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Channel equalization to achieve high bit rates in discrete multitone systems
textMulticarrier modulation (MCM) techniques such as orthogonal frequency division
multiplexing (OFDM) and discrete multi-tone (DMT) modulation are attractive
for high-speed data communications due to the ease with which MCM can combat
channel dispersion. With all the benefits MCM could give, DMT modulation has an
extra ability to perform dynamic bit loading, which has the potential to exploit fully
the available bandwidth in a slowly time-varying channel. In broadband wireline
communications, DMT modulation is standardized for asymmetric digital subscribe
line (ADSL) and very-high-bit-rate digital subscriber line (VDSL) modems. ADSL
and VDSL standards are used by telephone companies to provide high speed data
service to residences and offices.
In an ADSL receiver, an equalizer is required to compensate for the channel’s
dispersion in the time domain and the channel’s distortion in the frequency domain
of the transmitted waveform. This dissertation proposes design methods for linear
equalizers to increase the bit rate of the connection. The methods are amenable
to implementation on programmable fixed-point digital signal processors, which are
employed in ADSL/VDSL transceivers.
A conventional ADSL equalizer consists of a time-domain equalizer, a fast
Fourier transform, and a frequency domain equalizer. The time domain equalizer
(TEQ) is a finite impulse response filter that when coupled with a discretized channel
produces an equivalent channel whose impulse response is shorter than that of
the discretized channel. This channel shortening is required by the ADSL standards.
In this dissertation, I first propose a linear phase TEQ design that exploits symmetry
in existing eigen-filter approaches such as minimum mean square error(MMSE),
maximum shortening signal to noise ratio (MSSNR) and minimum intersymbol interference
(Min-ISI) equalizers. TEQs with symmetric coefficients can reach the
same performance as non-symmetric ones with much lower training complexity.
Second, I improve Min-ISI design. I reformulate the cost function to make
long TEQs design feasible. I remove the dependency of transmission delay in order
to reduce the complexity associated with delay optimization. The quantized
weighting is introduced to further lower the complexity. I also propose an iterative
optimization procedure of Min-ISI that completely avoids Cholesky decomposition
hence is better suited for a fixed-point implementation.
Finally I propose a dual-path TEQ structure, which designs a standard singleFIR
TEQ to achieve good bit rate over the entire transmission bandwidth, and
designs another FIR TEQ to improve the bit rate over a subset of subcarriers. Dualpath
TEQ can be viewed as a special case of a complex valued filter bank structure
that delivers the best bit rate of existing DMT equalizers. However, dual-path
TEQ provides a very good tradeoff between achievable bit rate vs. implementation
complexity on a programmable digital signal processor.Electrical and Computer Engineerin
Efficient channel equalization algorithms for multicarrier communication systems
Blind adaptive algorithm that updates time-domain equalizer (TEQ) coefficients by Adjacent Lag Auto-correlation Minimization (ALAM) is proposed to shorten the channel for multicarrier modulation (MCM) systems. ALAM is an addition to the family of several existing correlation based algorithms that can achieve similar or better performance to existing algorithms with lower complexity. This is achieved by designing a cost function without the sum-square and utilizing symmetrical-TEQ property to reduce the complexity of adaptation of TEQ to half of the existing one. Furthermore, to avoid the limitations of lower unstable bit rate and high complexity, an adaptive TEQ using equal-taps constraints (ETC) is introduced to maximize the bit rate with the lowest complexity. An IP core is developed for the low-complexity ALAM (LALAM) algorithm to be implemented on an FPGA. This implementation is extended to include the implementation of the moving average (MA) estimate for the ALAM algorithm referred as ALAM-MA. Unit-tap constraint (UTC) is used instead of unit-norm constraint (UNC) while updating the adaptive algorithm to avoid all zero solution for the TEQ taps. The IP core is implemented on Xilinx Vertix II Pro XC2VP7-FF672-5 for ADSL receivers and the gate level simulation guaranteed successful operation at a maximum frequency of 27 MHz and 38 MHz for ALAM-MA and LALAM algorithm, respectively. FEQ equalizer is used, after channel shortening using TEQ, to recover distorted QAM signals due to channel effects. A new analytical learning based framework is proposed to jointly solve equalization and symbol detection problems in orthogonal frequency division multiplexing (OFDM) systems with QAM signals. The framework utilizes extreme learning machine (ELM) to achieve fast training, high performance, and low error rates. The proposed framework performs in real-domain by transforming a complex signal into a single 2–tuple real-valued vector. Such transformation offers equalization in real domain with minimum computational load and high accuracy. Simulation results show that the proposed framework outperforms other learning based equalizers in terms of symbol error rates and training speeds
A novel single lag auto-correlation minimization (SLAM) algorithm for blind adaptive channel shortening
A blind adaptive channel shortening algorithm based on minimizing
the sum of the squared autocorrelations (SAM) of
the effective channel was recently proposed. We submit
that identical channel shortening can be achieved by minimizing
the square of only a single autocorrelation. Our
proposed single lag autocorrelation minimization (SLAM)
algorithm has, therefore, very low complexity and also it
does not require, a priori, the knowledge of the length of the
channel. We also constrain the autocorrelation minimization
with a novel stopping criterion so that the shortening
signal to noise ratio (SSNR) of the effective channel is not
minimized by the autocorrelation minimization. The simulations
have shown that SLAM achieves higher bit rates
than SAM
A blind lag-hopping adaptive channel shortening algorithm based upon squared auto-correlation minimization (LHSAM)
Recent analytical results due to Walsh, Martin and Johnson showed that optimizing the single lag autocorrelation minimization (SLAM) cost does not guarantee convergence to high signal to interference ratio (SIR), an important metric in channel shortening applications. We submit that we can overcome this potential limitation of the SLAM algorithm and retain its computational complexity advantage by minimizing the square of single autocorrelation value with randomly selected lag. Our proposed lag-hopping adaptive channel shortening algorithm based upon squared autocorrelation minimization (LHSAM) has, therefore, low complexity as in the SLAM algorithm and, more importantly, a low average LHSAM cost can guarantee to give a high SIR as for the SAM algorithm. Simulation studies are included to confirm the performance of the LHSAM algorithm
Blind adaptive channel shortening with a generalized lag-hopping algorithm which employs squared auto-correlation minimization [GLHSAM].
A generalized blind lag-hopping adaptive channel shortening
(GLHSAM) algorithm based upon squared auto-correlation
minimization is proposed. This algorithm provides the ability
to select a level of complexity at each iteration between
the sum-squared autocorrelation minimization (SAM) algorithm
due to Martin and Johnson and the single lag autocorrelation
minimization (SLAM) algorithm proposed by Nawaz
and Chambers whilst guaranteeing convergence to high signal
to interference ratio (SIR). At each iteration a number of
unique lags are chosen randomly from the available range so
that on the average GLHSAM has the same cost as the SAM
algorithm. The performance of the proposed GLHSAM algorithm
is confirmed through simulation studies
Random partial update sum-squared autocorrelation minimization algorithm for channel shortening (RPUSAM).
Partial updating is an effective method for
reducing computational complexity in adaptive filter implementations.
In this work, a novel random partial update
sum-squared auto-correlation minimization (RPUSAM)
algorithm is proposed. This algorithm has low computational
complexity whilst achieving improved convergence
performance, in terms of achievable bit rate, over a
partial update sum-squared auto-correlation minimization
(PUSAM) algorithm with a deterministic coefficient update
strategy. The performance advantage of the RPUSAM
algorithm is shown on eight different carrier serving area
test loops (CSA) channels and comparisons are made with
the original SAM and the PUSAM algorithms
A blind channel shortening for multiuser, multicarrier CDMA system over multipath fading channel
In this paper we derive the Multicarrier Equalization by Restoration of Redundancy (MERRY) algorithm: A blind, adaptive channel shortening algorithm for updating a Time-domain Equalizer (TEQ) in a system employing MultiCarrier Code Division Multiple Access (MC-CDMA) modulation. We show that the MERRY algorithm applied to the MC-CDMA system converges considerably more rapidly than in the Orthogonal Frequency Division Multiplexing (OFDM) system [1]. Simulations results are provided to demonstrate the performance of the algorithm
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