siso_ofdm_mf_sim.m File Reference

Functions
Modulation	order (2/4/16/64=BSPK/QPSK/16-QAM/64-QAM) TX_SCALE
Scale for Tx	waveform ([0:1]) % OFDM params SC_IND_PILOTS
Number of data	symbols (one per data-bearing subcarrier per OFDM symbol) N_LTS
Number of CP samples to use in	FFT (on average) LTS_CORR_THRESH=0.8
MAX_TX_LEN, 2^20	min ()
id	lts_f ()
1/sqrt(2	modvec_bpsk ()
mod_fcn_16qam, tx_data	arrayfun ()
otherwise	fprintf ('Invalid MOD_ORDER(%d)! Must be in[2, 4, 16, 64]\n', MOD_ORDER)
other subcarriers will remain at	ifft_in_mat_pl (SC_IND_DATA, :)
	ifft_in_mat_pl (SC_IND_PILOTS, :)
Insert the cyclic prefix	if (CP_LEN > 0) tx_cp
Interpolate Zero pad then	filter (same as interp or upfirdn without signal processing toolbox) tx_vec_air
abs(tx_vec_air	max ()
id	filter: (id a)
	subplot (2, 1, 1)
	plot (real(rx_vec_air), 'b')
	axis ([0 length(rx_vec_air) -TX_SCALE TX_SCALE]) grid on
	title ('Rx Waveform(I)')
	subplot (2, 1, 2)
	plot (imag(rx_vec_air), 'r')
	title ('Rx Waveform(Q)')
Stop if no valid correlation peak was found	if (isempty(lts_peaks)) fprintf('No LTS Correlation Peaks Found!\n')
end Rx payload processing Extract the payload	samples (integral number of OFDM symbols following preamble) payload_vec
Remove the cyclic keeping FFT_OFFSET samples of	CP (on average) payload_mat_noCP
	Equalize (zero-forcing, just divide by complex chan estimates) syms_eq_mat
	switch (MOD_ORDER) case 2 % BPSK rx_data
	figure (cf)
	plot (real(tx_vec_air), 'b')
	title ('Tx Waveform(I)')
	plot (imag(tx_vec_air), 'r')
	title ('Tx Waveform(Q)')
	if (WRITE_PNG_FILES) print(gcf
	sprintf ('wl_ofdm_plots_%s_txIQ', example_mode_string)
	sprintf ('wl_ofdm_plots_%s_rxIQ', example_mode_string)
	plot (lts_to_plot, '.-b', 'LineWidth', 1)
	line ([1 length(lts_to_plot)], LTS_CORR_THRESH *max(lts_to_plot) *[1 1], 'LineStyle', '--', 'Color', 'r', 'LineWidth', 2)
	title ('LTS Correlation and Threshold') xlabel('Sample Index') myAxis
	sprintf ('wl_ofdm_plots_%s_ltsCorr', example_mode_string)
	plot (payload_syms_mat(:), 'ro', 'MarkerSize', 1)
	axis (1.5 *[-1 1 -1 1])
	plot (tx_syms_mat(:), 'bo')
	title ('Tx and Rx Constellations') legend('Rx'
	sprintf ('wl_ofdm_plots_%s_constellations', example_mode_string)
	set (h, 'Color',[1 0 0]) set(h
bold	set (h, 'FontSize', 10) set(h
bold	set (h, 'BackgroundColor',[1 1 1]) hold off xlabel('Data Symbol Index') ylabel('EVM(%)')
	legend ('Per-Symbol EVM', 'Average EVM', 'Location', 'NorthWest')
	title ('EVM vs. Data Symbol Index') grid on subplot(2
	imagesc (1:N_OFDM_SYMS,(SC_IND_DATA - N_SC/2), 100 *fftshift(evm_mat, 1)) grid on xlabel('OFDM Symbol Index') ylabel('Subcarrier Index') title('EVM vs.(Subcarrier &OFDM Symbol)') h

Variables
siso_ofdm_mf_sim m A sane example of Simulated OFDM sysetm Copyright(c) 2015 Mango Communications - All Rights Reserved % Distributed under the WARP License(http	Params
Enable writing plots to PNG	CHANNEL = 11
Channel to tune Tx and Rx radios	SIM_snr_db = 30
simulation data SC SNR Waveform params	N_OFDM_SYMS = 320
Number of OFDM symbols	MOD_ORDER = 16
Pilot subcarrier indices	SC_IND_DATA = [2:7 9:21 23:27 39:43 45:57 59:64]
Data subcarrier indices	N_SC = 64
Number of subcarriers	CP_LEN = 16
Cyclic prefix length	N_DATA_SYMS = N_OFDM_SYMS * length(SC_IND_DATA)
Rx processing params	FFT_OFFSET = 16
Normalized threshold for LTS correlation	DO_APPLY_CFO_CORRECTION = 0
Enable CFO estimation correction	DO_APPLY_SFO_CORRECTION = 0
Enable SFO estimation correction	DO_APPLY_PHASE_ERR_CORRECTION = 0
Enable Residual CFO estimation correction WARPLab experiment params	USE_AGC = true
Use the AGC if running on WARP hardware	MAX_TX_LEN = 2^20
Maximum number of samples to use for this experiment	TRIGGER_OFFSET_TOL_NS = 3000
	SAMP_FREQ = 40e6
	example_mode_string = 'sim'
Generate a payload of random integers	tx_data = randi(MOD_ORDER, 1, N_DATA_SYMS) - 1
	modvec_16qam = (1/sqrt(10)) .* [-3 -1 +3 +1]
	modvec_64qam = (1/sqrt(43)) .* [-7 -5 -1 -3 +7 +5 +1 +3]
	mod_fcn_bpsk = @(x) complex(modvec_bpsk(1+x),0)
	mod_fcn_qpsk = @(x) complex(modvec_bpsk(1+bitshift(x, -1)), modvec_bpsk(1+mod(x, 2)))
	mod_fcn_16qam = @(x) complex(modvec_16qam(1+bitshift(x, -2)), modvec_16qam(1+mod(x,4)))
	mod_fcn_64qam = @(x) complex(modvec_64qam(1+bitshift(x, -3)), modvec_64qam(1+mod(x,8)))
Map the data values on to complex symbols switch MOD_ORDER case BPSK	tx_syms = arrayfun(mod_fcn_bpsk, tx_data)
	return
end Reshape the symbol vector to a matrix with one column per OFDM symbol	tx_syms_mat = reshape(tx_syms, length(SC_IND_DATA), N_OFDM_SYMS)
Define the pilot tone values as BPSK symbols	pilots = [1 1 -1 1].'
Repeat the pilots across all OFDM symbols	pilots_mat = repmat(pilots, 1, N_OFDM_SYMS)
IFFT Construct the IFFT input matrix	ifft_in_mat_pl = zeros(N_SC, N_OFDM_SYMS)
Insert the data and pilot	values
	ifft_in_mat = [repmat(lts_f.', 1, N_LTS) ifft_in_mat_pl]
Perform the IFFT	tx_payload_mat = ifft(ifft_in_mat, N_SC, 1)
end	lts_t = tx_payload_mat(:,1:N_LTS)
Reshape to a vector	tx_payload_vec = reshape(tx_payload_mat, 1, numel(tx_payload_mat))
Calculate the noise variance	SIM_snr =10^(0.1* SIM_snr_db)
	tx_vec_pow_avg = mean( abs(TX_SCALE .* tx_vec ./ max(abs(tx_vec))).^2)
Average power on each SC	sim_N0 = tx_vec_pow_avg / SIM_snr
Pad with zeros for transmission	tx_vec_padded = [zeros(1,100) tx_vec]
	TX_NUM_SAMPS = length(tx_vec_air)
AWGN	__pad1__
	rx_vec_air = rx_vec_air + sqrt(sim_N0/2)*(randn(size(rx_vec_air)) + 1i*randn(size(rx_vec_air)))
	unos = ones(size(lts_t))'
	v0 = filter(fliplr(lts_t'),a, rx_vec_air)
	v1 = filter(unos,a,abs(rx_vec_air).^2)
	m_filt = (abs(v0).^2)./v1
	pkt_strt = ipos - N_LTS*(N_SC + CP_LEN)+1
	lts_peaks = find(m_filt(1:800) > LTS_CORR_THRESH*rho_max)
Rx signal	figure
	clf
	payload_mat = reshape(payload_vec, (N_SC+CP_LEN), N_LTS + N_OFDM_SYMS)
Remove the cyclic	prefix
Take the FFT	syms_f_mat_sc = fft(payload_mat_noCP, N_SC, 1)
	syms_f_mat = syms_f_mat_sc(SC_IND_DATA,:)
	rx_lts_f = syms_f_mat(:,1:N_LTS)
	rx_H_est0 = rx_lts_f ./repmat(lts_f(SC_IND_DATA).', 1, N_LTS)
	rx_H_est = mean(rx_H_est0,2)
Apply the pilot phase correction per symbol	payload_syms_mat =syms_eq_mat
Demodulate	rx_syms = reshape(payload_syms_mat, 1, N_DATA_SYMS)
	demod_fcn_bpsk = @(x) double(real(x)>0)
	demod_fcn_qpsk = @(x) double(2*(real(x)>0) + 1*(imag(x)>0))
	demod_fcn_16qam = @(x) (8*(real(x)>0)) + (4*(abs(real(x))<0.6325)) + (2*(imag(x)>0)) + (1*(abs(imag(x))<0.6325))
	demod_fcn_64qam = @(x) (32*(real(x)>0)) + (16*(abs(real(x))<0.6172)) + (8*((abs(real(x))<(0.9258))&&((abs(real(x))>(0.3086))))) + (4*(imag(x)>0)) + (2*(abs(imag(x))<0.6172)) + (1*((abs(imag(x))<(0.9258))&&((abs(imag(x))>(0.3086)))))
case QPSK	rx_data = arrayfun(demod_fcn_qpsk, rx_syms)
end Plot Results	cf = 0
	lts_to_plot = m_filt(1:1000)
hold	on
axis	square
	Tx
	Location
	EastOutside
	evm_mat = abs(payload_syms_mat - tx_syms_mat).^2
	aevms = mean(evm_mat(:))
	snr = 10*log10(1./aevms)
subplot(2, 1, 1) plot(100 *evm_mat(	h = text(round(.05*length(evm_mat(:))), 100*aevms+ .1*(myAxis(4)-myAxis(3)), sprintf('Effective SNR: %.1f dB', snr))
	FontWeight
bold	EdgeColor

Function Documentation

arrayfun()

mod_fcn_16qam, tx_data arrayfun ( )

virtual

axis() [1/2]

axis

(

1.5 *

[-1 1 -1 1]

)

axis() [2/2]

axis

(

)

CP()

Remove the cyclic keeping FFT_OFFSET samples of CP

(

on

average

)

Equalize()

Equalize	(	zero-	forcing,
		just divide by complex chan	estimates
	)

FFT()

Number of CP samples to use in FFT ( on  average )

pure virtual

figure()

figure

(

cf

)

filter()

Interpolate Zero pad then filter

(

same as interp or upfirdn without signal processing

toolbox

)

filter:()

id filter: ( id  a )

virtual

fprintf()

otherwise fprintf	(	'Invalid MOD_ORDER(%d)! Must be in\n'	[2, 4, 16, 64],
		MOD_ORDER
	)

if() [1/3]

Insert the cyclic prefix if	(	CP_LEN	,
		0
	)

if() [2/3]

Stop if no valid correlation peak was found if

(

isempty(lts_peaks)

)

if() [3/3]

if

(

WRITE_PNG_FILES

)

ifft_in_mat_pl() [1/2]

other subcarriers will remain at ifft_in_mat_pl	(	SC_IND_DATA	,
		:
	)

ifft_in_mat_pl() [2/2]

ifft_in_mat_pl	(	SC_IND_PILOTS	,
		:
	)

imagesc()

imagesc	(	1:N_OFDM_SYMS	,
		(SC_IND_DATA - N_SC/2)	,
		100 *	fftshiftevm_mat, 1
	)		&

legend()

legend	(	'Per-Symbol EVM'	,
		'Average EVM'	,
		'Location'	,
		'NorthWest'
	)

line()

line	(	LTS_CORR_THRESH *max(lts_to_plot) *	[1 1],
		'LineStyle'	,
		'--'	,
		'Color'	,
		'r'	,
		'LineWidth'	,
		2
	)

lts_f()

id lts_f ( )

virtual

max()

abs(tx_vec_air max ( )

staticvirtual

min()

MAX_TX_LEN, 2^20 min ( )

virtual

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modvec_bpsk()

1/sqrt(2 modvec_bpsk ( )

virtual

order()

Modulation order

(

2/4/16/

64 = BSPK/QPSK/16-QAM/64-QAM

)

plot() [1/7]

plot	(	imag(rx_vec_air)	,
		'r'
	)

plot() [2/7]

plot	(	imag(tx_vec_air)	,
		'r'
	)

plot() [3/7]

plot	(	lts_to_plot	,
		'.-b'	,
		'LineWidth'	,
		1
	)

plot() [4/7]

plot	(	payload_syms_mat(:)	,
		'ro'	,
		'MarkerSize'	,
		1
	)

plot() [5/7]

plot	(	real(rx_vec_air)	,
		'b'
	)

plot() [6/7]

plot	(	real(tx_vec_air)	,
		'b'
	)

plot() [7/7]

plot	(	tx_syms_mat(:)	,
		'bo'
	)

samples()

end Rx payload processing Extract the payload samples

(

integral number of OFDM symbols following

preamble

)

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set() [1/3]

bold set	(	h	,
		'BackgroundColor'
	)

set() [2/3]

set	(	h	,
		'Color'
	)

set() [3/3]

bold set	(	h	,
		'FontSize'	,
		10
	)

sprintf() [1/4]

sprintf	(	'wl_ofdm_plots_%s_constellations'	,
		example_mode_string
	)

sprintf() [2/4]

sprintf	(	'wl_ofdm_plots_%s_ltsCorr'	,
		example_mode_string
	)

sprintf() [3/4]

sprintf	(	'wl_ofdm_plots_%s_rxIQ'	,
		example_mode_string
	)

sprintf() [4/4]

sprintf	(	'wl_ofdm_plots_%s_txIQ'	,
		example_mode_string
	)

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subplot() [1/2]

subplot	(	2	,
		1	,
		1
	)

subplot() [2/2]

subplot	(	2	,
		1	,
		2
	)

switch()

switch

(

MOD_ORDER

)

symbols()

Number of data symbols

(

one per data-bearing subcarrier per OFDM

symbol

)

title() [1/7]

title

(

'EVM vs. Data Symbol Index'

)

title() [2/7]

title

(

'LTS Correlation and Threshold'

)

title() [3/7]

title

(

'Rx Waveform(I)'

)

title() [4/7]

title

(

'Rx Waveform(Q)'

)

title() [5/7]

title

(

'Tx and Rx Constellations'

)

title() [6/7]

title

(

'Tx Waveform(I)'

)

title() [7/7]

title

(

'Tx Waveform(Q)'

)

waveform()

Scale for Tx waveform

(

)

Variable Documentation

__pad1__

AWGN __pad1__

aevms

aevms = mean(evm_mat(:))

cf

Tx signal cf = 0

CHANNEL

Enable writing plots to PNG CHANNEL = 11

clf

clf

CP_LEN

Number of subcarriers CP_LEN = 16

demod_fcn_16qam

demod_fcn_16qam = @(x) (8*(real(x)>0)) + (4*(abs(real(x))<0.6325)) + (2*(imag(x)>0)) + (1*(abs(imag(x))<0.6325))

demod_fcn_64qam

demod_fcn_64qam = @(x) (32*(real(x)>0)) + (16*(abs(real(x))<0.6172)) + (8*((abs(real(x))<(0.9258))&&((abs(real(x))>(0.3086))))) + (4*(imag(x)>0)) + (2*(abs(imag(x))<0.6172)) + (1*((abs(imag(x))<(0.9258))&&((abs(imag(x))>(0.3086)))))

demod_fcn_bpsk

demod_fcn_bpsk = @(x) double(real(x)>0)

demod_fcn_qpsk

demod_fcn_qpsk = @(x) double(2*(real(x)>0) + 1*(imag(x)>0))

DO_APPLY_CFO_CORRECTION

Normalized threshold for LTS correlation DO_APPLY_CFO_CORRECTION = 0

DO_APPLY_PHASE_ERR_CORRECTION

Enable SFO estimation correction DO_APPLY_PHASE_ERR_CORRECTION = 0

DO_APPLY_SFO_CORRECTION

Enable CFO estimation correction DO_APPLY_SFO_CORRECTION = 0

EastOutside

EastOutside

EdgeColor

bold EdgeColor

evm_mat

evm_mat = abs(payload_syms_mat - tx_syms_mat).^2

example_mode_string

example_mode_string = 'sim'

FFT_OFFSET

Rx processing params FFT_OFFSET = 16

figure

Rx signal figure

FontWeight

FontWeight

h

subplot (2,1,1) plot(100*evm_mat( h = text(round(.05*length(evm_mat(:))), 100*aevms+ .1*(myAxis(4)-myAxis(3)), sprintf('Effective SNR: %.1f dB', snr))

ifft_in_mat

ifft_in_mat = [repmat(lts_f.', 1, N_LTS) ifft_in_mat_pl]

ifft_in_mat_pl

IFFT Construct the IFFT input matrix ifft_in_mat_pl = zeros(N_SC, N_OFDM_SYMS)

Location

Location

lts_peaks

lts_peaks = find(m_filt(1:800) > LTS_CORR_THRESH*rho_max)

lts_t

lts_t = tx_payload_mat(:,1:N_LTS)

lts_to_plot

lts_to_plot = m_filt(1:1000)

m_filt

m_filt = (abs(v0).^2)./v1

MAX_TX_LEN

Use the AGC if running on WARP hardware MAX_TX_LEN = 2^20

mod_fcn_16qam

mod_fcn_16qam = @(x) complex(modvec_16qam(1+bitshift(x, -2)), modvec_16qam(1+mod(x,4)))

mod_fcn_64qam

mod_fcn_64qam = @(x) complex(modvec_64qam(1+bitshift(x, -3)), modvec_64qam(1+mod(x,8)))

mod_fcn_bpsk

mod_fcn_bpsk = @(x) complex(modvec_bpsk(1+x),0)

mod_fcn_qpsk

mod_fcn_qpsk = @(x) complex(modvec_bpsk(1+bitshift(x, -1)), modvec_bpsk(1+mod(x, 2)))

MOD_ORDER

Number of OFDM symbols MOD_ORDER = 16

modvec_16qam

modvec_16qam = (1/sqrt(10)) .* [-3 -1 +3 +1]

modvec_64qam

modvec_64qam = (1/sqrt(43)) .* [-7 -5 -1 -3 +7 +5 +1 +3]

N_DATA_SYMS

Cyclic prefix length N_DATA_SYMS = N_OFDM_SYMS * length(SC_IND_DATA)

N_OFDM_SYMS

simulation data SC SNR Waveform params N_OFDM_SYMS = 320

N_SC

Data subcarrier indices N_SC = 64

on

hold on

Params

siso_ofdm_mf_sim m A sane example of Simulated OFDM sysetm Copyright (c) 2015 Mango Communications - All Rights Reserved % Distributed under the WARP License (http Params

payload_mat

payload_mat = reshape(payload_vec, (N_SC+CP_LEN), N_LTS + N_OFDM_SYMS)

payload_syms_mat

Apply the pilot phase correction per symbol payload_syms_mat =syms_eq_mat

pilots

Define the pilot tone values as BPSK symbols pilots = [1 1 -1 1].'

pilots_mat

Repeat the pilots across all OFDM symbols pilots_mat = repmat(pilots, 1, N_OFDM_SYMS)

pkt_strt

pkt_strt = ipos - N_LTS*(N_SC + CP_LEN)+1

prefix

Remove the cyclic prefix

return

return

rx_data

case QPSK rx_data = arrayfun(demod_fcn_qpsk, rx_syms)

rx_H_est

rx_H_est = mean(rx_H_est0,2)

rx_H_est0

rx_H_est0 = rx_lts_f ./repmat(lts_f(SC_IND_DATA).', 1, N_LTS)

rx_lts_f

rx_lts_f = syms_f_mat(:,1:N_LTS)

rx_syms

Demodulate rx_syms = reshape(payload_syms_mat, 1, N_DATA_SYMS)

rx_vec_air

rx_vec_air = rx_vec_air + sqrt(sim_N0/2)*(randn(size(rx_vec_air)) + 1i*randn(size(rx_vec_air)))

SAMP_FREQ

SAMP_FREQ = 40e6

SC_IND_DATA

Pilot subcarrier indices SC_IND_DATA = [2:7 9:21 23:27 39:43 45:57 59:64]

sim_N0

Average power on each SC sim_N0 = tx_vec_pow_avg / SIM_snr

SIM_snr

Calculate the noise variance SIM_snr =10^(0.1* SIM_snr_db)

SIM_snr_db

Channel to tune Tx and Rx radios SIM_snr_db = 30

snr

snr = 10*log10(1./aevms)

square

axis square

syms_f_mat

syms_f_mat = syms_f_mat_sc(SC_IND_DATA,:)

syms_f_mat_sc

Take the FFT syms_f_mat_sc = fft(payload_mat_noCP, N_SC, 1)

TRIGGER_OFFSET_TOL_NS

Maximum number of samples to use for this experiment TRIGGER_OFFSET_TOL_NS = 3000

Tx

Tx

tx_data

Generate a payload of random integers tx_data = randi(MOD_ORDER, 1, N_DATA_SYMS) - 1

TX_NUM_SAMPS

TX_NUM_SAMPS = length(tx_vec_air)

tx_payload_mat

tx_payload_mat = ifft(ifft_in_mat, N_SC, 1)

tx_payload_vec

Reshape to a vector tx_payload_vec = reshape(tx_payload_mat, 1, numel(tx_payload_mat))

tx_syms

case QPSK tx_syms = arrayfun(mod_fcn_bpsk, tx_data)

tx_syms_mat

end Reshape the symbol vector to a matrix with one column per OFDM symbol tx_syms_mat = reshape(tx_syms, length(SC_IND_DATA), N_OFDM_SYMS)

tx_vec_padded

Pad with zeros for transmission tx_vec_padded = [zeros(1,100) tx_vec]

tx_vec_pow_avg

tx_vec_pow_avg = mean( abs(TX_SCALE .* tx_vec ./ max(abs(tx_vec))).^2)

unos

unos = ones(size(lts_t))'

USE_AGC

Enable Residual CFO estimation correction WARPLab experiment params USE_AGC = true

v0

v0 = filter(fliplr(lts_t'),a, rx_vec_air)

v1

v1 = filter(unos,a,abs(rx_vec_air).^2)

values

Insert the data and pilot values