-biting convolutional encoder.
This special type of convolutional encoder has the memory initialized
with the last data bits of the FEC block that are encoded, which the Viterbi
decoder exploits.
f For more information on the Altera Viterbi Compiler, refer to the Viterbi
Compiler User Guide and Viterbi Tail-Biting Double-Pass Decoding (P = TB)
on the Altera website at www.altera.com/support/examples/dsp-
The Altera Viterbi Compiler also supports soft decision decoding. Table 1
gives an example of the format of a three-bit soft decision input. This
format is used in this reference design, but with six bits of precision.
Table 1. Soft Symbol Input Representation
Soft Symbol Meaning
011 Strongest “0”
010 Strong “0”
001 Weak “0”
000 Weakest “0”
111 Weakest “1”
110 Weak “1”
101 Strong “1”
100 Strongest “1”
Implementation Digital signal processing (DSP) system design in Altera programmable
logic devices (PLDs) requires both high-level algorithm and HDL
with DSP Builder development tools. The Altera DSP Builder integrates these tools by
Altera Corporation 5
Constellation Mapper and Demapper for WiMAX
combining the algorithm development, simulation, and verification
capabilities of MATLAB and Simulink system-level design tools (from
The MathWorks) with VHDL synthesis, simulation, and Altera
development tools.
The DSP Builder shortens DSP design cycles by helping you create the
hardware representation of a DSP design in an algorithm-friendly
development environment. The existing MATLAB functions and
Simulink blocks can be combined with Altera DSP Builder blocks and
Altera intellectual property (IP) MegaCore functions to link system-level
design and implementation with DSP algorithm development. DSP
Builder allows system, algorithm, and hardware designers to share a
common development platform.
Designers can use the blocks in DSP Builder to create a hardware
implementation of a system modeled in Simulink in sampled time. DSP
Builder contains bit- and cycle-accurate Simulink blocks, which cover
basic operations such as arithmetic or storage functions. Complex
functions can be integrated by using MegaCore functions in DSP Builder
You can verify the fixed point performance of the algorithms using DSP
Builder and compare the results to a bit-accurate MATLAB simulation,
which is useful when prototyping the physical layer using the MATLAB
environment. You can integrate these features into a powerful testbench,
to give an ideal development environment for wireless system engineers.
Functional This section describes the functionality of the constellation mapper and
the constellation demapper.
Constellation Mapper
The constellation mapper takes a bitstream as an input and maps it onto
appropriate constellation symbols, according to the modulation method
that you specify.
Figure 3 shows the architecture of constellation mapper.
6 Altera Corporation
Functional Description
Figure 3. Constellation Mapper
Bits Avalon-ST Avalon-ST
Sink Source Symbols
Interface Address Serial to Interface
Generator Parallel IQ
The interleaver presents the input data as a serial bit stream. To generate
the symbols, you must group together a number of bits and calculate
which constellation point it corresponds to. The address generator groups
M/2 bits together to formulate an address where M is the constellation
order. You can use this address to index a lookup table. The lookup table
stores the constellation point corresponding to the group of bits.
To reduce the size of the lookup table, the design uses M/2 bits. The same
lookup table is shared for I and Q. You can generate an address location
in the lookup table for each constellation point, but it is not memory
efficient. The output of the lookup table is a serial stream of I and Q
samples (I, Q, I, Q, and so on). This output is converted into two parallel
output I and Q interfaces by the serial to parallel IQ converter.
Table 2 shows how the modulation input is encoded.
Table 2. Encoding for Modulation Input
Modulation Input Associated Modulation Scheme
00 Invalid Mode
10 16QAM
11 64QAM
You can modify the amount of precision (bitwidth) and the slope
(maximum constellation point) of the fixed point representation. The
maximum constellation point must be greater than the maximum value
of the three constellation schemes. It must also be large enough to
accommodate additional headroom for noise and boosted BPSK pilots.
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Constellation Mapper and Demapper for WiMAX
Interface Specifications
The Avalon® Streaming (Avalon-ST) input and output interfaces make it
easy to integrate this module with other IP from Altera and with any
other proprietary interface.
f For more information on Avalon-ST interfaces, refer to the Avalon
Streaming Interface Specification.
The Avalon-ST interface has the following parameters:
■ Ready latency: 1
■ Sink symbols per beat: 1
■ Source symbols per beat: 2 (I and Q are conveyed synchronously)
The block supports packetized transfers using the start and end of packet
signals. The start of a packet signal resets the state of the block so that the
module can recover from a bad packet.
Constellation Demapper
The constellation demapper takes packets of received constellation points
as an input, and outputs the corresponding soft decision bitstream.
Figure 4 shows the architecture of the constellation demapper.
Figure 4. Constellation Demapper
+ Avalon-ST
Received Soft
Decisions Sink Soft Source Decisions
Interface Parallel Decision Parallel Interface
to Serial Calc to Serial
To achieve maximum hardware efficiency, this constellation demapper is
fully time division multiplexed. Backpressure is applied to the upstream
module so that data is only provided at a maximum rate of one complex
sample for every six clock cycles. If data is acquired every six clock cycles,
the output bus fully conveys the soft decisions when operating in 64QAM
modulation mode. In the 16QAM and QPSK modes, the output bus is not
fully used.
8 Altera Corporation
Reference Design Throughput
The constellation demapper multiplexes the IQ data onto a single bus,
and passes the serial data stream on to the soft decision calculator where
the appropriate metrics for the modulation scheme are calculated (see
“Soft Information Calculations” on page 4). These metrics determine the
confidence in the polarity of each constellation bit. These metrics are time
multiplexed onto a single bus, before they are passed on to a quantization
module that reduces the bitwidth of the signal according to a
quantization interval.
You can modify the amount of precision (bitwidth) and the slope
(maximum constellation point) of the fixed point representation. The
maximum constellation point must be greater than the maximum value
of the three constellation schemes. It must also be large enough to
accommodate additional headroom for noise.
Interface Specifications
The Avalon Streaming (Avalon-ST) input and output interfaces make it
easy to integrate this module with other IP from Altera and with any
other proprietary interface.
The Avalon-ST interface has the following parameters:
■ Ready latency: 1
■ Sink symbols per beat: 1
■ Source symbols per beat: 2 (I and Q are conveyed synchronously)
The block supports packetized transfers using the start and end of packet
Reference For the 64QAM mode, one complex symbol of information is
characterized by a group of six bits. The maximum symbol throughput is
Design equal to one sixth of the maximum bitrate or soft decision throughput.
Altera Corporation 9
Constellation Mapper and Demapper for WiMAX
Table 3 shows the relationship between the FFT size and required
baseband symbol throughput. Assuming a clock frequency of
182.784 MHz, you can show how many independent bitstreams can
be mapped or demapped using a single constellation
mapper/demapper module, which is useful for multiple-antenna or
multiple-carrier basestations.
Table 3. Constellation Mapper Processing Capability
Baseband Symbol Rate Clock Frequency Oversampling Number of
FFT Size
(MSPS) (MHz) Factor Streams
128 2.428 182.784 128 21
512 5.712 182.784 32 5
1024 11.424 182.784 16 2
2048 22.848 182.784 8 1
Getting Started This section contains the following information:
■ System Requirements
■ Installing the Reference Design
■ Running the Reference Design
■ Testbench Features
■ Synthesis Results
System Requirements
The scalable OFDM engine requires the following hardware and
■ A PC running the Windows XP operating system
■ Quartus II version 7.1
■ DSP Builder version 7.1
■ MATLAB version R2006B
■ Simulink version R2006B
To take advantage of some of the testbench features, Altera
recommends the MATLAB signal processing blockset.
Installing the Reference Design
To install the reference design, run the an439-v1.0.exe file to launch
InstallShield and follow the installation instructions.
10 Altera Corporation
Getting Started
1 The default installation directory is
c:\altera\reference_designs\constellation. If you have
other WiMAX reference designs from Altera, install this
reference design to the path
and into a directory called \constellation.
Figure 5 shows the directory structure after installation.
Figure 5. Directory Structure
Contains the following files:
- DSP Builder constellation mapper custom library component
- DSP Builder testbench for constellation mapper (mapper_tb.mdl)
- MATLAB data file containing testbench stimulus / golden data
- DSP Builder constellation demapper custom library component
- DSP Builder testbench for constellation demapper
- MATLAB data file containing testbench stimulus / golden data
- Simulink library containing links to both constellation components
- Simulink library initialization file (slblocks.m)
Contains this document (an439.pdf)
Running the Reference Design
To run the reference design follow these steps:
1. Open MATLAB.
2. Change the MATLAB directory to the installation directory.
3. Open Simulink, and go to the Simulink library browser.
4. Verify that the Altera WiMAX Constellation Map/Demap
reference design library exists.
5. Open the testbench associated with the desired reference design
(mapper_tb.mdl or demapper_tb.mdl). The testbench
automatically loads the necessary testbench stimulus from the
6. Simulate the design.
Altera Corporation 11
Constellation Mapper and Demapper for WiMAX
Testbench Features
You can experiment with various input and output throughputs by
modifying the output ready signal. Also, you can modify the input
throughput, by providing a new piece of data only when the input
interface is ready, and by providing another randomly generated
binary number that is equal to one, which leads to a more exhaustive
The constellation mapper reference design is connected to an X/Y
plot, so you can visualize the output constellation.
Both the constellation mapper and demapper testbenches verify the
correct behavior when packets containing data associated with
different modulation schemes are passed through the block.
12 Altera Corporation
Synthesis Results
Table 4 and Table 5 show results using the Quartus II software,
version 7.1.
Table 4. Constellation Mapper Synthesis Results
Combinational Logic Memory 9×9
Device fMAX (MHz)
ALUTs/LUTs Registers M512 M9K multipliers
Stratix III 40 108 0 1 0 418
Cyclone III 59 108 0 1 0 400
Table 5. Constellation Demapper Synthesis Results
Combinational Logic Memory 9×9
Device fMAX (MHz)
ALUTs/LUTs Registers M512 M9K multipliers
Stratix III 338 809 0 1 0 258
Cyclone III 378 741 0 1 0 224
Conclusion A number of wireless applications including GSM, wideband code
division multiple access (W-CDMA), high-speed downlink packet
access (HSDPA), WiMAX, and 3GPP LTE require constellation
mapping and demapping. This reference design shows how you can
easily and efficiently implement these functions on Altera FPGAs
using DSP Builder-based design methodology.
Altera Corporation 13
Constellation Mapper and Demapper for WiMAX
Copyright © 2007 Altera Corporation. All rights reserved. Altera, The Programmable Solutions Company,
the stylized Altera logo, specific device designations, and all other words and logos that are identified as
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Corporation in the U.S. and other countries. All other product or service names are the property of their re-
spective holders. Altera products are protected under numerous U.S. and foreign patents and pending
101 Innovation Drive applications, maskwork rights, and copyrights. Altera warrants performance of its semiconductor products
San Jose, CA 95134 to current specifications in accordance with Altera's standard warranty, but reserves the right to make chang-
www.altera.com es to any products and services at any time without notice. Altera assumes no responsibility or liability
arising out of the application or use of any information, product, or service described
Literature Services: herein except as expressly agreed to in writing by Altera Corporation. Altera customers
[email protected] are advised to obtain the latest version of device specifications before relying on any pub-
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14 Altera Corporation

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