Orthogonal Frequency Division Multiplexing Quiz

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Questions and Answers

Which condition indicates frequency selective fading?

  • $T_o > T_s$
  • $f_o < W$ (correct)
  • $f_o > T_s$
  • $f_d < T_s$

What characterizes flat fading channels compared to fast fading channels?

  • Lower attenuation (correct)
  • Higher levels of distortion
  • Greater need for equalizers
  • Higher symbol rates

What is typically true for a fast fading channel?

  • $f_o > f_d$
  • $f_o < W$
  • $T_o < T_s$ (correct)
  • $W < T_o$

In OFDM, what is the desired relationship between coherence bandwidth, symbol rate, and fading rate?

<p>Coherence bandwidth &gt; symbol rate &gt; fading rate (A)</p> Signup and view all the answers

Which factors are managed using traditional equalization techniques?

<p>Flat fading and slow fading (C)</p> Signup and view all the answers

What happens when the number of subcarriers $N_C$ is appropriately chosen in OFDM?

<p>It avoids frequency selective fading. (C)</p> Signup and view all the answers

What aspect defines the worst-case fading profiles?

<p>Frequency-selective fading and/or fast fading (B)</p> Signup and view all the answers

What condition is necessary to obtain flat fading and slow fading channels in OFDM?

<p>$f_o &gt; f_d$ and $f_o &lt; W$ (C)</p> Signup and view all the answers

What is the coherence bandwidth $f_0$ calculated in the solution?

<p>10 kHz (A)</p> Signup and view all the answers

What is the minimum number of required subcarriers $(N_c)_{min}$ based on the provided bandwidth?

<p>10 (C)</p> Signup and view all the answers

Which factor determines the maximum number of required subcarriers $(N_c)_{max}$?

<p>Channel coherence time (A)</p> Signup and view all the answers

What is the relationship between the wavelength $ au$ and the velocity $v$ when $T_0 = 10 ms$?

<p>$T_0 = au/v$ (D)</p> Signup and view all the answers

How many bits per second is the coded data rate $R_C$ given a bit rate $R = 1 Mbit/s$ with a code rate of 1/2?

<p>2 M bit/s (C)</p> Signup and view all the answers

What is the maximum multipath spread $T_m$ calculated from the rms delay $ au$?

<p>15 μsec (B)</p> Signup and view all the answers

What main advantage does OFDM provide over traditional modulation methods?

<p>Reduced inter-symbol interference (ISI) (D)</p> Signup and view all the answers

Given 8-PSK modulation, what is the symbol rate $R_S$ if the coded bit rate $R_C$ is $2 × 10^6$ bps?

<p>0.67 M symbols/s (C)</p> Signup and view all the answers

What is the purpose of the inverse discrete Fourier transform (IDFT) in the context of OFDM?

<p>To convert high-data-rate inputs into lower-data-rate outputs (D)</p> Signup and view all the answers

How does the lengthened symbol time in OFDM affect rms smearing?

<p>It reduces rms smearing to approximately 3% of the lengthened symbol time (A)</p> Signup and view all the answers

What is the function of the cyclic prefix (CP) in OFDM systems?

<p>To maintain orthogonality of received signals under multipath conditions (A)</p> Signup and view all the answers

What effect does the introduction of guard periods have in an OFDM system?

<p>It prohibits overlap between symbols, thus reducing ISI (B)</p> Signup and view all the answers

How does OFDM handle multipath spread compared to non-OFDM systems?

<p>OFDM lengthens symbol duration, reducing the impact of multipath spread (D)</p> Signup and view all the answers

What is a defining characteristic of the channel impulse response in an OFDM system?

<p>It should be longer than the cyclic prefix to maintain orthogonality (B)</p> Signup and view all the answers

When comparing high-rate signals segmented into low-rate subchannels in OFDM, what is a result that occurs?

<p>The distortion experienced is negligible due to longer symbols (C)</p> Signup and view all the answers

What happens to the maximum multipath spread when OFDM is used?

<p>It is significantly reduced due to lengthened symbols (C)</p> Signup and view all the answers

In BPSK modulation, what phasor is assigned to the bit 0?

<p>-1 (D)</p> Signup and view all the answers

What does the parameter $m$ represent in the context of 64-QAM?

<p>The number of bits per phasor (A)</p> Signup and view all the answers

What is the significance of the IDFT in the context of constellation mapping?

<p>It converts frequency domain data to time domain. (A)</p> Signup and view all the answers

What condition must the subcarriers satisfy in an OFDM system?

<p>They must be orthogonal. (C)</p> Signup and view all the answers

What does the formula $\Delta f = R_s = 1/T_s$ describe?

<p>The spacing between adjacent subcarriers. (C)</p> Signup and view all the answers

What type of envelope do the output sinusoids from the IDFT have?

<p>Rectangular (B)</p> Signup and view all the answers

What role does the cyclic prefix play in an OFDM symbol?

<p>It prevents inter-symbol interference. (A)</p> Signup and view all the answers

How many bits do the phasors in a QPSK system represent?

<p>2 (D)</p> Signup and view all the answers

What is the total number of samples per OFDM symbol in the 802.11a standard?

<p>80 (D)</p> Signup and view all the answers

How is the symbol rate of an OFDM system calculated?

<p>It is the inverse of the OFDM symbol time duration. (B)</p> Signup and view all the answers

What is the effect of increasing the transform size N in an OFDM system?

<p>It raises the sample rate without affecting bandwidth. (B)</p> Signup and view all the answers

What does reducing the spacing between subcarriers (Δ f) affect?

<p>Increases the length of the data-symbol. (D)</p> Signup and view all the answers

What is the approximate modulation bandwidth (Wmod) of the 802.11a system?

<p>16 MHz (D)</p> Signup and view all the answers

Which of the following is the sample time duration for a 20 MHz OFDM system?

<p>0.05 μs (D)</p> Signup and view all the answers

What is the relationship between the sample rate (fS) and the number of subcarriers (Nc)?

<p>Sample rate is directly proportional to Nc. (A)</p> Signup and view all the answers

What is the total time duration of an OFDM symbol in the 802.11a standard?

<p>4 μs (A)</p> Signup and view all the answers

What does the Cyclic Prefix (CP) do in an OFDM system?

<p>It maintains orthogonality and simplifies equalization. (B)</p> Signup and view all the answers

In discrete Fourier transforms, what does spectral multiplication correspond to in time?

<p>Circular convolution. (C)</p> Signup and view all the answers

Why is it essential for continuous time signals to be band limited?

<p>To avoid aliasing during sampling. (B)</p> Signup and view all the answers

What key property allows the transformation of linear convolution into circular convolution in OFDM?

<p>Application of the Cyclic Prefix. (A)</p> Signup and view all the answers

What is essential for reconstructing correct OFDM subcarriers at the receiver?

<p>Maintaining signal orthogonality. (B)</p> Signup and view all the answers

What happens to the spectrum of a continuous time waveform as its frequency approaches infinity?

<p>Spectral sidelobes decay as 1/f. (A)</p> Signup and view all the answers

How is frequency represented in the DFT of a sampled rectangular function?

<p>As a circular coordinate. (A)</p> Signup and view all the answers

What modification occurs to the continuous transmitted waveform in OFDM during the DFT process?

<p>It is circularly convolved with the channel impulse response. (B)</p> Signup and view all the answers

Flashcards

OFDM

Orthogonal Frequency-Division Multiplexing; a method of transmitting data by dividing a high-rate signal into multiple lower-rate subchannels, significantly reducing the disruptive effects of multipath interference.

Symbol Interval (TS)

The time duration for one symbol in a data transmission system.

Multipath Interference (ISI)

Distortion of a signal caused by multiple copies of the signal arriving at the receiver from different paths, resulting in a smeared signal.

Cyclic Prefix (CP)

A portion of a data symbol added to the beginning of the symbol, used to maintain orthogonality of the received signals even with severe multipath conditions.

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64-point IDFT

The inverse Discrete Fourier Transform algorithm used to transform a high-data-rate, short-symbol input into a lower-data-rate, lengthened-symbol output in OFDM systems.

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RMS Smearing (sigma_tau)

The root-mean-square delay spread in a signal resulting from multipath propagation.

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Channel Impulse Response

A representation of how a communication channel affects a signal in the time domain.

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Frequency Selective Fading

A type of fading where the signal strength varies significantly across different frequency components.

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Flat Fading

A type of fading where the signal strength varies roughly the same across all frequency components.

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Fast Fading (Doppler Rate)

Rapid changes in signal strength due to the relative movement between transmitter and receiver.

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Slow Fading

Slower variations in signal strength than fast fading.

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Coherence Bandwidth (W)

The range of frequencies over which the channel characteristics remain relatively constant.

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Symbol Rate (fd)

The rate at which symbols are transmitted in a communication system.

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Coherence Time (To)

The duration over which the channel characteristics remain relatively constant.

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Symbol Time (Ts)

The duration of a single symbol in a communication system.

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OFDM (Orthogonal Frequency-Division Multiplexing)

A communication technique that transmits data on multiple orthogonal subcarriers.

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Number of Subcarriers (Nc)

The number of individual carriers used in an OFDM system.

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Channel Wish List (OFDM)

Desired characteristics of the communication channel for optimal OFDM performance.

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Condition for avoiding frequency-selective fading in OFDM

Coherence bandwidth > symbol rate > fading rate

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Coherence Bandwidth (f0)

The bandwidth over which the channel characteristics remain relatively constant. A measure of how stable the signal is in the channel.

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Minimum Subcarriers (Nc min)

The smallest number of subcarriers needed for a given system to avoid significant inter-symbol interference.

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Maximum Subcarriers (Nc max)

The largest number of subcarriers allowed by the channel coherence time.

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Channel Coherence Time (T0)

The duration over which the channel properties remain relatively constant.

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Velocity (v)

The speed of the mobile or moving device experiencing the channel.

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OFDM (Orthogonal Frequency-Division Multiplexing)

A modulation technique that transmits data over multiple frequencies (subcarriers) simultaneously to reduce interference.

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Inter-Symbol Interference (ISI)

A distortion effect in digital communication where a signal from one symbol interferes with subsequent symbols.

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RMS Delay Spread (στ)

The statistical measure of the time difference between the strongest and all other signals.

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Symbol Rate (Rs)

The rate at which symbols are transmitted.

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Maximum Delay (Tm)

The largest amount of time a signal from one path takes to travel through the channel.

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Constellation Mapping

A process in OFDM where successive bits are mapped to phasors in a constellation diagram.

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BPSK

Binary Phase Shift Keying; uses 1 and -1 phasors to represent 1 and 0 bits.

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QPSK

Quadrature Phase Shift Keying; uses four phasors to represent pairs (dibits) of bits.

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Phasor

A complex number representing magnitude and phase in the frequency domain.

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Subcarrier

A distinct frequency component in OFDM.

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IDFT

Inverse Discrete Fourier Transform; converts from frequency to time domain.

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OFDM Symbol

Composite signal containing multiple subcarriers in time domain after Inverse Transform.

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Cyclic Prefix

Added to the OFDM symbol to prevent inter-symbol interference.

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Orthogonal Subcarriers

Subcarriers that do not overlap in frequency.

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64-QAM

Quadrature Amplitude Modulation scheme that uses 6 bits for mapping to a phasor.

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Circular Convolution

A type of convolution operation performed on discrete-time signals that treats the signals as periodic. This is important in OFDM because it simplifies equalization.

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Cyclic Prefix (CP)

A special sequence added to the beginning of each OFDM symbol, used to maintain orthogonality and turn linear convolution into circular convolution.

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Orthogonality in OFDM

The property that ensures the different subcarriers in OFDM don't interfere with each other during transmission and reception.

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Spectral Multiplication (DFT)

Multiplying the spectra (frequency domain representations) of two signals in the frequency domain is equivalent to performing circular convolution on the corresponding time domain signals.

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Linear Convolution

The standard convolution between two continuous-time or discrete-time signals.

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OFDM Subcarrier Reconstruction

The process of recovering the individual subcarrier signals at a receiver, which is important to accurately recover the transmitted data.

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Discrete Fourier Transform (DFT)

A mathematical tool that transforms a discrete sequence of values from the time domain to the frequency domain.

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Equalization (OFDM)

The process of adjusting signals to compensate for distortion introduced by a channel during transmission. In OFDM, a spectral scaling adjustment is often used, made easier by using Circular Convolution.

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OFDM Subcarriers

Number of independent frequency channels used in Orthogonal Frequency-Division Multiplexing (OFDM).

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Transform Size (N)

Number of samples used in the Inverse Discrete Fourier Transform (IDFT).

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Cyclic Prefix (CP) Samples (Ncp)

Number of samples added to the beginning of each OFDM symbol to mitigate intersymbol interference (ISI).

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OFDM Symbol Samples (NL)

Total number of samples in one OFDM symbol; sum of transform size and cyclic prefix samples.

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Sample Rate (fs)

Rate at which samples are taken from the analog signal to be converted into the digital domain. Often expressed in MHz.

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OFDM Data Symbol Time (Ts)

Duration of the actual data portion in an OFDM symbol.

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Cyclic Prefix Time (Tcp)

Duration of the cyclic prefix in an OFDM symbol.

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OFDM Symbol Time (Tofdm)

Total duration of an OFDM symbol, sum of data and cyclic prefix time.

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OFDM Symbol Rate (Rofdm)

Frequency with which OFDM symbols are transmitted.

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Subcarrier Spacing (Δf)

Frequency difference between adjacent OFDM subcarriers.

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Modulation Bandwidth (Wmod)

Total spread of frequencies occupied by the modulated signal.

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LTE

Long-Term Evolution standard, for 4G radio communication.

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Inter-symbol Interference (ISI)

Distortion of a signal caused by the overlap of neighboring symbols.

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Study Notes

Orthogonal Frequency Division Multiplexing (OFDM)

  • OFDM is a multi-carrier signaling technique
  • It is a combination of modulation and multiplexing
  • Carrier frequencies are orthogonal
  • Saves bandwidth due to frequency overlap between neighboring signals
  • Demultiplexing uses no filtering
  • Effective in fading channels, mitigating their degrading effects for high data rates

FDM versus OFDM

  • FDM (Conventional Multi-Channel):
    • Adjacent channels do not overlap.
    • Guard bands between channels for separation using filters
    • Higher bandwidth required compared to OFDM for the same data rate
  • OFDM (Multi-Channel):
    • Adjacent channels do partially overlap
    • No guard bands; 50% overlap is acceptable, unlike FDM, but orthogonality is maintained
    • Lower total bandwidth needed compared to FDM for the same data rate

OFDM in Fading Channels

  • Coherence Bandwidth: fo
    • The range of frequencies, treated by the channel in a similar manner.
    • Range of a signal's spectral components traversing the channel with the same gain and linear phase.
  • Coherence Time: To
    • The range of time during which a signal is treated similarly by the channel.
    • Max delay Tm between the longest and shortest signal paths in the multipath channel
    • Doppler frequency (shift) during motion can affect coherence bandwidth and time
    • Doppler spread is reciprocally related to coherence time
  • Frequency Selective Fading: Occurs when fo < W, where W represents the signal bandwidth in Hertz.
  • Flat Fading: Fo > W
  • Relationship between delay spread and coherence bandwidth: fo ≈ 1/Tm, and To ≈ 1/fd

OFDM Subcarrier Design

  • Calculations: Given values of channel coherence time (Tm), coherence bandwidth (fo), transmission bandwidth (W), and carrier frequency. Calculate the minimum and maximum number of subcarriers needed for flat fading and slow fading. Additional calculations may involve maximum allowed velocity, wavelengths, and sampling rates.

Modem Without OFDM and With OFDM

  • High data-rate signals are divided into smaller lower-rate orthogonal subchannels by OFDM to mitigate the impacts of frequency selective fading channels.

Cyclic Prefix (CP)

  • OFDM uses guard periods (equal to max delay spread) between symbols to reduce ISI
  • CP helps maintain orthogonality, allowing simple spectral scaling in equalization
  • CP is used to avoid overlap in transmitted symbols and allow circular convolution

OFDM System Block Diagram

  • Operations: The system converts a serial data stream into parallel streams, maps bits to constellation points, performs an inverse discrete Fourier transform (IDFT), and adds a cyclic prefix (CP) before transmission. The receiver performs the reverse operations.

DAC (Digital-to-Analog Converter)

  • Converts digital data to analog signals to prepare the signal for transmission.

LP Filter (Low-Pass Filter)

  • Limits the signal bandwidth of real and imaginary parts of the baseband composite symbol, preventing interference.
  • This is required for bandpass modulation

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