Digital Communications and LFSR Properties
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Questions and Answers

What is the primary purpose of using non-maximal codes such as Gold codes?

  • To improve signal distinguishing against background noise (correct)
  • To create very long codes for quick synchronization
  • To provide maximum cross-correlation
  • To eliminate all signals during synchronization

    • In the linear summation process of codes, what is the result when shifting the second code by 2 chips?

  • 0111111
  • 1001101
  • 0101000 (correct)
  • 0010001

    • Which statement best describes the process used to obtain a DSSS signal?

  • The code sequence is summed with information logic signals before modulation (correct)
  • Information signals are sent without modification to the code sequence
  • Only continuous signals are utilized for code modification
  • BPSK is used exclusively without any prior processing

    • What characteristic of JPL codes makes them particularly suitable for ranging applications?

    <p>Fast synchronization capabilities</p> Signup and view all the answers

    In the context of orthogonal codes, what is the significance of the integral expression provided?

    <p>It indicates successful isolation of signals</p> Signup and view all the answers

    What is the statistical distribution of '1' and '0' in maximum sequences?

    <p>The position changes, but the amount remains constant.</p> Signup and view all the answers

    Which state must not exist for a functioning n-column generator?

    <p>The state of all '0'.</p> Signup and view all the answers

    What is the autocorrelation function used for in relation to signals?

    <p>To determine the delay of signal propagation.</p> Signup and view all the answers

    In a given code shift of 1, what is the result of coincidences minus discrepancies?

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

    What is the total number of slots in the maximum sequence when p equals 1?

    <p>32</p> Signup and view all the answers

    What is one of the main purposes of the m-sequence autocorrelation function?

    <p>To suppress inter-symbol interference.</p> Signup and view all the answers

    For which slot index does the m-sequence contain only '0's?

    <p>6</p> Signup and view all the answers

    What is the maximum length of a binary maximum sequence generated by an n-column shift register?

    <p>2n-1</p> Signup and view all the answers

    How many units of logical '1' are present in a binary maximum sequence generated by a length-10 generator?

    <p>512</p> Signup and view all the answers

    What does the autocorrelation function of a maximal sequence return for all shifts except one?

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

    In the context of a code sequence, what does U=1 correspond to?

    <p>Logical '1'</p> Signup and view all the answers

    What is the relationship between the number of logical '1's and '0's in a maximal sequence of length n?

    <p>The number of '1's equals the number of '0's plus one</p> Signup and view all the answers

    What does a transition of 0→1 signify in a code sequence?

    <p>A logical '1' at time ti</p> Signup and view all the answers

    Which statement regarding the statistical distribution in maximal sequences is accurate?

    <p>The sequence has a strictly defined statistical distribution of '1's and '0's</p> Signup and view all the answers

    What is the result when summing the sequence according to modulo-2 with its own displacement?

    <p>The same sequence</p> Signup and view all the answers

    What is the relationship between Tb and t in synchronization?

    <p>Tb = KT t</p> Signup and view all the answers

    In BPSK, what does the symbol m(t) represent?

    <p>Data represented by ±1</p> Signup and view all the answers

    What is the purpose of the chip generator in a DSSS signal modulator?

    <p>To generate the spreading code pN(t)</p> Signup and view all the answers

    Which coding method is employed for data synchronization in the DSSS signal modulator?

    <p>NRZ coding</p> Signup and view all the answers

    What is true about orthogonal codes in synchronization?

    <p>They allow for the elimination of unnecessary signals</p> Signup and view all the answers

    What must be true about the data rates of input signals in this system?

    <p>They must be equal</p> Signup and view all the answers

    What type of signal is produced by the code generator in the DSSS modulator?

    <p>Discrete multilevel signal</p> Signup and view all the answers

    What is the main function of the carrier generator in relation to the DSSS signal?

    <p>To multiply the frequency of the BPSK signal</p> Signup and view all the answers

    What is the impact of using large n in sequences during synchronization?

    <p>It prolongs the synchronization process.</p> Signup and view all the answers

    In the context of cross-correlation function Y(r), what does the function represent?

    <p>The integral of two functions over time.</p> Signup and view all the answers

    What happens when two m-sequences of the same length but different phases are combined?

    <p>The output produces a sequence whose phase does not coincide with elements from either input.</p> Signup and view all the answers

    What is a characteristic of Gold codes when comparing two different m-sequences?

    <p>They generate a non-maximal sequence of equal length.</p> Signup and view all the answers

    How does the length of the output code change when combining m-sequences of different lengths?

    <p>The output length equals the product of the lengths of the two sequences.</p> Signup and view all the answers

    What indicates a poor result in the cross-correlation analysis of the given chip codes?

    <p>High number of discrepancies.</p> Signup and view all the answers

    What is the correct interpretation of 'coincidences' in the context of chip code correlation?

    <p>Instances where values match between codes.</p> Signup and view all the answers

    What is the formula used to calculate the efficiency of an FDMA system?

    <p>$m_f = \frac{B_v}{B_c N_c}$</p> Signup and view all the answers

    Which feature does NOT apply to non-maximal sequences formed from two different m-sequences?

    <p>They have excellent cross-correlation properties.</p> Signup and view all the answers

    In a hexagonal cell, what is the minimal S/I ratio represented as?

    <p>$\frac{S}{I} = (3N_c)^2$</p> Signup and view all the answers

    Given a path loss exponent $ν= 4$, what is the efficiency equation for the FDMA system?

    <p>$m_f = 1.22$</p> Signup and view all the answers

    What variable represents the total bandwidth in the context of FDMA?

    <p>B_v</p> Signup and view all the answers

    How is minimal S/I for hexagonal cell derived?

    <p>From the relationship $\frac{S}{I} = (3N_c)^2$</p> Signup and view all the answers

    If $B_v = 12.5 MHz$ and $B_k = 200 kHz$, how many frequency channels can be formed?

    <p>64</p> Signup and view all the answers

    Which formula represents the efficiency for a TDMA system?

    <p>$m_f = \frac{B_v}{B_c k}$</p> Signup and view all the answers

    What does k represent in the context of TDMA?

    <p>The number of time multiplexed channels</p> Signup and view all the answers

    Study Notes

    Code Sequence and Properties

    • Code sequence is a periodic sequence of logical 1s and 0s.
    • The sequence often follows a pseudo-random order.
    • Transitions between 0 and 1 are possible at specific time moments.
    • Time moments are defined by tᵢ = iTₜ, where Tₛ = nT₁, and n is a large value.
    • A logical "1" corresponds to U = 1.
    • A logical "0" corresponds to U = −1.
    • Rₖ = 1/Tₜ, represents the chip rate.

    Linear Feedback Shift Register (LFSR)

    • An LFSR is a sequence generator using an n-column shift register.
    • The maximum (longest) sequence generated by an LFSR of n columns is 2ⁿ⁻¹.
    • The length of the binary maximum sequence is 2ⁿ⁻¹ clock periods.
    • The n-column register contains n stages (D₁ to Dₙ).
    • An equation to represent the data output is S(f) = U 2Tₜ sin²(πfT₁).

    Properties of m-Sequences

    • The number of "1"s equals the number of "0"s plus 1.
    • Statistical distribution of "1"s and "0"s is well-defined.
    • Autocorrelation function is -1 for all shifts, but +1 for shifts of ±1 chip period (varies linearly within range −1...2ⁿ⁻¹).
    • Summing the sequence with a time displacement results in the same sequence with a time shift, that does not coincide with any other original sequence.

    Code Autocorrelation and Cross-Correlation

    • Autocorrelation function Ψ(r) = ∫₀∞ f(t)f(t − r)dt
    • For binary bipolar sequences (P(t) = ±1) and code offsets (rᵢ = iTₜ).
    • Ψ(r) = Coincidences - Σ Discrepancies.
    • 7-chip code example provided.

    m-Sequence Autocorrelation Function

    • Useful in determining signal propagation delay, suppressing inter-symbol interference.
    • Less useful for synchronization with long sequence periods.

    m-Sequence Cross-Correlation Function

    • Cross-correlation function Ψ(r) = ∫₀∞ f(t)g(t − r)dt for binary bipolar sequences.
    • Ψ(r) = Σ Coincidences - Σ Discrepancies for code offsets rᵢ = iTₜ.
    • Example using 7-chip codes 1110100 and 1110010 is given.

    Linear Summation of Codes

    • Adding m-sequences (with the same or differing phases) can produce maximal output in specific cases.
    • If the sequences have the same length but different phases , the result is a sequence similar to the input.
    • If lengths differ the results in non-maximal sequences.

    Autocorrelation Function of Nonmaximal Code

    • Non-maximal codes are frequently used for distinguishing signals from the background of other signals.
    • Gold codes have low cross-correlation.
    • JPL codes are suitable for rapid synchronization.
    • Orthogonal codes eliminate unused signals in multiply compressed signals.

    Insertion of Information into DSSS Signal

    • Modifying a code sequence with an information signal.
    • Used in BFSK, QPSK.
    • The process involves summing data and code sequence according to modulus 2.

    DSSS Signal Modulator

    • Block diagram of the modulator is provided.
    • Components include data synchronization, coder, bipolar PN sequence generator, carrier generator, BPSK modulator

    DSSS Signal Modulator - Multiple Sources

    • Block diagram for multiple data inputs.
    • Uses Orthogonal codes to effectively eliminate interference.
    • Uses spreading with Orthogonal codes to avoid interference and simplify synchronization.

    Efficiency of FDMA System

    • Formulas to calculate the number of physical channels for a given bandwidth.
    • Ratios for hexagonal cell scenarios (S/I ratio).
    • Derives efficiency formulas.

    Efficiency of FDMA and TDMA Systems

    • Formulas based on path loss exponent to evaluate efficiency.
    • Including the number of physical channels
    • Using the path loss exponent to determine the efficiency.

    Exercise – FDMA/TDMA Efficiency

    • Example parameters for efficiency calculation (bandwidth, multiplexing, S/I).

    CDMA System Efficiency

    • Formulas for signal-to-noise ratio (SNR) with multiple CDMA users.
    • Formulas to calculate the maximum number of active users based on Eb/No.
    • Calculations for single-user conditions and interference dominance.
    • Calculations for various noise and power conditions.

    Exercise – CDMA System Efficiency

    • Calculation examples for maximum number of users under different conditions (interference, power levels).

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    Related Documents

    Code Sequence and Properties PDF

    Description

    This quiz covers key concepts related to code sequences, linear feedback shift registers (LFSRs), and the properties of maximum-length sequences (m-sequences). Test your understanding of the mathematical principles and statistical properties that govern these digital communication tools.

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