A library with SDR DSP primitives
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libosmo-dsp/src/iqbal.c

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/*
* iqbal.c
*
* IQ balance correction / estimation utilities
*
* Copyright (C) 2013 Sylvain Munaut <tnt@246tNt.com>
*
* All Rights Reserved
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
/*! \addtogroup iqbal
* @{
*/
/*! \file iqbal.c
* \brief IQ balance utils implementation
*
* The actual algorithm used for estimation of the imbalance and its
* optimization is inspired by the IQ balancer of SDR# by Youssef Touil
* and described here :
*
* http://sdrsharp.com/index.php/automatic-iq-correction-algorithm
*
* The main differences are:
* - Objective function uses complex correlation of left/right side of FFT
* - Optimization based on steepest gradient with dynamic step size
*/
#include <complex.h>
#include <stdlib.h>
#include <string.h>
#include <fftw3.h>
#include <osmocom/dsp/cxvec.h>
#include <osmocom/dsp/cxvec_math.h>
#include <osmocom/dsp/iqbal.h>
/* ------------------------------------------------------------------------ */
/* IQ balance correction and estimation */
/* ------------------------------------------------------------------------ */
/*! \brief Apply IQ balance correction to a given complex buffer
* \param[out] out Complex output buffer
* \param[in] in Complex input buffer
* \param[in] len Number of complex samples to process
* \param[in] mag Magnitude correction (approximated)
* \param[in] phase Phase correction (approximated)
*
* The input and output buffers can be the same for in-place modification.
*
* The applied transform is out[i] = (a * (1 + mag)) + (b + phase * a) * i
* (with in[i] = a+bi).
*/
void
osmo_iqbal_fix(float complex *out, float complex *in, unsigned int len,
float mag, float phase)
{
int i;
for (i=0; i<len; i++) {
float complex v = in[i];
out[i] = (crealf(v) * (1.0f + mag)) +
(cimagf(v) + phase * crealf(v)) * I;
}
}
/*! \brief Apply IQ balance correction to a given complex vector
* \param[in] in Complex input vector
* \param[in] mag Magnitude correction (approximated)
* \param[in] phase Phase correction (approximated)
* \param[out] out Complex output vector (can be NULL or equal to 'in')
* \returns The output complex vector (or NULL if error)
*
* If the 'out' parameter is NULL, a new vector will be allocated
* See \ref osmo_iqbal_fix for details of the correction applied.
*/
struct osmo_cxvec *
osmo_iqbal_cxvec_fix(const struct osmo_cxvec *in, float mag, float phase,
struct osmo_cxvec *out)
{
if (!out)
out = osmo_cxvec_alloc(in->len);
if (!out || out->max_len < in->len)
return NULL;
osmo_iqbal_fix(out->data, in->data, in->len, mag, phase);
out->len = in->len;
out->flags = in->flags;
return out;
}
/*! \brief Cache for \ref _osmo_iqbal_estimate when doing lots of calls */
struct _iqbal_estimate_state {
float complex *fft; /*!< \brief Temporary memory for FFT */
fftwf_plan fft_plan; /*!< \brief FFTW plan */
};
/*! \brief Release a cache object created by \ref _osmo_iqbal_estimate */
static void
_osmo_iqbal_estimate_release(struct _iqbal_estimate_state *state)
{
if (!state)
return;
fftwf_destroy_plan(state->fft_plan);
free(state->fft);
free(state);
}
/*! \brief Objectively estimate IQ balance in a given complex buffer
* \param[in] data Input complex buffer (at least fft_size * fft_count samples)
* \param[in] fft_size Size of the FFT to use internally
* \param[in] fft_count The number of consecutive FFT to use internally
* \param[out] state_p Cache object for multiple calls (can be NULL)
* \returns A number >= 0.0f estimating the IQ balance (the lower, the better)
*
* The Cache object should only be used for multiple calls with the same parameters
* and the same size of input vector. Once you don't plan on using it anymore,
* you should call \ref _osmo_iqbal_estimate_release . The initial pointer value
* should also be initialized to NULL.
*/
static float
_osmo_iqbal_estimate(const float complex *data, int fft_size, int fft_count,
struct _iqbal_estimate_state **state_p)
{
float complex *fft;
float est = 0.0f;
fftwf_plan fft_plan;
int i, j;
if (state_p && *state_p) {
fft = (*state_p)->fft;
fft_plan = (*state_p)->fft_plan;
} else {
fft = malloc(sizeof(float complex) * fft_size);
fft_plan = fftwf_plan_dft_1d(fft_size, fft, fft, FFTW_FORWARD, FFTW_ESTIMATE);
}
for (i=0; i<fft_count; i++)
{
float complex corr = 0.0f;
memcpy(fft, &data[i*fft_size], sizeof(float complex) * fft_size);
fftwf_execute(fft_plan);
for (j=1; j<fft_size/2; j++)
corr += fft[fft_size-j] * conjf(fft[j]);
est += osmo_normsqf(corr); /* / (fft_size / 2); */
}
/* est /= fft_count; */
if (state_p && !*state_p) {
*state_p = malloc(sizeof(struct _iqbal_estimate_state));
(*state_p)->fft = fft;
(*state_p)->fft_plan = fft_plan;
} else if (!state_p) {
fftwf_destroy_plan(fft_plan);
free(fft);
}
return est;
}
/*! \brief Objectively estimate IQ balance in a given complex buffer
* \param[in] data Input complex buffer (at least fft_size * fft_count samples)
* \param[in] fft_size Size of the FFT to use internally
* \param[in] fft_count The number of consecutive FFT to use internally
* \returns A number >= 0.0f estimating the IQ balance (the lower, the better)
*/
float
osmo_iqbal_estimate(const float complex *data, int fft_size, int fft_count)
{
return _osmo_iqbal_estimate(data, fft_size, fft_count, NULL);
}
/*! \brief Objectively estimate IQ balance in a given complex vector
* \param[in] sig Input complex vector (at least fft_size * fft_count samples)
* \param[in] fft_size Size of the FFT to use internally
* \param[in] fft_count The number of consecutive FFT to use internally
* \returns A number >= 0.0f estimating the IQ balance (the lower, the better)
*/
float
osmo_iqbal_cxvec_estimate(const struct osmo_cxvec *sig,
int fft_size, int fft_count)
{
if (sig->len < fft_size * fft_count)
return -1.0f;
return osmo_iqbal_estimate(sig->data, fft_size, fft_count);
}
/* ------------------------------------------------------------------------ */
/* IQ balance optimization */
/* ------------------------------------------------------------------------ */
/*! \brief Default values for the optimization algorithm */
const struct osmo_iqbal_opts osmo_iqbal_default_opts = {
.fft_size = 1024,
.fft_count = 8,
.max_iter = 25,
.start_at_prev = 1,
};
/*! \brief Internal state structure for the IQ balance optimization algorithm */
struct _iqbal_state
{
const struct osmo_iqbal_opts *opts; /*!< \brief Options */
const struct osmo_cxvec *org; /*!< \brief Original vector */
struct osmo_cxvec *tmp; /*!< \brief Temporary vector */
int feval; /*!< \brief # of function evaluation */
struct _iqbal_estimate_state *cache; /*!< \brief Cache for estimate func */
};
/*! \brief Optimization objective function - Value
* \param[in] state Current state object of optimization loop
* \param[in] x An array of 2 float for (mag,phase) point to evaluate at
* \returns The value of the objective function at point 'x'
*/
static inline float
_iqbal_objfn_value(struct _iqbal_state *state, float x[2])
{
state->feval++;
osmo_iqbal_cxvec_fix(state->org, x[0], x[1], state->tmp);
return _osmo_iqbal_estimate(state->tmp->data,
state->opts->fft_size, state->opts->fft_count,
&state->cache);
}
/*! \brief Optimization objective function - Gradient estimation
* \param[in] state Current state object of optimization loop
* \param[in] x An array of 2 float for (mag,phase) point to evaluate at
* \param[in] v The value of the objective function at point 'x'
* \param[out] grad An array of 2 float for the estimated gradient at point 'x'
*/
static void
_iqbal_objfn_gradient(struct _iqbal_state *state, float x[2], float v, float grad[2])
{
const float GRAD_STEP = 1e-6f;
float xd[2], vd[2];
xd[0] = x[0] + GRAD_STEP; xd[1] = x[1];
vd[0] = _iqbal_objfn_value(state, xd);
xd[0] = x[0]; xd[1] = x[1] + GRAD_STEP;
vd[1] = _iqbal_objfn_value(state, xd);
grad[0] = (vd[0] - v) / GRAD_STEP;
grad[1] = (vd[1] - v) / GRAD_STEP;
}
/*! \brief Optimization objective function - Value & Gradient estimation
* \param[in] state Current state object of optimization loop
* \param[in] x An array of 2 float for (mag,phase) point to evaluate at
* \param[out] grad An array of 2 float for the estimated gradient at point 'x'
* \returns The value of the objective function at point 'x'
*/
static inline float
_iqbal_objfn_val_gradient(struct _iqbal_state *state, float x[2], float grad[2])
{
float v = _iqbal_objfn_value(state, x);
_iqbal_objfn_gradient(state, x, v, grad);
return v;
}
/*! \brief Finds the best IQ balance correction parameters for a given signal
* \param[in] sig The input signal to optimize for
* \param[in,out] mag Magnitude correction (See \ref osmo_iqbal_fix)
* \param[in,out] phase Phase correction (See \ref osmo_iqbal_fix)
* \param[in] opts Options of the optimization process (See \ref osmo_iqbal_opts)
*
* The mag and phase parameters are pointers to float. If in the options,
* the 'start_at_prev' is enabled, the initial values of those will be used
* and so they should be initialized appropriately.
*/
int
osmo_iqbal_cxvec_optimize(const struct osmo_cxvec *sig, float *mag, float *phase,
const struct osmo_iqbal_opts *opts)
{
struct _iqbal_state _state, *state = &_state;
float cv, nv, step;
float cx[2], nx[2];
float cgrad[2];
float p;
int i;
if (!opts)
opts = &osmo_iqbal_default_opts;
if (sig->len < (opts->fft_size * opts->fft_count))
return -1;
state->org = sig;
state->tmp = osmo_cxvec_alloc(sig->len);
state->opts = opts;
state->feval = 0;
state->cache = NULL;
if (opts->start_at_prev) {
cx[0] = *mag;
cx[1] = *phase;
} else {
cx[0] = 0.0f;
cx[1] = 0.0f;
}
cv = _iqbal_objfn_val_gradient(state, cx, cgrad);
step = cv / (fabs(cgrad[0]) + fabs(cgrad[1]));
for (i=0; i<opts->max_iter; i++)
{
nx[0] = cx[0] - step * (cgrad[0] / (fabs(cgrad[0]) + fabs(cgrad[1])));
nx[1] = cx[1] - step * (cgrad[1] / (fabs(cgrad[0]) + fabs(cgrad[1])));
nv = _iqbal_objfn_value(state, nx);
if (nv <= cv) {
p = (cv - nv) / cv;
cx[0] = nx[0];
cx[1] = nx[1];
cv = nv;
_iqbal_objfn_gradient(state, cx, cv, cgrad);
if (p < 0.01f)
break;
} else {
step /= 2.0 * (nv / cv);
}
}
osmo_cxvec_free(state->tmp);
_osmo_iqbal_estimate_release(state->cache);
*mag = cx[0];
*phase = cx[1];
return 0;
}
/*! @} */