求助专业人士帮忙！QPSK

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/4就是Pi/4

1. Overview
This project report is organized as follows.
• Simulation Setup and Block Diagram - explains the Simulation Block Diagram,
Simulation Parameters and a brief description of each of the Simulation blocks.
• /4 - DQPSK Modulation - explains the basic math behind /4 - DQPSK
Modulation and some implementation details.
• Rayleigh Fading Envelope Generation - explains the basic methodology adopted
to generate the Rayleigh Fading envelope and to implement Spectral Shaping.
• Results - provide the results for the simualtion.
• MATLAB Modules for Simulation Blocks - provides the MATLAB code for
each and every simulation block.
• MATLAB Code - contains the MATLAB code used for the simulation cases. The
code presented in this section uses the simulation blocks presented in the previous
section.
• Appendix A - Raised Cosine Filtering - explains the method used to generate
the square root raised cosine filter coefficents that can be used directly in the code
with minor modifications.
• Appendix B - Rayleigh Fading Generation (Clarke/Gans Model) - explains
the method and the MATLAB code to generate Rayleigh Fading using the
Clarke/Gans Model.
2.1. Monte-Carlo Simulation Technique. The simulation methodology followed was
the well-known Monte-Carlo simulation technique. In the context of BER estimation in
Digital Communication Systems, the MC Simulation technique involves the following steps
:
(1) Decide on the minimum target BER to be estimated. (Here, it is 10−3).
(2) Set the number of bits per simulation run to be atleast 10 times the inverse of the
minimum target BER to be estimated. (Here, it is atleast 104 bits).
(3) Setup the baseband modulators, demodulators, Transmit/Receive Filters and Channel
Simulators.
(4) Run the BER simulation and estimate the BER.
(5) Iterate the simulation for some specified number of iterations and compute the
average of the BERs obtained in these iterations. (Here, the number of simulation
runs was chosen to be 20).
The various simulation blocks are explained in the following sections.
EECS 865 SIMULATION PROJECT 7
2.2. Serial to Parallel Converter. This block converts the incoming information bits
into two streams, one containing the even numbered bits and the other containing the odd
numbered bits. The output pair of bits constitute the input symbol stream to the /4 -
DQPSK Modulator.
MATLAB Prototype.
function [BitStreamOne, BitStreamTwo] = SerialToParallel(BitStream)
2.3. /4 - DQPSK Encoder. This block encodes the input information bits {b1k, b2k} into Modulation Symbols {Ik,Qk} using /4-DQPSK Signal Mapping.
MATLAB Prototype.
function [I_SymbolsTx, Q_SymbolsTx] = DQPSKEncoder(BitStreamOne,BitStreamTwo)
2.4. Transmit Filter. This block converts the Modulation Symbols to Baseband Waveforms
to be transmitted over the channel. In the given problem, this tranmit filter is just
a symbol repeater (represented by an FIR impulse response of all ones for the symbol interval).
This block can also be used to perform Raised Cosine filtering if provided with the
proper FIR filter coefficients for the SQRC filter.
MATLAB Prototype.
function [I_WaveformTx,Q_WaveformTx] = TransmitFilter(I_SymbolsTx, \\
Q_SymbolsTx, hTransmitFilter, numSamplesPerSymbol)
2.5. Delays. This block introduces a delay of specific duration (represented as the number
of samples).
2.6. Channel Simulators. These blocks simulate the channel response. They take the I
and Q baseband waveforms and apply channel-specific distortions to them. Two types of
channel simulators are provided.
• AWGN Channel Simulator.
• Rayleigh Fading Channel Simulator.
Fading and Noise addition are done independently for the I and Q components.
MATLAB Prototypes.
function [I_WaveformRx,Q_WaveformRx] = AWGNChannel(I_WaveformTx,Q_WaveformTx,No)
function [I_WaveformOut , Q_WaveformOut] = RayleighFader(I_WaveformIn, \\
Q_WaveformIn, AvgFadePower);
2.7. Receive Filter. This blocks performs Matched Filtering of the received signal. In
the case of an all-ones FIR impulse response (i.e, symbol repetition), this filter essentially
does an integrate and dump operation. The output of this filter are the received symbols
that are fed into the demodulator.
MATLAB Prototype.
function [I_SymbolsRx,Q_SymbolsRx] = ReceiveFilter(I_WaveformRx, \\
Q_WaveformRx, hReceiveFilter, numSamplesPerSymbol)
8 VIJAYA CHANDRAN RAMASAMI, KUID 698659
2.8. /4-DQPSK Decoder. This block performs the Maximum-Likelihood decoding of
the received symbols and retrieves the information bits.
MATLAB Prototype.
function [BitStreamOneRx, BitStreamTwoRx] = DQPSKDecoder(I_SymbolsRx, Q_SymbolsRx)
2.9. Parallel to Serial Converter. This block does the inverse of the Serial to Parallel
Converter block.
MATLAB Prototype.
function [BitStream] = ParallelToSerial(BitStreamOneRx, BitStreamTwoRx)
2.10. Comparator and BER Counter. The blocks compute the Probability of error
(Pe), by counting the number of discrepancies between the input and the received bits.
2.11. Noise Power Calculations. The value of No for a given operating point (i.e,
(Eb/No)o) can be obtained as follows :
• If Nb is the number of bits used for simulation and Ik and Qk represent the inphase
and quadrature phase components of the baseband signalling waveform, then the
Average Energy per Bit (Eb) 1 is given by,
(1) Eb =
1
Nb
Nb/2 Xi=1
(I2
k + Q2
k)
It is important to note that Ik and Qk are represented by their sample values (8
samples/symbol).
• The value of the noise PSD No can be found simply as,
(2) No = Eb
(Eb/No)o
1This was the value of Eb that gave the desired result during the simulation
EECS 865 SIMULATION PROJECT 9
3. /4 Shifted Differential Quadrature Phase Shift Keying (DQPSK)
This section deals with the math behind the /4 Shifted DQPSK Modulation Technique.
This digital modulation technique is a special case of Differential M-ary Phase Shift Keying
(D-MPSK) where M = 4. In such differential techniques, the information bits are mapped
into phase transitions rather than absolute phase values. This encoding of information in
the phase transitions overcomes the phase ambiguity problems resulting from the estimation
of carrier phase in non-differential PSK systems. (The term “/4 Shifted” appears in the
context of constellation diagrams and will be explained later). Further, in /4-DQPSK,
the maximum phase shift is restricted to ±135o (as compared to 180o for QPSK and 90o
for OQPSK). Hence, the bandlimited /4-DQPSK signal preserves the constant envelope
property better than bandlimited QPSK, but is more susceptible to envelope variations
than OQPSK.
3.1. I and Q Components. The In-phase (I) and Quadrature Phase (Q) components of
/4 DQPSK can be expressed as :
I(i) = I(i − 1) (3)  cos(
i) − Q(i − 1)  sin(
i)
(4) Q(i) = I(i − 1)  sin(
i) + Q(i − 1)  cos(
i)
Or,
(5) S(i) = S(i − 1)  ej
i
Where,
• I(i) and Q(i) are the in-phase and the quadrature phase components of the /4
DPSK Modulated Symbol at the ith signalling interval.
• S(i) is the ith modulated symbol.
•
i is the phase difference between the symbols at the ith and the (i−1)th signalling
intervals.
3.2. Phase Shift Mapping. The Phase shift
i depends on the input symbol di =
{00,01,11,10}. Thus, the information bits that consitute the input symbol are encoded into
one of the 4 possible phase transitions, defined by the following table.
bi1 bi2
i = f(bi1, bi2)
0 0 Pi/4
0 1 3/4
1 0 −3/4
1 1 −/4
Where, bi1 and bi2 are the information bits that constitute the input symbol di.
3.3. Constellation. The Constellation of /4 DQPSK Modulation is shown in fig(2). The
constellation diagram shows that /4 DQPSK is a combination of 2 QPSK constellations
shifted with respect to each other by /4 (and hence the name). Further, in /4 DQPSK,
there is an inherent feedback, since the decoding of the present symbol depends upon the
decoding (i.e, the phase) of the past symbol.
3.4. /4-DQPSK Encoder Implementation. The encoding operation can be easily implemented
using the recursive relations given in equations (4).
3.5. /4-DQPSK Decoder Implementation. /4-DQPSK decoding is generally accomplished
using differentially coherent detection.
• Compute the phase angles of all the received baseband symbols.
• Compute the difference in phase angles between succesive symbols.
(6)
k = \Sk − \Sk−1
• Demap the phase values into information bits using the inverse of the phase mapping
function.
Once the value of
k is obtained, the /4-DQPSK decision rule becomes,
(7) b1k = (sin
k > 0)
(8) b2k = (cos
k > 0)

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