Computationally Simple
OFDM
Todor Cooklev
IPFW Wireless Technology Center
cooklevt@ipfw.edu
Presentation Overview
1.
2.
3.
4.
Introduction
Simple OFDM
Preliminary Results
Conclusions and directions for future
research
Conventional OFDM
Conventional OFDM is based on the discrete Fourier transform;
IFFT performs multicarrier modulation
S/P
bit-to-symbol
mapping
xcp [m]
x[n]
X [k ]
N-point
IFFT
Add
CP
P/S
Conventional OFDM receiver:
FFT performs demodulation
Xˆ [k ]
P/S
symbol
-to-bit
H [k ]
synchronization
Y [k ]
N-point
FFT
Remove
CP
S/P
N-point
FFT
channel
impulse
response
channel
estimation
Simple OFDM idea
• Can we simplify the DFT/FFT operations?
– What would be the system performance
– Can we simply the algorithms further?
• Make a detailed comparison
Rounded DFT idea
• The DFT, implemented by the Fast Fourier
Transform algorithm (FFT), can be
simplified via the rounded sine and cosine
functions
rcos2
2cos(t )

(t ) 
2
rsin 2
2sin(t )

(t ) 
2
• Any number of quantization levels can be
used
5-level: -1, -0.5, 0, 0.5, 1
9 level: add -0.75, -0.25, 0.25, 0.75 to the above
Simple OFDM
Definition of standard DFT:
k = 0,1,…,N – 1
Using the relationship:
the rounded DFT is derived with substitution
as follows:
k = 0,1,…,N – 1
Two possible inverses
• Approximate - the conjugate transpose
• Exact – possible, but in general is not
multiplierless
Simulation
• Models of conventional OFDM were created to
compare with standard OFDM performance
characteristics
• Many simulations have be run using the
following key parameters:
•
•
•
•
64 parallel data channels (64 point DFT/RDFT)
QPSK and 16 QAM modulation schemes
Quantization levels of 5, 9 and 17
Pairing of IFFT with RDFT
Preliminary Results
Comparison of conventional OFDM bit error rate with 5 level rounded system
-1
10
-2
Bit Error Rate
10
-3
10
-4
10
OFDM QPSK
OFDM 16QAM
R5L OFDM QPSK
R5L OFDM 16QAM
-5
10
-6
10
0
5
10
Eb/N0
15
20
Preliminary Results
Comparison of conventional OFDM bit error rate with 9 level rounded system
-1
10
-2
Bit Error Rate
10
-3
10
-4
10
OFDM QPSK
OFDM 16QAM
R9L OFDM QPSK
R9L OFDM 16QAM
-5
10
-6
10
0
5
10
Eb/N0
15
20
Preliminary Results
Comparison of conventional OFDM bit error rate with 17 level rounded system
-1
10
-2
Bit Error Rate
10
-3
10
-4
10
OFDM QPSK
OFDM 16QAM
R17L OFDM QPSK
R17L OFDM 16QAM
-5
10
-6
10
0
5
10
Eb/N0
15
20
Preliminary Results
Comparison of conventional OFDM bit error rate with 5 level RDFT paired with
standard IFFT
-1
10
-2
Bit Error Rate
10
-3
10
-4
10
OFDM QPSK
OFDM 16QAM
R5L OFDM QPSK
R5L OFDM 16QAM
-5
10
-6
10
0
5
10
Eb/N0
15
20
Benefits
• Currently ASICs are used to implement
OFDM
• A dedicated OFDM chip (ASIC) contains
multiple FFTs
– Reduction in chip area
• Make possible reconfigurable hardware
implementation (FPGA) or even an entirely
software implementation (on a DSP or
GPP)
What we have achieved
• Built a software simulation of the new
idea
• The rounded transform leads to viable
OFDM communication systems at
specific quantization levels
• With performance that approaches
conventional OFDM systems
• With reduced computational complexity
Future Research
• Investigate system performance when faced with
carrier offset error
• Investigate system performance when faced with
inter-symbol interference (short cyclic prefix)
• Apply the results to systems with multiple
antennas
• Develop new and simplified algorithms
• Investigate the implementation in greater detail
Thank you!