Generation of DIFFERENTIAL PHASE SHIFT KEYING , DPSK Signals | DPSK full form , Definition ?

**Geometrical Representation of Non-Orthogonal BFSK Signals**

** **As a matter of fact, whenever the carriers _{1}(*t*) and _{2}(*t*) are non-orthogonal, then the signal point S_{H}(t) or S_{L}(t) would not lie exactly on the axes _{1}(*t*) and _{2}(*t*). Such a representation has been shown in figure 8.19.

The distance ‘*d*‘ for non-orthogonal signal shown in figure 8.20 may be given approximately as,

**equation**

**diagram**

**FIGURE 8.19** Geometrical representation of non-orthogonal BFSK signal.

**8.7.8. Salient Features of BFSK**

(i) BFSK is relatively easy to implement.

(ii) It has better noise immunity than ASK. Hence, the probability of error free reception of data is high.

**8.7.9. Drawback of BFSK**

The major drawback is its high bandwidth requirement. Therefore, FSK is extensively used in low speed modems having bit rates below 1200 bits/sec.

**8.8 NON-COHERENT BINARY MODULATION TECHNIQUES **

DO YOU KNOW? |

Frequency shift keying (FSK) uses two (and occasicnally more than two) transmitted frequencies to achieve modest data rates with good performance in noisy channel. |

As discussed earlier, coherent detection exploits knowledge of the carrier wave’s phase reference, and thus providing the optimum error performance attainable with a digital modulation format of interest. However, when it is impractical to have knowledge of the carrier phase at the receiver, we make use of **non-coherent detection.** Thus, in this section, we shall study non-coherent binary modulation techniques i.e., we shall study non-coherent detection of ASK and FSK. In the case of phase-shift keying (PSK), we cannot have “non-coherent PSK” since non-coherent means doing without phase information. However, there is a ‘pseudo PSK’ technique known as differential phase-shift keying (DPSK) which can be viewed as the non-coherent form of PSK.

**8.9 NON-COHERENT BINARY AMPLITUDE SHIFT KEYING (ASK) **

In the binary ASK case, the transmitted signal is defined as

s(t) =

Binary ASK signal can also be demodulated non-coherently using envelope detector. This greatly simplifies the design consideration required in synchronous detection. Non-coherent detection schemes do not require a phase-coherent local oscillator. This method involves some form of rectification and low pass filtering at the receiver. The block diagram of a non-coherent receiver for ASK signal has been shown in figure 8.20.

**diagram**

**FIGURE 8.20** *Non-coherent ASK detector.*

**8.10 NON-COHERENT DETECTION OF FSK**

** **Binary FSK waves may be demodulated non-coherently using envelope detector. The received FSK signal is applied to a bank of two bandpass filters, one tuned to frequency f_{c1} and the other tuned to f_{c2}. Each filter is followed by an envelope detector. The resulting outputs of the two envelope detectors are sampled and then compared with each other. The arrangement for non-coherent detection of FSK signal has been shown in figure 8.21.

**diagram**

**FIGURE 8.21** Non-coherent detection of FSK binary signals.

A decision is made in favour of symbol ‘1’ if the envelope detector output derived from the filter tuned to frequency f_{cl} is larger than that derived from the second filter. Otherwise, a decision is made in favour of the symbol 0.

**8.11 DIFFERENTIAL PHASE SHIFT KEYING (DPSK)**

*(U.P. Tech., Semester, Examination, 2003-2004) (10 marks) *

**(i) Definition**

** **We can view differential phase-shift keying as the non-coherent version of the PSK. Differential phase shift keying (DPSK) is differentially coherent modulation method. DPSK does not need a synchronous (coherent) carrier at the demodulator. The input sequence of binary bits is modified such that the next bit depends upon the previous bit. Therefore, in the receiver, the previous received bits are used to detect the present bit.

**8.11.1. Generation of DPSK**

**(i) Encoding Technique**

** **Thus, in order to eliminate the need for phase synchronisation of coherent receiver with PSK, a differential encoding system can be used with PSK. The digital information content of the binary data is encoded in terms of signal transitions. As an example, the symbol 0 may be used to represent transition in a given binary sequence (with respect to the previous encoded bit) and symbol. ‘1’ to indicate no transition. This new signaling technique which combines dif-ferential encoding with phase-shift keying (PSK) is known as differential phase-shift keying (DPSK).

**diagram**

**FIGURE 8.22** *Illustration of the scheme to generate DPSK signals.*

**(ii) Schematic Diagram**

** **A schematic arrangement for generating DPSK signal has been shown in figure 8.23. The data stream b(t) is applied to the input of the encoder. The output of the encoder is applied to one input of the product modulator. To the other input of this product modulator, a sinusoidal carrier of fixed amplitude and frequency is applied. The relationship between the binary sequence and its differentially encoded version is illustrated in Table 8.4 for a assumed data sequence 0 0 1 0 0 1 0 0 1 1 1. In this illustration it has been assumed that the encoding has been done in such a way that transition in the given bianry sequence with respect to the previous encoded bit is represented by a symbol 0 and no transition by symbol ‘1’. It may be noted that an extra bit (symbol 1) has been arbitrarily added as an initial bit. This is essential to determine the en-coded sequence. The phase of the generated DPSK signal has been shown in the third row of Table 8.4.

**Table 8.4. Differentially encoded sequences with phase.**

Binary data {b(k)} | 0 0 1 0 0 1 0 0 1 1 |

Differentially encoded data {d(k)} | 1* 0 1 1 0 1 1 0 1 1 1 |

Phase of DPSK | 0 0 0 0 0 0 0 0 |

Shifted differentially encoded data {d_{k-1}} |
1 0 1 1 0 1 1 0 1 1 |

Phase of shifted DPSK | 0 0 0 0 0 0 0 |

Phase comparison output | — — + — — + — — + + |

Detected binary sequence | 0 0 1 0 0 1 0 0 1 1 |

* Arbitrary starting reference bit. |

**8.11.2. Detection of DPSK**

For detection of the differentially encoded PSK (i.e., DPSK), we can use the receiver arrangement as shown in figure 8.23. The received DPSK signal is applied to one input of the multiplier. To the other input of the multiplier, a delayed version of the received DPSK signal by the time interval T_{b} is applied. The delayed version of the received DPSK signal (in the absence of channel noise) has been shown in the 4th row of the table. The output of the difference is proportional to cos (), here is the difference between the carrier phase angle of the received DPSK signal and its delayed version, measured in the same bit interval. The phase angle of the DPSK signal and its delayed version have been shown in 3rd and 5th rows respectively. The phase difference between the two sequences for each bit interval is used to determine the sign of the phase comparator output. When = 0, the integrator output is positive whereas when = , the integrator output is negative. By comparing the integrator output with a decision level of zero volt, the decision device can reconstruct the binary sequence by assigning a symbol ‘0’ for negative output and a symbol ‘1’ for positive output. The reconstructed binary data is shown in the last row of the table. It is thus seen that in the absence of noise, the receiver can reconstruct the transmitted hianry (lath exactly. DPSK may be viewed as a non-coherent version of PSK. h may also be noted that 1/u reconstruction is invariant with the choice of the initial bit in the encoded data. This has been illustrated in the example 8.1 given below.

**diagram**

**FIGURE 8.23** *Receiver for the detection of DPSK signals*

**EXAMPLE 8.1. A binary data strem 0 0 1 0 0 1 0 0 1 1 needs to be transmitted using DPSK technique. Prove that the reconstruction of the DPSK signal by the technique discussed in the previous article is independent of the choice of the extra bit. **

**Solution:** In the last article, we have observed that DPSK signal can be detected accurately (in the absence of channel noise) without having a local oscillator for generation of synchronous carrier. The initial bit in the differentially encoded data was assumed to be ‘1’. In this example, we use the initial bit to be symbol ‘0’ and verify that the reconstruction is invariant with the choice of the initial bit. The results obtained for this case are given in Table 8.5. It can be easily verified that the extra chosen bit 0 changes the phase of the DPSK sequence but the detected sequence remains invariant.

**Table 8.5. Differentially encoded sequences with phase.**

Binary data {b(k)} | 0 0 1 0 0 1 0 0 1 1 |

Differentially encoded data {d(k)} | 0* 1 0 0 1 0 0 1 0 0 0 |

Phase of DPSK | p 0 p p 0 p p 0 p p p |

Shifted differentially encoded data {d_{k-1}} |
0 1 0 0 1 0 0 1 0 0 |

Phase of shifted DPSK | p 0 p p 0 p p 0 p p |

Phase comparison output | – – + – – + – – + + |

Detected binary sequence | 0 0 1 0 0 1 0 0 1 1 |

* Starting reference bit. |

** **

**8.11.3. Evaluation of Bandwidth of DPSK Signal**

As discussed earlier that one previous bit is used to decide the phase shift of next bit. Thus, change in b(t) occurs only if input bit is at level T. No change happens if input bit is at level ‘0’. Because, one previous bit is always used to define the phase shift in next bit, therefore, the symbol can be said to have two bits. Hence, one symbol duration (T) is equivalent to two bits duration (2T_{b}) i.e.,

Symbol duration T = 2T_{b} …(8.48)

_{ }Bandwidth is expressed as

BW = …(8.49)

Hence, the minimum bandwidth in DPSK is equal to f* _{b}*, i.e., maximum baseband signal frequency.

**8.11.4. Advantages and Disadvantages of DPSK**

**We have observed in above discussion that DPSK has some advantages over BPSK, however, at the same time, it has some drawbacks.**

*(i) Salient Features***(i) DPSK does not need carrier at the receiver end. This means that the complicated circuity’ for generation of local carrier is not required.**

(ii) The bandwidth requirement of DPSK is reduced as compared to that of BPSK.

**(ii) Drawbacks**

**(i) The probability or error (i.e., bit error rate) of DPSK is higher than that of BPSK.**

(ii) Because DPSK uses two successive bits for its reception, error in the first bit creates error in the second bit. Therefore, error propagation in DPSK is more. On the other hand, in BPSK single bit can go in error since detection of each bit is independent.

(iii) Noise interference in DPSK is more.

**NOTE**: In DPSK, previous bit is used to detect next bit. Hence, if error is present in previous bit, detection of next bit can also be wrong. Hence, error is created in next bit also. Therefore, there is tendency of appearing errors in pairs in DPSK.

**8.11.5. Performance comparison of BPSK and DPSK**

**We can carry out the performance comparison of BPSK and DPSK in the form of table 8.6.**

**Table 8.6.**

S.N. |
Parameters of Comparison |
BPSK |
DPSK |

1. | Variable characteristics phase | phase | phase |

2 | Bandwidth | f_{b} |
f_{b} |

3 | Probability of error | Low | Higher than BPSK |

4. | System complexity | Lower than DPSK | Higher than BPSK |

5. | Demodulation technique | Synchronous | Synchronous |

6. | Noise effect | Low | Higher than BPSK |

7. | Requirement of synchronous carrier | is required | not required |

8. | Bit determination at the receiver | Based on single bit interval | Based on signal received in two sucessive bit intervals |