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Abstract — Information sent and received in wireless communication systems can suffer from data losses due to multipath propagation, further leading to intersymbol interference. These conditions compromise the integrity of the information transmitted. This paper explores the Viterbi algorithm used to combat error bounds in convolutional codes, and develops a MATLAB-based alternative model of the algorithm for continuous time applications that is shown to significantly diminish the effects of intersymbol interference in the wireless transmission of a signal.
I. INTRODUCTION
Wireless communications is part of everyday life. Whether we speak on the phone with a friend, or hear the news on the radio. However, the usage of the frequency spectrum …show more content…
An example of this is ionospheric reflection and refraction: a fraction of any message sent from Earth to space can reflect back to Earth on the surface of the ionosphere, and then a small fraction of this signal can be reflected back to space on the planet’s surface, and so on. When receiver circuits read a multipath signal, the original message becomes distorted due to echoes and reverberation, and the data can suffer heavy losses.
Signals can be divided into equal sized fractions of the original signal. Each piece is called a “symbol”. When a signal is propagated via multiple paths, the receiver circuit reads the same message multiple times with a certain delay. This is because of the time it takes for reflected signals to move through their whole trajectory. In a situation as such, each symbol will smear into their neighboring symbol, generating noise and distortion. This phenomenon is called intersymbol interference, and a graphical representation of said phenomenon is shown in Fig. 1.
Fig. 1. Intersymbol interference on an amplitude-modulated …show more content…
As we model this Markov process, we observe the state-dependent output, yet initially we are not able to note any of the states. Each state has a unique probability distribution over each possible output. Thus, information about the sequence of states through which the model makes its way can be obtained from the sequence of outputs generated, while the rest of the model remains hidden.
The algorithm tracks a stochastic process through its states by using a recursive method that is optimal in specific situations.
Fig. 2. State transition diagram for a four-state shift register process.
A visual representation of the behavior of a discrete time Markov process, as shown in Fig. 2, can be converted to what is called a trellis, which can be observed in Fig. 3. Each node represents a specific discrete time state, and each branch is specified to have a certain length, which is dependent on the data received.
The application of the algorithm in discrete time is mostly related to decoding convolutional codes in both GSM and CDMA digital cellular, dial-up modems, satellite communications, and other digital applications. However, the notion of the algorithm can be expanded to fit analog applications as well.
The algorithm can be formally described as
Abstract — Information sent and received in wireless communication systems can suffer from data losses due to multipath propagation, further leading to intersymbol interference. These conditions compromise the integrity of the information transmitted. This paper explores the Viterbi algorithm used to combat error bounds in convolutional codes, and develops a MATLAB-based alternative model of the algorithm for continuous time applications that is shown to significantly diminish the effects of intersymbol interference in the wireless transmission of a signal.
I. INTRODUCTION
Wireless communications is part of everyday life. Whether we speak on the phone with a friend, or hear the news on the radio. However, the usage of the frequency spectrum …show more content…
An example of this is ionospheric reflection and refraction: a fraction of any message sent from Earth to space can reflect back to Earth on the surface of the ionosphere, and then a small fraction of this signal can be reflected back to space on the planet’s surface, and so on. When receiver circuits read a multipath signal, the original message becomes distorted due to echoes and reverberation, and the data can suffer heavy losses.
Signals can be divided into equal sized fractions of the original signal. Each piece is called a “symbol”. When a signal is propagated via multiple paths, the receiver circuit reads the same message multiple times with a certain delay. This is because of the time it takes for reflected signals to move through their whole trajectory. In a situation as such, each symbol will smear into their neighboring symbol, generating noise and distortion. This phenomenon is called intersymbol interference, and a graphical representation of said phenomenon is shown in Fig. 1.
Fig. 1. Intersymbol interference on an amplitude-modulated …show more content…
As we model this Markov process, we observe the state-dependent output, yet initially we are not able to note any of the states. Each state has a unique probability distribution over each possible output. Thus, information about the sequence of states through which the model makes its way can be obtained from the sequence of outputs generated, while the rest of the model remains hidden.
The algorithm tracks a stochastic process through its states by using a recursive method that is optimal in specific situations.
Fig. 2. State transition diagram for a four-state shift register process.
A visual representation of the behavior of a discrete time Markov process, as shown in Fig. 2, can be converted to what is called a trellis, which can be observed in Fig. 3. Each node represents a specific discrete time state, and each branch is specified to have a certain length, which is dependent on the data received.
The application of the algorithm in discrete time is mostly related to decoding convolutional codes in both GSM and CDMA digital cellular, dial-up modems, satellite communications, and other digital applications. However, the notion of the algorithm can be expanded to fit analog applications as well.
The algorithm can be formally described as