Decision Feedback Equalization Technique Computer Science Essay

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In a high data rate closed wireless personal communication system, Inter symbol interference (ISI) can be produced as a result of delay spread due to the effect of multipath propagation. This can lead to a significant increase in the transmission bit error rate (BER). To resolve this problem of ISI, we employ the use of an efficient approach in the use of a decision feedback equalizer (DFE). The tap-coefficient vector of the DFE for an ISI-free transmission is constantly updated using the recursive least squares (RLS) algorithm with an adapting forgetting factor.

This paper discusses the development of a decision feedback equalization technique using the RLS algorithm to converge the fading effects. Finally MATLAB is used to simulate the effects according to some simplified mathematical models. This simulation result serves as an extremely useful research tool which can be used for comparing and measuring the effectiveness of different communication techniques.

Path Loss can be defined as decrease in power of signal being transmitted, which is mainly as a result of the physical distance of separation between the communications devices. Shadowing means the loss of power attributed to large obstacles such as hills and tall buildings. And finally, Fading, the focus topic in this paper, takes on a more deep view. In a mobile wireless communication system, a signal from the transmitter usually arrives at the receiver through more than a single path. This is due to refraction, reflection and scattering of the transmitted radio waves by structures around. The result of this action is called multipath fading. The mobile wireless channel is mostly characterized by fluctuations in the amplitude, carrier phase jitter and delay spread of propagation. During a high bit rate transmission, transmitted bandwidth of a signal is larger than the coherence bandwidth of the channel, as a result, the delay spread leads to an inter symbol interference (ISI) hence, an increase in the transmission bit error rate (BER). To resolve this ISI, We employ the use of a channel equalization technique. The decision-feedback equalizer (DFE) is a more

efficient nonlinear equalizer for combating a severe fading channels scenario (Cavers, James K, 2000). Usually, the recursive least squares (RLS) algorithm is an algorithm used to adjust the tap coefficient vector of the DFE adaptively in order to track down the dynamic fading channels thereby minimizing the equalization error of the receiver. The RLS algorithm is known to achieve the best performance for a steady state stationary environment.


Additive White Gaussian Noise (AWGN) could be described as unavoidable degradation in the capabilities and performance of a communication system. Therefore a good understanding of both the nature and origins of AWGN is vital if effective measures, for example channel coding, are to be designed to counter this effect.

The cause of a communication system degradation performance in noisy channel situations normally results from noisy sources, such as terrestrial noise, galactic noise and amplifier noise, interference from other communication systems also contribute to degradation, and finally, the thermal noise from by movement of electrons in a conducting media. Taking into consideration the primary characteristics of all the above mentioned noises, we can describe a Gaussian amplitude distribution by the PDF below. (T.S. Rappaport, 2006)

where is the noise variance or power.

A. Signal Fading

The Fading channel that is experienced by a signal propagating via multipath fading channel is dependent on nature, the transmitted signal and the channel characteristics.

Frequency and time dispersion mechanisms in multipath fading channels can lead to four different types of signal fading as discussed below.

Multipath Time Delay Spread Fading Effect

A multipath signal fading channel can undergo either frequency flat or frequency selective fading, due to time dispersion caused by multipath propagation.

These effects are discussed below.

1. Flat fading. The channel coherence bandwidth is bigger than the signal bandwidth. Here, same magnitude of fading will be experienced by all the frequency components.

2 Frequency Selective Fading: The channel coherence bandwidth is smaller than the signal bandwidth. Decorrelated fading or different fading will be experienced by different frequency components.

Doppler Spread Fading Effect

A multipath fading channel signal can either be a fast or slow fading, this can be as a result of the rate of change of the transmission channel due to the relative motion that exist between a transmitter and a receiver. These effects are briefly discussed below.

1. Fast fading: If a channel impulse response varies rapidly with the symbol duration of the transmitted signal, such channel is said to be a fast fading channel. This means that the channel coherence time is smaller than the reciprocal of the signal bandwidth.

2. Slow Fading: If a channel impulse response varies at a rate that is much slower than the signal�s rate of change, such channel is assumed to be static over a period of time larger than the reciprocal of the signal�s bandwidth interval.

B. Fading Manifestation

To fully understand wireless communications, it is necessary to explore what happens to the signal as it travels from the transmitter to the receiver. As explained earlier, one of the important aspects of this path between the transmitter and receiver is the occurrence of multipath fading which is a result of signal arriving from different paths. This occurrence is further emphasized below as received at the receiver

Rayleigh Fading

Instead of the mobile antenna to receive the transmitted signal over one line-of-sight path, it will receive a numerous number of reflected, refracted and scattered waves, as depicted in figure: 2.1 below. As a result of these varying path lengths, the receiver experience random phases and consequently, the instantaneous signal power received becomes random variable.

Let us assume that there are no Line-of-sight (LOS component, the received signal s(t), can be represented as

where N is the number of paths. is phase which depends on the varying path lengths.

Fig 1. Mechanism of radio propagation in a mobile environment.

A number of indirect paths and a line-of-sight path are shown.

Source:, retrieved 2011.

Coherence Bandwidth

The coherence bandwidth is normally used to measure of the frequency range over which a multipath fading channels frequency response can be considered to be flat. In defined terms, the coherence bandwidth is the maximum frequency separation between two frequency components propagating through the channel, after which two signals will experience uncorrelated fading.


The figure below depicts a simplified functional block diagram of a mobile wireless communication system. Although this paper considers an encoded M-ary phase-shift-keying (BPSK) here, the proposed algorithm in this paper can be applied directly to other modulation schemes.

Fig 2. Block of a functional system model.

Source: W. Zhuang, 1995.

A. Transmitter

At the transmitter, we encode the binary sequence, then modulate into a transmitted signal s(t ).

An equiprobable, independent m-bit information words m is generated by the data source. The phase mapper maps the uncoded binary sequence m, with an M-ary PSK symbol.

The transmitted information signal is given by


is the complex envelope of the transmitted signal. P is the power of the transmitted signal, fc is the carrier frequency, f is the carrier phase at t = 0, and s(t) is the baseband pulse waveform.

B. Frequency Selective Fading Channel

Here, the channel coherent bandwidth is smaller than the transmitted signal bandwidth. Therefore, the channel will exhibit a frequency-selective fading. The fading channel is described by its baseband complex impulse response

The frequency-selective fading channel does corrupts the transmitted signal s(t) by adding multiplicative envelope distortion. The multiple propagation paths also results in time dispersion of the transmitted signal. Finally, the signal transmitted is also corrupted by Gaussian noise.

The received signal is represented as

is the complex envelope of the signal received and n(t) is the complex envelope of the additive Gaussian noise. (Zhuang, W.A. Krzymien and P.A. Goud, 1995)

C. Receiver

At the receiver, the demodulator block consist of matched filters with an oscillator which separates the carrier component exp( j2pfct ) from the received signal. Here, the DFE jointly performs the equalization and the carrier phase synchronization at the baseband.

Decision Feedback Equalization (DFE)

The DFE is a nonlinear equalizer normally employed in applications where channel distortion is too severe for a linear equalizer to handle. The basic principle is that an information symbol is detected and decided upon; the induced ISI is then estimated and subtracted on future symbols before detection of the subsequent symbol that follows.

Fig 3. Schematic of a DFE

Source:, retrieved 20th October, 2007.

The RLS algorithm for DFE

The Recursive Least Square (RLS) algorithm is an adaptive filter algorithm that is used to update the tap coefficients of the DFE. However, the system will be inadequate for long period of time; this can be overcome by introducing some exponential forgetting factor into the filtering algorithm.


Briefly, the follow chart below describes the RLS algorithm with an adaptive forgetting factor for the tap coefficient vector.

Fig 4. Flowchart of RLS algorithm with adaptive forgetting factor

Flowchart steps of the RLS:

1. Set the initial values

2. Calculate the filtering gain and update the estimate of the tap-coefficient vector based on previous value, current gain, input and desired signal

3. Update

4. Update the forgetting factor based on current input

5. Update based on its previous value, current forgetting factor and filtering gain


A. Results

The flowing simulated graphs depict the equalization and the BER performance of a mobile communications system in a fading channel environment. The RLS algorithm with the adaptive forgetting factor is used to update the tap coefficient vector of the DFE according to channel status.

At 20km/hr

At 50km/hr

At 75km/hr


B. Discussion


It was discovered that the BER performance is much better in a low SNR and severe in high SNR. This is due to the fact that in low SNR, the white Gaussian noise dominates the BER error, this can be improved by increasing SNR. While in high SNR, phase estimation error dominates the BER error, this cannot be improved by simply increasing SNR.

In mobile communication systems, the channel fading rate and the Doppler spread are determined by the speed of the mobile device. Both factors are related to coherence time of the channel.

This speed effect based on the variation is shown in the graphs above. As speed increases, fading effect becomes more severe thus equalization becomes difficult to implement.

Based on the above stated observations, the following inferences were drawn:

1. Rayleigh fading channel is much more difficult environment than AWGN. Over 10dB extra power is needed in transmission to have equal results (BER).

2. Non-linear Equalizer can be used in a situation whereby channel distortion (ISI) is too severe, unlike in linear equalizer which cannot modify itself to severe distortions.

3. The effectiveness of the algorithm for the DFE in this project is clearly demonstrated by the simulation results. The RLS algorithm used provides the DFE with a good balance between the input noise suppression capability and a dynamics tracking capability of the system. Using the RLS algorithm can provide a system with a good BER performance.


Mobile-radio fading is an extremely difficult problem to overcome in communication system. Yet, in view of the market�s apparently insatiable appetite for mobile communication services, it seems likely that the urgency for dealing squarely with fading-related issues will only increase with time.

Therefore, it is not a surprise that there are many techniques for fading compensation. This paper proposed DFE as it was discussed. The algorithm chosen, RLS, can more effectively handle the equalization error and ISI due to channel dynamics as it is the dominant factor responsible for errors transmission.

Finally, the results demonstrated the DFE equalizer using the RLS algorithm is able to deal with the equalization errors.