Skip to main content

Function of a Decision Feedback Equalizer (DFE) Equalizer (with MATLAB)

 

Decision Feedback Equalizer is the abbreviation for this. We know that in a typical wireless communication scenario, different multipath cause the signal to arrive at the receiver at different times after transmitting it from the transmitter. Our signal may show a slight spatial frequency shift as a result. By using several taps to receive signals with varying time delays or signals with a slight frequency shift, equalizers solve this problem by changing their tap weights.

Decision feedback equalizers continuously update their tap coefficient vectors by reducing the error between the desired signal and adaptive filter output.

Inter-symbol interference (ISI) happens in a typical wireless communication system when the modulation bandwidth exceeds the radio channel's coherence bandwidth. Equalization reduces the ISI produced by multipath within a time-dispersive channel.

** Coherence bandwidth is the bandwidth (range of frequencies) over which the channel is constant is called coherence bandwidth

Both feed-forward taps and feed-backward taps are used in a DFE equalizer. 

'Input' - Input signal, specified as a column vector
'Desired' - Training symbols (column vector). The vector length of the desired must be less than or equal to the length of the input.
'Train' - Train equalizer flag. It starts training when the value changes from 0 to 1.
'Error' - Error signal (column vector)
'Weight' - Tap weights

The error between the feedforward and feedback signal is used to adjust the tap weights. To recover the original signal, it also converges the tap weights. DFE uses an adaptive algorithm at the receiver side to track the changing channel and modifies the weight of its filter to recover the known pilot signal most of the time. The data bits are then appropriately corrected. Pilot signals are provided at short intervals and are known to the receiver to track the communication channel or medium's frequently changing characteristics.

 


QPSK + Multipath + Decision Feedback Equalizer (DFE)

20 BER Before: 0 | BER After: 0

Simulator Workflow & Mathematics

1 The Signal Path

  1. QPSK Modulation Random bits are grouped into pairs and mapped to complex symbols: s = exp(j * (Ļ€/4 + kĻ€/2)).
  2. Multipath Channel The signal is convolved with a multi-tap impulse response, simulating reflections that cause Inter-Symbol Interference (ISI).
  3. DFE Equalization A Feedforward Filter (FFF) suppresses precursor ISI, while a Feedback Filter (FBF) subtracts post-cursor ISI using previous symbol decisions.

2 The DFE Equations

// 1. Equalizer Output

y[n] = Ī£(w_f[k] * x[n-k]) - Ī£(w_b[k] * d[n-k])

(Feedforward Output - Feedback Correction)

// 2. Error Calculation

e[n] = d_known[n] - y[n]

// 3. LMS Weight Update

w_f[k] = w_f[k] + Ī¼ * e[n] * x*[n-k]

w_b[k] = w_b[k] - Ī¼ * e[n] * d*[n-k-1]

Where Ī¼ is the step size, x* is the conjugate of the received signal, and d are previous decisions.
Return to Home →

Also read about

[2] Adaptive Equalizer to mitigate Channel Distortion (in MATLAB)

[3] Roll of an Equalizer in Channel Estimation


šŸ“Š MATLAB & ONLINE SIMULATIONS
šŸŽ“ GATE SOLUTIONS
šŸ“” WIRELESS & THEORY

Contact Us

Name

Email *

Message *

Popular Posts

Q-function in BER vs SNR Calculation

Q-function in BER vs. SNR Calculation In digital communications and signal processing, the Q-function plays a significant role in predicting system reliability. It allows engineers to quantify the probability that Gaussian noise will exceed a specific threshold, causing a bit error. What is the Q-function? The Q-function is a mathematical function representing the tail probability of the standard normal (Gaussian) distribution. It is the complementary cumulative distribution function (CCDF) of a standard Gaussian distribution. Q(x) = (1 / √(2Ļ€)) ∫ā‚“∞ e^(-t² / 2) dt Q-Function Interactive Simulator Move the slider to see how the "Tail Probability" (the area in red) changes. This area represents the Probability of Error (BER) . Threshold Distance ( x ) — (Simulates Increasing SNR) x = 1.0 Q(x) = 0.1587 ...
Read more

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. šŸ“˜ Theory šŸ§® Simulators šŸ’» MATLAB Code šŸ“š Resources BER Definition SNR Formula BER Calculator MATLAB Comparison šŸ“‚ Explore M-ary QAM, PSK, and QPSK Topics ▼ šŸ§® Constellation Simulator: M-ary QAM šŸ§® Constellation Simulator: M-ary PSK šŸ§® BER calculation for ASK, FSK, and PSK šŸ§® Approaches to BER vs SNR What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figure of merit f...
Read more

RMS Delay Spread, Excess Delay Spread and Multi-path ...(with MATLAB + Simulator)

šŸ“˜ Overview of Delay Spread and Multi-path šŸ§® Excess Delay spread šŸ§® Power delay Profile šŸ§® RMS Delay Spread šŸ“š Further Reading šŸ“‚ Other Topics on RMS Delay Spread, Excess Delay ... šŸ§® Multipath Components or MPCs šŸ§® Online Simulator for Calculating RMS Delay Spread šŸ§® Why is there significant multipath in the case of very high frequencies? šŸ§® Why RMS Delay Spread is essential for wireless communication? šŸ§® Why the Power Delay Profile is essential? šŸ§® MATLAB Codes for Calculating Different Types of delay Spreads Delay Spread, Excess Delay Spread, and Multipath (MPCs) The fundamental distinction between wireless and wired connections is that in wireless connections signal reaches at receiver thru multipath signal propagation rather than directed transmission like co-axial cable. Wireless Communication has no set communication path between the transmitter and the receiver. The line...
Read more

FM Bandwidth and FM Band Explained

FM radio uses the frequency band from 88 MHz to 108 MHz , which is a 20 MHz-wide spectrum . This is the range of carrier frequencies available to stations. 108 MHz − 88 MHz = 20 MHz However, a single FM station occupies only about 200 kHz . This is the bandwidth of the modulated FM signal. 1. Why One FM Station Needs ~200 kHz FM uses frequency modulation . The bandwidth depends on how far the carrier swings. Carson's Rule gives the approximate FM bandwidth: B = 2 ( Ī”f + f m ) ...
Read more

OFDM Symbols and Subcarriers Explained

This article explains how OFDM (Orthogonal Frequency Division Multiplexing) symbols and subcarriers work. It covers modulation, mapping symbols to subcarriers, subcarrier frequency spacing, IFFT synthesis, cyclic prefix, and transmission. Step 1: Modulation First, modulate the input bitstream. For example, with 16-QAM , each group of 4 bits maps to one QAM symbol. Suppose we generate a sequence of QAM symbols: s0, s1, s2, s3, s4, s5, …, s63 Step 2: Mapping Symbols to Subcarriers Assume N sub = 8 subcarriers. Each OFDM symbol in the frequency domain contains 8 QAM symbols (one per subcarrier): Mapping (example) OFDM symbol 1 → s0, s1, s2, s3, s4, s5, s6, s7 OFDM symbol 2 → s8, s9, s10, s11, s12, s13, s14, s15 … OFDM sym...
Read more

Orthogonal Time Frequency Space (OTFS) (with MATLAB)

In OTFS (Orthogonal Time Frequency Space) modulation — a scheme designed for high-Doppler and time-varying wireless channels — the terms ISFFT and SFFT are key mathematical transformations used to move between different representation domains. Figure: OTFS block diagram 1. ISFFT — Inverse Symplectic Finite Fourier Transform Purpose: Transforms data symbols from the delay-Doppler domain to the time-frequency domain . \[ X[n, m] = \frac{1}{\sqrt{NM}} \sum_{k=0}^{N-1} \sum_{l=0}^{M-1} x[k, l] \, e^{j2\pi \left( \frac{nk}{N} - \frac{ml}{M} \right)} \] Here, \( N \) is the number of Doppler bins (time slots), and \( M \) is the number of delay bins (subcarriers). The ISFFT maps each data symbol from the delay-Doppler grid (where the channel is sparse and easier to equalize) to the time-frequency grid (where standard multicarrier modulation like OFDM can be applied). 2. SFFT — Symplectic Finite Fourier Transform Purpose: Performs the reverse operation ...
Read more

Intel 8086 Transistor Count: Architecture, Specifications, and Comparison with Other Microprocessors

Intel 8086 Transistor Count: Architecture, Specifications, and Comparison with Other Microprocessors Intel 8086 Transistor Count: Complete Guide with Architecture and Processor Comparison The Intel 8086 microprocessor is one of the most important processors in computer history. Released in 1978 , it introduced the x86 architecture that still influences modern CPUs. One of the most frequently asked questions in computer architecture and microprocessor courses is: How many transistors are present in the Intel 8086? The commonly accepted answer is approximately 29,000 transistors . However, reverse-engineering studies have shown that the actual number of physical transistors is closer to 19,618 , while Intel's published figure includes programmable transistor locations used in ROM and PLA structures. Intel 8086 Transistor Count Metric Value Published transistor count ~29,000 Physical transistor count ~19,618 Release year 1978 Word ...
Read more