Question

I a doing a weird project, and looking to convert some short, simple datagrams to audio – send them over a (physical) radio – then to receive and decode them on another device (think – embedded devices with audio out jack and GSM/GPRS-type radios).

(I have to use a physical, existing external radio).

Does anyone know of a good, simple software modem library good for such a project? I’m not so concerned about data rate, and would prefer simplicity over functionality. Even something akin to a basic 1200 baud modem would be fantastic.

Looking at this more of a learning experience and potential building block, rather than anything horribly practical.

Answer 1

As an exercise I’ve implemented a simple V.23-like modem using FSK modulation and supporting a data rate of 1200 bits/second (960 bits/second effective because of the start and stop bits).

I’m curious to see if it works with your radio. Noise, signal reflection and imperfect demodulation can all affect the performance of the modem.

Prior to trying to integrate this code into your project, first see if it works with audio recorded from your radio.

Code:

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <limits.h>
#include <math.h>

#ifndef M_PI
#define M_PI 3.14159265358979324
#endif

typedef unsigned char uchar, uint8;
typedef signed char schar, int8;
typedef unsigned short ushort, uint16;
typedef short int16;
typedef unsigned int uint;
typedef unsigned long ulong;
#if UINT_MAX >= 0xFFFFFFFF
typedef int int32;
typedef unsigned int uint32;
#else
typedef long int32;
typedef unsigned long uint32;
#endif
typedef long long int64;
typedef unsigned long long uint64;

typedef struct
{
  double x, y;
} tComplex;

tComplex complexAdd(const tComplex* a, const tComplex* b)
{
  tComplex c;
  c.x = a->x + b->x;
  c.y = a->y + b->y;
  return c;
}

tComplex complexMul(const tComplex* a, const tComplex* b)
{
  tComplex c;
  c.x = a->x * b->x - a->y * b->y;
  c.y = a->x * b->y + a->y * b->x;
  return c;
}

void dft(tComplex out[], const tComplex in[], size_t n, int direction)
{
  size_t k, i;
  for (k = 0; k < n; k++)
  {
    tComplex r = { 0, 0 }, e;
    for (i = 0; i < n; i++)
    {
      e.x = cos(-2 * direction * M_PI / n * ((double)k - n / 2) * ((double)i - n / 2));
      e.y = sin(-2 * direction * M_PI / n * ((double)k - n / 2) * ((double)i - n / 2));
      e = complexMul(&e, &in[i]);
      r = complexAdd(&r, &e);
    }
    out[k] = r;
  }
}

#define FILTER_LENGTH 64

typedef struct tTx
{
  enum
  {
    stSendingOnes,
    stSendingData
  } State;

  uint SampleRate;
  uint OnesFreq;
  uint ZeroesFreq;
  uint BitRate;

  uint32 SampleCnt;
  uint BitSampleCnt;
  uint Data;
  uint DataLeft;

  double Phase;
  double PhaseIncrement;

  uint (*pTxGetDataCallBack)(struct tTx*, uint8*);
} tTx;

void TxInit(tTx* pTx,
            uint SampleRate,
            uint (*pTxGetDataCallBack)(tTx*, uint8*))
{
  memset(pTx, 0, sizeof(*pTx));
  pTx->State = stSendingOnes;
  pTx->SampleRate = SampleRate;
  pTx->OnesFreq = 1300;
  pTx->ZeroesFreq = 2100;
  pTx->BitRate = 1200;
  pTx->pTxGetDataCallBack = pTxGetDataCallBack;

  pTx->SampleCnt = 0;
  pTx->BitSampleCnt = pTx->SampleRate;
  pTx->Data = 0;
  pTx->DataLeft = 0;
  pTx->Phase = 0.0;
  pTx->PhaseIncrement = 2 * M_PI * pTx->OnesFreq / pTx->SampleRate;
}

int16 TxGetSample(tTx* pTx)
{
  int16 sample;

  if (pTx->State == stSendingOnes &&
      pTx->SampleCnt >= pTx->SampleRate)
  {
    // Sent 1 second worth of 1's, can now send data
    pTx->State = stSendingData;
  }

  if (pTx->State == stSendingData &&
      pTx->BitSampleCnt >= pTx->SampleRate)
  {
    // Another data bit can now be sent
    uint8 d;

    pTx->BitSampleCnt -= pTx->SampleRate;

    if (!pTx->DataLeft)
    {
      // Get the next data byte (if any)
      if (pTx->pTxGetDataCallBack(pTx, &d) != 0)
      {
        pTx->Data = d & 0xFF;
        pTx->Data |= 1 << 8; // insert the stop bit
        pTx->Data <<= 1; // insert the start bit
        pTx->DataLeft = 10;
      }
      else
      {
        pTx->Data = 0x3FF; // no data, send 10 1's
        pTx->DataLeft = 10;
      }
    }

    // Extract the next data bit to send
    d = pTx->Data & 1;
    pTx->Data >>= 1;
    pTx->DataLeft--;

    // Choose the appropriate frequency for 0 and 1
    if (d)
    {
      pTx->PhaseIncrement = 2 * M_PI * pTx->OnesFreq / pTx->SampleRate;
    }
    else
    {
      pTx->PhaseIncrement = 2 * M_PI * pTx->ZeroesFreq / pTx->SampleRate;
    }
  }

  // Generate the next sample, advance the generator's phase
  sample = (int16)(16000 * cos(pTx->Phase));
  pTx->Phase += pTx->PhaseIncrement;
  if (pTx->Phase >= 2 * M_PI)
  {
    pTx->Phase -= 2 * M_PI;
  }

  if (pTx->State == stSendingData)
  {
    pTx->BitSampleCnt += pTx->BitRate;
  }

  pTx->SampleCnt++;

  return sample;
}

typedef struct tRx
{
  enum
  {
    stCarrierLost,
    stCarrierDetected,
    stReceivingData
  } State;

  uint SampleRate;
  uint OnesFreq;
  uint ZeroesFreq;
  uint MidFreq;
  uint BitRate;

  uint32 SampleCnt;
  uint BitSampleCnt;
  uint Data;

  double Phase;
  double PhaseIncrement;

  tComplex Filter[FILTER_LENGTH];
  double Delay[FILTER_LENGTH];

  double LastAngle;
  int LastDelta;
  int32 Deltas;

  int32 CarrierAngle;
  int32 CarrierCnt;

  double LongAvgPower;
  double ShortAvgPower;

  void (*pRxGetDataCallBack)(struct tRx*, uint8);
} tRx;

void RxInit(tRx* pRx,
            uint SampleRate,
            void (*pRxGetDataCallBack)(struct tRx*, uint8))
{
  tComplex tmp[FILTER_LENGTH];
  uint i;

  memset(pRx, 0, sizeof(*pRx));
  pRx->State = stCarrierLost;
  pRx->SampleRate = SampleRate;
  pRx->OnesFreq = 1300;
  pRx->ZeroesFreq = 2100;
  pRx->MidFreq = (pRx->OnesFreq + pRx->ZeroesFreq) / 2;
  pRx->BitRate = 1200;
  pRx->pRxGetDataCallBack = pRxGetDataCallBack;

  pRx->SampleCnt = 0;
  pRx->BitSampleCnt = 0;
  pRx->Data = 0x3FF;
  pRx->Phase = 0.0;
  pRx->PhaseIncrement = 2 * M_PI * pRx->MidFreq / pRx->SampleRate;
  pRx->LastAngle = 0.0;
  pRx->LastDelta = 0;
  pRx->Deltas = 0;
  pRx->CarrierAngle = 0;
  pRx->CarrierCnt = 0;
  pRx->LongAvgPower = 0.0;
  pRx->ShortAvgPower = 0.0;

  for (i = 0; i < FILTER_LENGTH; i++)
  {
    pRx->Delay[i] = 0.0;
  }

  for (i = 0; i < FILTER_LENGTH; i++)
  {
    if (i == 0) // w < 0 (min w)
    {
      pRx->Filter[i].x = 0;
      pRx->Filter[i].y = 0;
    }
    else if (i < FILTER_LENGTH / 2) // w < 0
    {
      pRx->Filter[i].x = 0;
      pRx->Filter[i].y = 0;
    }
    else if (i == FILTER_LENGTH / 2) // w = 0
    {
      pRx->Filter[i].x = 0;
      pRx->Filter[i].y = 0;
    }
    else if (i > FILTER_LENGTH / 2) // w > 0
    {
      pRx->Filter[i].x = 0;
      pRx->Filter[i].y = -1;

      // Extra filter to combat channel noise
      if (i - FILTER_LENGTH / 2 < 875UL * FILTER_LENGTH / pRx->SampleRate ||
          i - FILTER_LENGTH / 2 > (2350UL * FILTER_LENGTH + pRx->SampleRate - 1) / pRx->SampleRate)
      {
        pRx->Filter[i].y = 0;
      }
    }
  }

  memcpy(tmp, pRx->Filter, sizeof(tmp));
  dft(pRx->Filter, tmp, FILTER_LENGTH, -1);
}

#define RX_VERBOSE 0
void RxGetSample(tRx* pRx, int16 Sample)
{
  tComplex s = { 0.0, 0.0 }, ss;
  double angle;
  uint i;
  int delta;
  double pwr;

  // Insert the sample into the delay line
  memmove(&pRx->Delay[0], &pRx->Delay[1], sizeof(pRx->Delay) - sizeof(pRx->Delay[0]));
  pRx->Delay[FILTER_LENGTH - 1] = Sample;

  // Get the next analytic signal sample by applying Hilbert transform/filter
  for (i = 0; i < FILTER_LENGTH; i++)
  {
    s.x += pRx->Delay[i] * pRx->Filter[FILTER_LENGTH - 1 - i].x;
    s.y += pRx->Delay[i] * pRx->Filter[FILTER_LENGTH - 1 - i].y;
  }

  // Frequency shift by MidFreq down
  ss.x = cos(-pRx->Phase);
  ss.y = sin(-pRx->Phase);
  s = complexMul(&s, &ss);
  pRx->Phase += pRx->PhaseIncrement;
  if (pRx->Phase >= 2 * M_PI)
  {
    pRx->Phase -= 2 * M_PI;
  }

  // Calculate signal power
  pwr = (s.x * s.x + s.y * s.y) / 32768 / 32768;
  pRx->LongAvgPower *= 1 - pRx->BitRate / (pRx->SampleRate * 8.0 * 8);
  pRx->LongAvgPower += pwr;
  pRx->ShortAvgPower *= 1 - pRx->BitRate / (pRx->SampleRate * 8.0);
  pRx->ShortAvgPower += pwr;

#if 0
  printf("LongAvgPower:%f ShortAvgPower:%f\n", pRx->LongAvgPower, pRx->ShortAvgPower);
#endif

  // Disconnect if the signal power changes abruptly.
  if (pRx->State != stCarrierLost &&
      pRx->LongAvgPower > pRx->ShortAvgPower * 8 * 8)
  {
    // N.B. The receiver may have received a few extra (garbage) bytes
    // while demodulating the abruptly changed signal.
    // Prefixing data with its size or using a more advanced protocol
    // may be a good solution to this little problem.
    pRx->State = stCarrierLost;
    pRx->BitSampleCnt = 0;
    pRx->Data = 0x3FF;
    pRx->Phase = 0.0;
    pRx->LastAngle = 0.0;
    pRx->LastDelta = 0;
    pRx->Deltas = 0;
    pRx->CarrierAngle = 0;
    pRx->CarrierCnt = 0;
  }

  // Get the phase angle from the analytic signal sample
  angle = (fpclassify(s.x) == FP_ZERO && fpclassify(s.y) == FP_ZERO) ?
    0.0 : 180 / M_PI * atan2(s.y, s.x);
  // Calculate the phase angle change and force it to the -PI to +PI range
  delta = (int)(360.5 + angle - pRx->LastAngle) % 360;
  if (delta > 180) delta -= 360;

  if (pRx->State == stCarrierLost)
  {
    // Accumulate the phase angle change to see if we're receiving 1's
    pRx->CarrierAngle += delta;
    pRx->CarrierCnt++;

    // Check whether or not the phase corresponds to 1's
    if (delta < 0)
    {
      if (pRx->CarrierCnt >= pRx->SampleRate / pRx->OnesFreq * 8)
      {
        double ph = (double)pRx->CarrierAngle / pRx->CarrierCnt;
#if RX_VERBOSE
        printf("ca:%5ld, cc:%4ld, ca/cc:%4ld\n",
               (long)pRx->CarrierAngle,
               (long)pRx->CarrierCnt,
               (long)(pRx->CarrierAngle / pRx->CarrierCnt));
#endif
        // Frequency tolerance is +/-16 Hz per the V.23 spec
        if (ph < (pRx->OnesFreq - 17.0 - pRx->MidFreq) * 360.0 / pRx->SampleRate ||
            ph > (pRx->OnesFreq + 17.0 - pRx->MidFreq) * 360.0 / pRx->SampleRate)
        {
          goto BadCarrier;
        }
      }
    }
    else
    {
BadCarrier:
      // Phase doesn't correspond to 1's
      pRx->CarrierAngle = 0.0;
      pRx->CarrierCnt = 0;
    }

    if (pRx->CarrierCnt >= pRx->SampleRate / 2 + pRx->SampleRate / 4)
    {
      // 0.75 seconds worth of 1's have been detected, ready to receive data

      // Adjust MidFreq to compensate for the DAC and ADC sample rate difference
      double f1 = (double)pRx->CarrierAngle / pRx->CarrierCnt / 360 * pRx->SampleRate + pRx->MidFreq;
      pRx->MidFreq = (uint)(pRx->MidFreq * f1 / pRx->OnesFreq);
      pRx->PhaseIncrement = 2 * M_PI * pRx->MidFreq / pRx->SampleRate;
#if RX_VERBOSE
      printf("f1:%u, new MidFreq:%u\n", (uint)f1, pRx->MidFreq);
#endif
      pRx->State = stCarrierDetected;
    }
  }
  else
  {
    // Detect frequency changes (transitions between 0's and 1's)
    int freqChange = ((int32)pRx->LastDelta * delta < 0 || pRx->LastDelta && !delta);
    int reAddDelta = 0;

#if RX_VERBOSE
    printf("%6lu: delta:%4d freqChange:%d BitSampleCnt:%u\n",
           (ulong)pRx->SampleCnt,
           delta,
           freqChange,
           pRx->BitSampleCnt);
#endif

    // Synchronize with 1<->0 transitions
    if (freqChange)
    {
      if (pRx->BitSampleCnt >= pRx->SampleRate / 2)
      {
        pRx->BitSampleCnt = pRx->SampleRate;
        pRx->Deltas -= delta;
        reAddDelta = 1;
      }
      else
      {
        pRx->BitSampleCnt = 0;
        pRx->Deltas = 0;
      }
    }

    // Accumulate analytic signal phase angle changes
    // (positive for 0, negative for 1)
    pRx->Deltas += delta;

    if (pRx->BitSampleCnt >= pRx->SampleRate)
    {
      // Another data bit has accumulated
      pRx->BitSampleCnt -= pRx->SampleRate;

#if RX_VERBOSE
      printf("bit: %u\n", pRx->Deltas < 0);
#endif

      pRx->Data >>= 1;
      pRx->Data |= (pRx->Deltas < 0) << 9;
      pRx->Deltas = delta * reAddDelta;

      if ((pRx->Data & 0x201) == 0x200)
      {
        // Start and stop bits have been detected
        if (pRx->State == stCarrierDetected)
        {
          pRx->State = stReceivingData;
        }
        pRx->Data = (pRx->Data >> 1) & 0xFF;
        pRx->pRxGetDataCallBack(pRx, (uint8)pRx->Data);

#if RX_VERBOSE
        printf("byte: 0x%02X ('%c')\n",
               pRx->Data,
               (pRx->Data >= 0x20 && pRx->Data <= 0x7F) ? pRx->Data : '?');
#endif

        pRx->Data = 0x3FF;
      }
    }

    pRx->BitSampleCnt += pRx->BitRate;
  }

  pRx->LastAngle = angle;
  pRx->LastDelta = delta;
  pRx->SampleCnt++;
}

typedef struct
{
  tTx Tx;
  FILE* DataFile;
  int CountDown;
} tTxTest;

uint TxGetDataCallBack(tTx* pTx, uint8* pTxData)
{
  tTxTest* pTxTest = (tTxTest*)pTx;
  uchar c;

  if (pTxTest->CountDown)
  {
    pTxTest->CountDown--;
    return 0;
  }

  if (fread(&c, 1, 1, pTxTest->DataFile) != 1)
  {
    pTxTest->CountDown = 20;
    return 0;
  }

  *pTxData = c;
  return 1;
}

int testTx(uint SampleRate,
           double NoiseLevel,
           const char* DataFileName,
           const char* AudioFileName)
{
  FILE *fData = NULL, *fAudio = NULL;
  int err = EXIT_FAILURE;
  tTxTest txTest;

  if ((fData = fopen(DataFileName, "rb")) == NULL)
  {
    printf("Can't open file \"%s\"\n", DataFileName);
    goto Exit;
  }

  if ((fAudio = fopen(AudioFileName, "wb")) == NULL)
  {
    printf("Can't create file \"%s\"\n", AudioFileName);
    goto Exit;
  }

  txTest.DataFile = fData;
  txTest.CountDown = 0;

  TxInit(&txTest.Tx,
         SampleRate,
         &TxGetDataCallBack);

  do
  {
    int16 sample = TxGetSample(&txTest.Tx);
    if (txTest.CountDown > 1 && txTest.CountDown <= 10)
    {
#if 0 // Enable this code to test disconnecting.
      // Finish with silence.
      sample = 0;
#endif
    }
    sample += (rand() - (int)RAND_MAX / 2) * NoiseLevel * 16000 / (RAND_MAX / 2);
    fwrite(&sample, 1, sizeof(sample), fAudio);
  } while (txTest.CountDown != 1); // Drain all data-containing samples

  err = EXIT_SUCCESS;

Exit:

  if (fData != NULL) fclose(fData);
  if (fAudio != NULL) fclose(fAudio);

  return err;
}

typedef struct
{
  tRx Rx;
  FILE* DataFile;
} tRxTest;

void RxGetDataCallBack(tRx* pRx, uint8 RxData)
{
  tRxTest* pRxTest = (tRxTest*)pRx;
  uchar c = RxData;
  fwrite(&c, 1, 1, pRxTest->DataFile);
}

int testRx(uint SampleRate,
           const char* AudioFileName,
           const char* DataFileName)
{
  uint lastState;
  FILE *fAudio = NULL, *fData = NULL;
  int err = EXIT_FAILURE;
  tRxTest rxTest;

  if ((fAudio = fopen(AudioFileName, "rb")) == NULL)
  {
    printf("Can't open file \"%s\"\n", AudioFileName);
    goto Exit;
  }

  if ((fData = fopen(DataFileName, "wb")) == NULL)
  {
    printf("Can't create file \"%s\"\n", DataFileName);
    goto Exit;
  }

  rxTest.DataFile = fData;

  RxInit(&rxTest.Rx,
         SampleRate,
         &RxGetDataCallBack);

  for (;;)
  {
    int16 sample;

    if (fread(&sample, 1, sizeof(sample), fAudio) != sizeof(sample))
    {
      if (rxTest.Rx.State != stCarrierLost) goto NoCarrier;
      break;
    }

    lastState = rxTest.Rx.State;
    RxGetSample(&rxTest.Rx, sample);

    if (rxTest.Rx.State != lastState && rxTest.Rx.State == stCarrierDetected)
    {
      printf("\nCONNECT %u\n\n", rxTest.Rx.BitRate);
    }

    if (rxTest.Rx.State != lastState && rxTest.Rx.State == stCarrierLost)
    {
NoCarrier:
      printf("\n\nNO CARRIER\n");
      break;
    }
  }

  err = EXIT_SUCCESS;

Exit:

  if (fAudio != NULL) fclose(fAudio);
  if (fData != NULL) fclose(fData);

  return err;
}

int main(int argc, char* argv[])
{
  uint sampleRate;
  double noiseLevel;

  if (argc < 2 ||
      !stricmp(argv[1], "-help") ||
      !stricmp(argv[1], "/help") ||
      !stricmp(argv[1], "-?") ||
      !stricmp(argv[1], "/?"))
  {
Usage:
    printf("Usage:\n\n"
           "  %s tx <sample rate> <noise level> <data input file> <PCM output file>\n"
           "  %s rx <sample rate> <PCM input file> <data output file>\n",
           argv[0],
           argv[0]);
    return 0;
  }

  if (!stricmp(argv[1], "tx") &&
      argc == 6 &&
      sscanf(argv[2], "%u", &sampleRate) == 1 &&
      sscanf(argv[3], "%lf", &noiseLevel) == 1)
  {
    return testTx(sampleRate, noiseLevel, argv[4], argv[5]);
  }
  else if (!stricmp(argv[1], "rx") &&
           argc == 5 &&
           sscanf(argv[2], "%u", &sampleRate) == 1)
  {
    return testRx(sampleRate, argv[3], argv[4]);
  }
  else
  {
    goto Usage;
  }
}

Typical usage:

modem.exe tx 8000 0.2 testin.txt test8000.pcm
modem.exe rx 8000 test8000.pcm testout.txt

The resulting testout.txt should be identical to testin.txt.