What is a Software-Defined Radio?

1
Implementing Adaptive Modulation in a
Software-Defined Radio Brandon Bilinski and
Faculty Advisor Dr. Michael Pursley
What is a Software-Defined Radio?
What Are Hadamard Matrices?
BPSK Modulation Cont.
Adapting 32-ary Orthogonal

• An SDR is a flexible radio
• where programmable hardware
• is controlled by software.
• SDRs can tune to any
• frequency band or change to
• any modulation type.
• I am employing adaptive modulation.

• A Hadamard matrix is a matrix of the form
  2(n-1) x 2(n-1) where every row is orthogonal.
• If you multiply the Hadamard matrix by the
  transpose of any row, you will get n in the
  appropriate row and 0s elsewhere.

• Transmit the following bits 11110101

• As previously stated, multiplying an nxn
  Hadamard matrix by a transpose of one row of the
  matrix theoretically results in an nx1 matrix of
  n and all 0s.
• To estimate the signal to noise ratio we can use
  the following equation 1 (second_largest/max_p
  roduct)
• The following example is for 4-ary modulation

Modulated
Demodulated
Why Adapt Modulations?
1 - (.7/3.9) .821

• If a channel is
• noisy it is better
• to change
• modulations
• rather than
• increasing the
• transmitter
• power.
• The following
• modulation
• types had constant power and bandwidth.

32-ary Orthogonal Modulation

• Transmit two words 00000 and 00001
• Corresponding Hadamard Rows
• 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1
• 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
  1 -1 1 -1 1 -1 1 -1 1 -1 1 -1

32-ary Ratio Statistic

• When the ratio gets above .38, then it is
  desirable to switch to BPSK.
• With additional orthogonal schemes included, a
  ratio lower than .38 would signify a switch to
  16-ary orthogonal.

Modulated
QPSK Modulation

• QPSK is less robust than BPSK, but it can send
  twice the bits in one transmission.
• QPSK has four possible words 00, 01, 10,
  11 that are modulated using a combination of
  sine and cosine.
• The constellation mapping is
• once again shown on the right

First Steps Of Adaptive Modulation
Demodulated

• Construct a library of various modulation types
• In the FPGA chip.
• My radio contains 32-ary Orthogonal, BPSK,
• QPSK, and 16-QAM
• All modulation types designed in Simulink using
  the Xilinx FPGA blockset.
• BPSK Binary Phase Shift Keying
• QPSK Quadrature Phase Shift Keying
• QAM Quadrature Amplitude Modulation

QPSK Modulation Cont.

• Transmit the following bits 11011000

Modulated
Adapting MPSK Modulation

• When the distance is greater than .6, switch to
  32-ary less than .6, switch to BPSK less than
  .37, switch to QPSK less than .19, switch to
  16-QAM.

BPSK Modulation

• The transmitter modulates only one bit at a
  time.
• A 0 is mapped to -1cosine while a 1 is
  mapped to 1cosine.
• The BPSK constellation is mapped on the complex
  plane to the right

32-ary Orthogonal Modulation
Demodulated

• This is the most robust modulation scheme used
  in my radio.
• This scheme uses 32 chips to represent 5 bits of
  data its the slowest
• Each signal is orthogonal as a result of the
  orthogonality of the Hadamard matrix.