Simulation of DPCM and ADM Systems Christopher Mansour
Roger Achkar
Department of Computer and Communications Engineering American University of Science and Technology, AUST Beirut, Lebanon
[email protected]
Department of Computer and Communications Engineering American University of Science and Technology, AUST Beirut, Lebanon
[email protected]
Gaby Abou Haidar Department of Computer and Communications Engineering American University of Science and Technology, AUST Beirut, Lebanon
[email protected] Abstract— Through years, Digital Communication systems, Pulse Coded Modulation (PCM), Linear Delta Modulation (LDM), Differential Pulse Coded Modulation (DPCM), and Adaptive Delta Modulation (ADM), have proven their unlimited advantages over analog communication systems, in term of error minimization, and distances of transmission enhancement. However two of these systems, the Pulse Coded Modulation and Linear Delta Modulation, still have some weaknesses limiting their advantages; these limitations negatively affect the communication process causing quantization error, slope overload distortion and granular noise. On the other hand, communication engineers have developed two additional digital communication systems which are the Adaptive Delta Modulation (ADM) and the Differential Pulse Coded Modulation (DPCM) in order to solve the aforementioned problems. This paper discusses the implementation and simulation of the aforementioned digital communication systems using Simulink (The Math Works, Inc., Natick, MA, USA) showing the effect of different types of noise when applied to the channel, thus, proving the importance of DPCM and ADM systems in eliminating such effects and ensuring a successful transfer of data. Keywords- Adaptive Delta Modulation, Differential Pulse Coded Modulation, Pulse Coded Modulation, Linear Delta Modulation.
I.
INTRODUCTION
Digital communications is the transfer of data over a point-to-point or even point-to-multipoint communication channel, examples of which are copper wires, optical fibers, and wireless communications media. The data is represented as an electromagnetic signal, such as an electrical voltage, radio-waves, or micro waves [1]. While analog communications is the transfer of continuously varying information signal, digital communications is the transfer of discrete messages. The messages are either represented by means of line codes, or by limited set of continuously varying form using the digital modulation methods [2]. Common techniques exist for the digital modulation process in order to make the process of transmitting data feasible, such as the PCM and the LDM. However, these two techniques have problems such as the quantization error
resulting from PCM, granular noise and slope overload distortion resulting from LDM. To observe the previously mentioned problems, and their solution, the digital modulation systems are implemented and simulated using Simulink. The relevance of this work lies in its ability to determine, by simulation, the effect of noise on the transmission channel of the data, and prove how two of these systems, the Differential Pulse Coded Modulation and the Adaptive Delta Modulation, work and eliminate the aforementioned problems. II.
BACKGROUND INFORMATION
A. Pulse Coded Modulation (PCM) Pulse Coded Modulation (PCM) is a method used to digitally represent sampled analog signals; in PCM a signal is represented by a sequence of coded pulses. A PCM stream is a digital representation of an analog signal where the magnitude of the analog signal is sampled regularly at uniform intervals, with each sample being quantized to the nearest value within a range of digital steps [3]. PCM has been used in digital telephone systems and is also the standard form for digital audio in computers and compact disks. However, PCM is not typically used for video in consumer applications such as DVD and DVR because it requires two high bit rate [3]. The performance of a PCM system is influenced by two major sources of noise, namely the channel noise which is introduced anywhere between the transmitter and the receiver; and the quantization noise which is introduced in the transmitter and is carried all the way to the receiver output. This noise is signal dependent in the sense that it disappears when the message signal is switched off [4]. The basic operations performed by the PCM transmitter are: sampling in which the signal is sampled with a train of narrow rectangular pulses and changed into a discrete time signal; quantizing in which the discrete values are approximated and changed into levels and this would be a new representation of the signal which is discrete in time and amplitude, and, encoding in which the obtained levels are changed to bits. As for the PCM receiver, it consists of the regenerative repeater for timing, equalization and
decision making. It is a decoder that changes the obtained bits to levels again, and the reconstruction filter that reconstructs the original signal. “Fig. 1” shows the block diagram representation of Pulse Coded Modulation PCM; as one can observe, the process is divided into three steps: transmitter, regenerative repeater, and receiver. Figure 2. Delta Modulation Encoder (adapted from Simon Haykin, “Communications Systems”, New York: John Wiley & Sons, Inc., 2000). Two types of distortions limit the performance of the Delta Modulation as shown in “Fig. 3”. The first is the slope overload distortion that is caused by the use of a step size delta which is too small to follow portions of the waveform that has a steep slope; and the granular noise, which is the result of a large step size signal parts with small slope [6].
Figure 1. Block Diagram showing the PCM process (adapted from Simon Haykin, “Communications Systems”, New York: John Wiley & Sons, Inc., 2000). B. Linear Delta Modulation Delta Modulation (DM) is an analog-to-digital and digital-to-analog signal conversion technique used for transmission of voice information where quality is not the primary concern. Delta Modulation is a special type of analog to digital quantizer, which is applicable to smoothly varying analog signals where there is a strong correlation from one sample to the next. DM is the simplest form of differential pulse coded modulation where the difference between successive samples is encoded into n-bits data stream; in Delta Modulation, the transmitted data is reduced to a 1-bit data stream [5]. The main feature of Delta Modulation is that the analog signal is approximated with series of segments which are then compared to the original analog wave to determine an increase or a decrease in relative amplitude; after that, the decision is made based on the comparison done. The Delta Modulation encoder shown in “Fig. 2” is known as a single integrator modulator. The input signal is compared to the integrated output pulses, and the delta (difference) signal is applied to the quantizer. The quantizer generates a positive pulse when the difference signal is negative and a negative pulse when the difference signal is positive. This difference signal moves the integrator step by step closer to the present value input, tracking the derivative of the input signal [5].
Figure 3. : Illustration of the Distortions facing LDM (adapted from Simon Haykin, “Communications Systems”, New York: John Wiley & Sons, Inc., 2000). To achieve a high signal to noise ratio (SNR), Delta Modulation uses oversampling techniques; that is, the analog signal is sampled at a rate several times higher than that of the Nyquist rate; this sampling is known as the Nyquist Criteria in digital signal processing [7]. III.
PROPOSED SOLUTIONS
A. Differential Pulse Coded Modulation (DPCM) The Differential Pulse Coded Modulation (DPCM) is a signal encoder that uses the baseline of Pulse Coded Modulation (PCM), discussed previously, but adds some functionality based on the prediction of the future values of the signal. Instead of taking a difference relative to the previous input sample, a difference relative to the output of a local model of the decoder process is taken. In this latter option, the difference can be quantized, securing a good way to incorporate a controlled loss in the encoding. Thus, the DPCM system reduces the error generated by the quantization process (known as the “quantization error”) at the transmitter of the PCM system. The DPCM transmitter is similar to the PCM transmitter, but it has a prediction filter for prediction of the future values of the signal; consequently, eliminating the quantization error [8].
To illustrate the advantages of DPCM over PCM, a typical example is taken into consideration; the same picture is coded in two ways. “Fig. 4” and “Fig. 5” are histograms showing the PCM and DPCM sample frequencies respectively.
using what is known as the “Adaptive Algorithm”. The principle that underlines all ADM adaptive algorithms is twofold: when to apply a maximum value of delta if successive errors are of the same polarity, and when to decrease delta if successive errors are of opposite polarity [9-10]. The block diagram representation of the Adaptive Delta Modulation (ADM) shown in “Fig. 6” consists of an input which is a sampled message signal, a one bit quantizer for the quantization process, and the adaptive algorithm which is the key element in the ADM system.
Figure 4. Histogram of PCM samples image (adapted from Anonymous, “Differential Pulse Coded Modulation”, http://www.rasip.ferhr/research/compress/algorithms/fund/p cm/dpcm/index.html
Figure 6. Block Diagram of ADM (adapted from Simon Haykin, “Communications Systems”, New York: John Wiley & Sons, Inc., 2000).
Figure 5. Histogram of DPCM samples image (adapted from Anonymous, “Differential Pulse Coded Modulation”, http://www.rasip.ferhr/research/compress/algorithms/fund/p cm/dpcm/index.html On the histogram shown in “Fig. 4”, a large number of samples have a significant frequency and we cannot pick only a few of them which would be assigned shorter code words to achieve compression. On the histogram shown in “Fig. 5”, all the samples are between -20 and +20, and were assigned short code, achieving a solid compression rate. B. Adaptive Delta Modulation Adaptive Delta Modulation (ADM) is the same as the Linear Delta Modulation (LDM), but the only difference is that the step size delta differs according to the input signal
The Adaptive Delta Modulation (ADM) system is the system that reduces the granular noise and slope overload distortion resulting from Linear Delta Modulation; the reduction is achieved due to the presence of the adaptive filter or algorithm in the system [11-12]. In the following sections, the systems discussed are implemented and simulated in Simulink (The Math Works, Inc., Natick, MA, USA) to test and observe the effect of noise on the transmission channel and to prove how ADM and DPCM reduce these effects. IV.
SIMULATIONS
A. Simulink Implementation of Pulse Coded Modulation The implementation of Pulse Coded Modulation (PCM) in Simulink, as shown in “Fig. 7”, requires the following: a sine wave source block that provides the test signal; a Bessel low pass filter of the 8th order to limit the signal’s frequency and prevent aliasing error; a Zero-Order-Hold block to allow the sampling process, thus changing the signal from a continuous varying signal to a discrete time signal; a quantizer for the quantization process which approximates the discrete values to levels; a uniform encoder to encode the obtained levels to a bit data stream; and, a decoder followed by a reconstruction filter in order to reconstruct the original signal.
blocks: a sine wave source block to provide the test signal; a Zero-Order-Hold block to act as a sampler for the sampling process, thus changing the continuous varying signal to a discrete time signal; a 1-bit quantizer for the quantization process; a unit delay; and an encoder for the encoding process. On the receiver side, the receiver consists of a decoder followed by Butter worth Filter of the 8th order for the reconstruction of the original signal.
Figure 7. Simulink Implementation of PCM system. In order to study the effect of noise on the PCM system, band limited White Gaussian noise was added to the transmission channel (between the encoder and the decoder). The results of simulation are as shown in “Fig. 8”.
Figure 9. Simulink Implementation of LDM. In order to study the effect of noise on the LDM system, band limited White Gaussian noise was added to the transmission channel between the encoder and the decoder as shown in “Fig. 8”; and an Integrate and Dump block followed by a gain and a low pass filter were added to act as a matched filter to the rectangular pulse which helps in the reconstruction process. Results of simulation are as shown in “Fig. 10”.
Figure 8. Reconstructed vs. original signal of PCM system. It is clear from these results that the reconstruction of the signal after the addition of band limited White Gaussian noise is a hard task within a PCM system, and that the reconstructed signal is distorted. The obtained signal has a different frequency and amplitude than the original signal, and even the shape of the signal is completely different than that of the original signal. B. Simulink Implementation of Linear Delta Modulation The implementation of Linear Delta Modulation (LDM) in Simulink, as shown in “Fig. 9”, requires the following
Figure 10. Addition of noise to LDM.
Figure 11. Original vs. reconstructed signal of LDM system. It is clear from the results shown in “Fig. 11” that the reconstruction of the signal after the addition of noise to the transmission channel is a hard task, and that the reconstructed signal is unstable and distorted. C. Simulink Implementation of Differential Pulse Coded Modulation The Simulink implementation of the Differential Pulse Coded Modulation (DPCM), shown in “Fig. 12”, consists of the following blocks: a sine wave source block to provide the test signal; a quantizer for the quantization process; a differentiator filter that acts as the prediction filter discussed previously; a uniform encoder for the encoding process; and, at the end, a low pass filter of type Bessel for filtering and reconstructing the original signal.
Figure 13. Reconstructed Signal after DPCM system's simulation. It is clear from the previous results that the Differential Pulse Coded Modulation system succeeded, to a certain extent, in reconstructing of the original signal, even after the addition of noise to the transmission channel; this is due to the usage of the prediction filter, which predicts the future values of the signal, hence, preventing the quantization error. D. Simulink Implementation of Adaptive Delta Modulation The Simulink implementation of Adaptive Delta Modulation (ADM), shown in “Fig. 14”, consists of the following blocks: a sine wave source to provide the test signal, a quantizer for the quantization process, and, a LMS filter with the LMS algorithm chosen to act as the adaptive filter with the adaptive algorithm, driving the input signal to the desired signal. On the receiver side, the same LMS filter with the same algorithm is used in order to get the successful reconstruction of the original signal, and to eliminate the errors resulting from the Linear Delta Modulation (LDM).
Figure 12. Simulink Implementation of DPCM. In order to study the effect of noise on the DPCM system, band limited White Gaussian noise was added to the transmission channel between the transmitter and the receiver; the results of the simulation are as shown in “Fig. 13”. Figure 14. Simulink implementation of ADM.
In order to study the effect of the noise on the transmission channel , band limited White Gaussian noise was added to the channel between the transmitter and the receiver; the results of the simulation are as shown in “Fig. 15”.
between the transmitted data from the transmitter’s side and the received data from the receiver’s side. The obtained results prove the importance of the two systems, the Adaptive Delta Modulation (ADM) and the Differential Pulse Coded Modulation (DPCM), in eliminating the effect of noise on the transmission channel, and in making the reconstruction of the original signal easier than when implementing the commonly used modulation techniques. VI. CONCLUSION AND FUTURE WORK As a conclusion, this project proves the importance of certain modulation techniques such as the Adaptive Delta Modulation and the Differential Pulse Coded Modulation in some environments and in solving the errors resulting from commonly used modulation techniques, the Pulse Coded Modulation and Linear Delta Modulation, such as granular noise and slope overload distortion. In the future, we will try to implement these two systems the Adaptive Delta Modulation System (ADM) and the Differential Pulse Coded modulation System (DPCM), in a real-time application.
Figure 15. Original vs. reconstructed signal of ADM system. The results shown in “Fig. 15” prove that the reconstructed signal was approximately the same as that of the original signal, which means that the Adaptive Delta Modulation system has successfully reconstructed the original signal without being affected by the noise that was added to the channel. The difference in amplitude is due to the LMS filter which acted as the adaptive algorithm. Therefore, the Adaptive Delta Modulation (ADM) system has eliminated the granular noise and slope overload distortion resulting from the Linear Delta Modulation (LDM). Upon the completion of the implementation and simulation parts, two of these systems were observed to be the best: the Differential Pulse Coded Modulation (DPCM) and the Adaptive Delta Modulation (ADM). These two techniques were chosen since they have produced the best results with the highest accuracy when simulated using Matlab. V. RESULTS AND DISCUSSIONS After the implementation and simulation of the digital modulation systems and testing them, the results were successful in two of these systems, the Differential Pulse Coded Modulation System (DPCM) and the Adaptive Delta Modulation System (ADM). The transmitted signal was successfully received and reconstructed without any error or disturbance. This fact was proved by a comparison done
Working in real-time is important because the conditions needed for the experiments are better than just testing them using software such as Simulink; working in real-time enhances the engineer’s knowledge and experience, encouraging him/her to better think. It also helps the engineer to figure out all the problems and try his/her best to solve them without relying on software to find the solution. REFERENCES [1]
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