Advanced telecommunications for wireless systems Investigating OFDM by MathCAD. Timo Korhonen, Communications Laboratory, TKK. Motto. If you tell me – I forget If you show me – I will remember If you involve me – I can understand - a Chinese proverb. Topics.
Timo Korhonen, Communications Laboratory, TKK
OFDM is spectral efficient, but not power efficient (due to linearity requirements of power amplifier=the PAPR-problem).
OFDM is primarily a modulation method; OFDMA is the corresponding multiple access scheme.
OFDM TX signal = Sequence of OFDM symbols gk(t) consisting of serially converted complex data symbols
The k:th OFDM symbol (in complex LPE form) is
where N = number of subcarriers, TG + TS= symbol period with the guard interval, and an,k is the complex data symbol modulating the n:th subcarrier during the k:th symbol period.
In summary, the OFDM TX signal is serially converted IFFT of complex data symbols an,k
Orthogonality over the FFT interval:
Phase shift in any subcarrier - orthogonality over the FFT interval should still be retained:
Square-windowed sinusoid in time domain
"sinc" shaped subchannel spectrum in frequency domain
See also A.13 in Xiong, Fuqin. Digital Modulation Techniques.
Norwood, MA, USA: Artech House, Incorporated, 2006. p 916.
Subcarrier spacing = 1/TFFT
Spectral nulls at other subcarrier frequencies
ofdm spectra by rect windowed sinc.mcd
http://www.eng.usf.edu/wcsp/OFDM_links.html ~ Aalborg-34-lecture13.pdf
To be able to equalize the frequency response of a frequency selective channel, pilot subcarriers must be inserted at certain frequencies:
Pilot subcarriers at some, selected frequencies
Between pilot subcarriers, some form of interpolation is necessary!
Subcarrier of an OFDM symbol
Pilot allocation example cont.- A set of pilot frequencies
The Shannon sampling theorem must be satisfied, otherwise error-free interpolation is not possible:
maximum delay spread
*Spike distance depends on impulse response
Pr: Received mean power
Gs: Shadow fading
Log r ~ Fast fading
Comment how realistic this simulation is? Rayleigh or Rice fading channel?
impulse response radio ch.mcd
Frequency response shown by swapping left-hand side of the fft
- Note that true pdf area equals unity, how could you adjust the above for this?
- Add comparison to the theoretical Rayleigh distribution!
N(0,s2): Log normal distribution
DELAY SPREAD IN TIME DOMAIN fading channel?
Small delay spread
Large delay spread
OFDM in a multipath channel.mcd
Determine by using MathCAD’s linterp-function the maximum rate for delay spread of 70 us!
Rate and delay spread.mcd fading channel?
cyclic prefix.mcd fading channel?
OFDM papr.mcd fading channel?
Prasad, Ramjee. OFDM for Wireless Communications Systems.
Norwood, MA, USA: Artech House, Incorporated, 2004. p 150.
b) peak cancellation
DESIGN fading channel?
How would you modify this function to fading channel?
simulate unipolar system?
http://www.eng.usf.edu/wcsp/OFDM_links.html fading channel?