Residual Intersymbol Interference Research Articles

Widely linear RLS constant modulus algorithm for complex-valued noncircular signals

Based on the constant modulus criterion, a new Widely Linear (WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.

Comparison between DF-TEQ and LCDF-TEQ in reducing CP length for long-haul direct-detection optical OFDM transmission by computational complexity and system performance

This paper presents the comparison of using Decision Feedback Time-domain Equalizer (DF-TEQ) and Low Complexity DF-TEQ (LCDF-TEQ) to reduce Cyclic Prefix (CP) length for Optical Orthogonal Frequency Division Multiplexing (O-OFDM) transmission over 1200km of Standard Single Mode Fiber (SSMF). Both TEQs are used immediately after the fiber channel. Numerical modeling results show that they can cancel the residual Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) caused by both the Group Velocity Dispersion (GVD) and the CP length being shorter than the Channel Impulse Response (CIR). Using these TEQs allows the reduction in size of CP, and consequently leading to system performance improvement. However, each of these TEQs adds computational complexity to the system. Therefore, the aim of this paper is to compare their performance and their computational complexities while considering different CP length and tap numbers.

Robust Decision Feedback Equalizer for OFDM System under Severe ISI Channel

Inter-symbol interference (ISI) problem is inevitable when the guard interval (GI) is shorter than the delay spread (DS) for an orthogonal frequency division multiplexing (OFDM) system. Iterative techniques have been proposed to overcome such a problem. However, most of existing algorithms are not efficient for an OFDM system with a small GI working under the channel with a large DS. Especially in the case of the DS spans a longer time than the half of the OFDM symbol duration. On the other hand, conventional algorithms, which can reduce the effects of the severe ISI, often employ several impractical assumptions to support the conclusions. In this paper, we present a robust decision feedback equalizer (DFE) for the OFDM system to overcome the severe ISI problem. The proposed DFE removes the ISI in a same manner as the residual inter-symbol interference cancellation (RISIC) algorithm. However, the inter-carrier interference (ICI) is reduced via cyclicity removal instead of the cyclicity restoration used in the conventional algorithms. The link-level simulation (LLS) results indicate that our proposed DFE scheme can dramatically improve the BER performance when the DS spans longer than the half of ODFM symbol duration.

Symbol Error Rate for Nonblind Adaptive Equalizers Applicable for the SIMO and FGn Case

A nonzero residual intersymbol interference (ISI) causes the symbol error rate (SER) to increase where the achievable SER may not answer any more on the system’s requirements. Recently, a closed-form approximated expression was derived by the same author for the residual ISI obtained by nonblind adaptive equalizers for the single-input single-output (SISO) case. Up to now, there does not exist a closed-form expression for the residual ISI obtained by nonblind adaptive equalizers for the single-input multiple-output (SIMO) case. Furthermore, there does not exist a closed-form expression for the SER valid for the SISO or SIMO case that takes into account the residual ISI obtained by nonblind adaptive equalizers and is valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of0.5≤H<1. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by nonblind adaptive equalizers for the SIMO case (where SISO is a special case of SIMO), valid for fGn input where the Hurst exponent is in the region of0.5≤H<1. Based on this new expression for the residual ISI, a closed-form approximated expression is obtained for the SER valid for the SIMO and fGn case.

An Approximated Expression for the Residual ISI Obtained by Blind Adaptive Equalizer and Biased Input Signals

Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. However, those expressions are not applicable for biased input signals. In this paper, a closed-form approximated expression is proposed for the residual ISI applicable for the noisy and biased input case. This new proposed expression is valid for blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. The new proposed expression depends on the equalizer’s tap length, input signal statistics, channel power, SNR, step-size parameter and on the input signal’s bias. Simulation results indicate a high correlation between the simulated results and those obtained from our new proposed expression.

Time-reversal-based underwater acoustic communication

Time reversal (TR) exploits spatial diversity to achieve spatial and temporal focusing in complex environments. Over the last decade its concept has been applied successfully to underwater acoustic communications in time-varying multipath environments with robustness and computational simplicity, as an alternative to conventional adaptive multichannel equalization. Temporal focusing (pulse compression) mitigates the intersymbol interference (ISI) and subsequent channel equalization removes the residual ISI, thus providing nearly optimal performance in theory. The spatial focusing capability facilitates multi-user communications without an explicit use of time, frequency, or code division, while an adaptive time reversal approach can further reduce the crosstalk among users. TR communications can be easily extended to time-varying channels using a block-based approach with periodic channel updates. This talk will present an overview of TR communications and recent advances including bidirectional equalization, single- versus multi-carrier approach, and communications with autonomous vehicles such as an AUV or Glider.

Using RLS-TEQ to reduce CP length for 20.48 Gb/s direct-detection optical OFDM transmission over 2400 km of SSMF

This paper uses a Recursive Least Squares-Time Domain Equalizer (RLS-TEQ) to reduce the Cyclic Prefix (CP) length in Direct-Detection Optical Orthogonal Frequency Division Multiplexing (O-OFDM) transmission over 2400km of Standard Single Mode Fiber (SSMF). The RLS-TEQ can cancel the residual Inter Symbol Interference (ISI) caused by both the Group Velocity Dispersion (GVD) and the CP length being shorter than the Channel Impulse Response (CIR). Using RLS-TEQ reduces size of the CP, and consequently leading to system performance improvement.

Design and Implementation of a Low-Complexity Symbol Detector for Sparse Channels

In this paper, we present a low-complexity symbol detector for communication channels which have long spanning durations but a sparse multipath structure. Traditional maximum-likelihood sequence estimation using the Viterbi algorithm can provide optimal error performance for eliminating the multipath effect, but the hardware complexity grows exponentially with channel length and it is not practical for long sparse channels. We implement a near-optimal algorithm and its architecture by cascading an adaptive partial response equalizer (PRE) with an iterative belief propagation (BP) detector. A sparse channel is first equalized by a PRE to a target impulse response (TIR) with only a few nonzero coefficients remaining. The residual intersymbol interference is then canceled by a BP detector whose complexity is solely dependent on the number of nonzero coefficients in the TIR. Moreover, we present a pipeline high-throughput implementation of the detector for channel length 30 with quadrature phase-shift keying modulation. The detector can achieve a maximum throughput of 206 Mb/s with an estimated core area of 3.162 mm2 using 90-nm technology node. At a target frequency of 515 MHz, the dynamic power is about 1.096 W.

Phase compensation communication technique against time reversal for ultra‐wideband channels

Phase compensation (PC) prefiltering is experimentally investigated for multipath channels over the frequency band spanning 2–12 GHz, a topic which to the best of the authors knowledge has not been studied in the literature on ultra-wideband (UWB) communications. The authors emphasis is to assess the capabilities of PC compared to time reversal (TR) prefilters over indoor UWB channels regarding multipath suppression, channel hardening, noise sensitivity and high-speed data transmission. Experiments were carried out for PC and TR prefilters in both line-of-sight (LOS) and non-LOS (NLOS) environments. The multipath compression effectiveness is characterised by computing the root-mean-square delay spread and peak-to-average power ratio for actual measured channels and for the IEEE 802.15.4(a) UWB model. The authors study suggests PC outperforms TR considerably in mitigating the multipath channel dispersion. Bit-error-rate (BER) curves have been simulated for data rates in the range of 125–4000 Mbps based on the measured channel responses. The BER simulations suggest that while the TR performance is prohibitively saturated by its residual intersymbol interference for data rates of 500 Mbps and above (especially in NLOS), PC can be used for high-speed data transmissions as fast as 2 Gbps in both LOS and NLOS environments.

Using NLMS-TEQ to reduce CP length for 20.48 Gb/s direct-detection optical OFDM transmission over 2400 km of SSMF

A Normalized Least Mean Squares-Time Domain Equalizer (NMLS-TEQ) is used to reduce the cyclic prefix (CP) length in direct-detection optical orthogonal frequency division multiplexing (O-OFDM) transmission over 2400km of Standard Single Mode Fiber (SSMF). The aim of using NLMS-TEQ is to solve the problem of choosing the gain of Least Mean Square (LMS) algorithm to make it stable since LMS algorithm is sensitive to the scaling of its input. The NMLS-TEQ can cancel the residual Inter Symbol Interference (ISI) caused by both the Group Velocity Dispersion (GVD) and the CP length being shorter than the Channel Impulse Response (CIR). Using NLMS-TEQ reduces size of the CP, and consequently leading to system performance improvement.

Residual ISI Obtained by Nonblind Adaptive Equalizers and Fractional Noise

Recently, a closed-form approximated expression was derived by the same author for the achievable residual intersymbol interference (ISI) case that depends on the step-size parameter, equalizer's tap length, input signal statistics, signal to noise ratio (SNR), and channel power and is valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of . But this expression was obtained for the blind adaptive case and cannot be applied to the nonblind adaptive version. Up to now, the achievable residual ISI for the non-blind adaptive case could be obtained only via simulation. In this paper, we derive a closed-form approximated expression (or an upper limit) for the residual ISI obtained by non-blind adaptive equalizers valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of . This new obtained expression depends on the step-size parameter, equalizer's tap length, input signal statistics, SNR, channel power, and the Hurst exponent parameter. Simulation results indicate that there is a high correlation between the calculated results (obtained from the new obtained expression for the residual ISI) and those obtained from simulating the system.

Residual ISI Obtained by Blind Adaptive Equalizers and Fractional Noise

Recently, a closed-form approximated expression was derived by the same author for the achievable residual intersymbol interference (ISI) case that depends on the step-size parameter, equalizer’s tap length, input signal statistics, signal-to-noise ratio (SNR), and channel power. But this expression was obtained by assuming that the input noise is a white Gaussian process where the Hurst exponent (H) is equal to 0.5. In this paper, we derive a closed-form approximated expression (or an upper limit) for the residual ISI obtained by blind adaptive equalizers valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of0.5≤H<1. Up to now, the statistical behaviour of the residual ISI was not investigated. Furthermore, the convolutional noise for the latter stages of the deconvolutional process was assumed to be a white Gaussian process (H=0.5). In this paper, we show that the Hurst exponent of the residual ISI is close to one, almost independent of the SNR or equalizer’s tap length but depends on the step-size parameter. In addition, the convolutional noise obtained in the steady state is a noise process having a Hurst exponent depending on the step-size parameter.

Symbol Error Rate as a Function of the Residual ISI Obtained by Blind Adaptive Equalizers for the SIMO and Fractional Gaussian Noise Case

A nonzero residual intersymbol interference (ISI) causes the symbol error rate (SER) to increase where the achievable SER may not answer any more on the system&#x2019;s requirements. In the literature, we may find for the single-input-single-output (SISO) case a closed-form approximated expression for the SER that takes into account the achievable performance of the chosen blind adaptive equalizer from the residual ISI point of view and a closed-form approximated expression for the residual ISI valid for the single-input-multiple-output (SIMO) case. Both expressions were obtained by assuming that the input noise is a white Gaussian process where the Hurst exponent (<i>H</i>) is equal to 0.5. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by blind adaptive equalizers for the SIMO case, valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of <svg style="vertical-align:-0.546pt;width:82.224998px;" id="M1" height="11.85" version="1.1" viewBox="0 0 82.224998 11.85" width="82.224998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g><g transform="matrix(.017,-0,0,-.017,8.222,11.113)"><path id="x2E" d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" /></g><g transform="matrix(.017,-0,0,-.017,12.098,11.113)"><path id="x35" d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8&#xA;l-26 -65h-233z" /></g><g transform="matrix(.017,-0,0,-.017,24.966,11.113)"><path id="x2264" d="M531 71l-474 214v50l474 215v-56l-416 -184l416 -183v-56zM531 -40h-474v50h474v-50z" /></g><g transform="matrix(.017,-0,0,-.017,39.67,11.113)"><path id="x1D43B" d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28&#xA;h263l-6 -28q-58 -5 -75.5 -21t-30.5 -81l-26 -153h377l29 153q12 67 2 81t-74 21l5 28h268z" /></g><g transform="matrix(.017,-0,0,-.017,59.303,11.113)"><path id="x3C" d="M512 -3l-437 233v51l437 233v-58l-378 -200v-2l378 -199v-58z" /></g><g transform="matrix(.017,-0,0,-.017,74.007,11.113)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g> </svg>. Based on this new expression for the residual ISI, a closed-form approximated expression is obtained for the SER valid for the SIMO and fGn case. In this paper, we show via simulation results that the SER might get improved for increasing values of <i >H</i>.

Two Blind Adaptive Equalizers Connected in Series for Equalization Performance Improvement

A variable step-size parameter is usually used to accelerate the convergence speed of a blind adaptive equalizer with N1 + N2 －1 coefficients where N1 and N2 are odd values. In this paper we show that improved equalization performance is achieved when using two blind adaptive equalizers connected in series where the first and second blind adaptive equalizer have N1 and N2 coefficients respectively compared with the case where a single blind adaptive equalizer is applied with N1 + N2 －1 coefficients. It should be pointed out that the same algorithm (cost function) is used for updating the filter taps for the different equalizers and that a fixed step-size parameter is used. Simulation results show that for the low signal to noise ratio (SNR) environment and for the case where the convergence speed is slow due to the channel characteristics, the new method has a faster convergence speed with a factor of approximately two while leaving the system with approximately the same or lower residual intersymbol interference (ISI).

Application of 3GPP LTE and IEEE 802.11p Systems to Ship Ad-Hoc Network with the Existence of ISI

In order to provide high data rate and real time services under maritime environment, link-level performance of ship ad-hoc network (SANET) based on 3GPP LTE and IEEE 802.11p (WAVE) specifications are investigated and discussed in this paper. The measured maritime channel, whose delay spread is longer than the length of guard interval (GI) of both 3GPP LTE and IEEE 802.11p specifications, is adopted for the link-level simulations. For the purpose of eliminating inter-symbol interference (ISI) due to insufficient GI length, double antenna pattern (DAP) scheme and advanced time-domain decision-feedback equalizer (DFE) are proposed for LTE and WAVE systems, respectively. The proposed DFE removes the ISI in a same manner as the residual inter-symbol interference cancellation (RISIC) algorithm, but the inter-carrier interference (ICI) is reduced via cyclicity removal instead of cyclicity restoration used in the RISIC algorithm. Compared with existing schemes, our proposed DFE is a robust technique to overcome the severe ISI channel which has a comparatively large delay spread. Based on simulation results, not only comparisons between systems are discussed, but also some reformative suggestions are given.

Single channel and WDM transmission of 28 Gbaud zero-guard-interval CO-OFDM

We report on the experimental demonstration of single channel 28 Gbaud QPSK and 16-QAM zero-guard-interval (ZGI) CO-OFDM transmission with only 1.34% overhead for OFDM processing. The achieved transmission distance is 5120 km for QPSK assuming a 7% forward error correction (FEC) overhead, and 1280 km for 16-QAM assuming a 20% FEC overhead. We also demonstrate the improved tolerance of ZGI CO-OFDM to residual inter-symbol interference compared to reduced-guard-interval (RGI) CO-OFDM. In addition, we report an 8-channel wavelength-division multiplexing (WDM) transmission of 28 Gbaud QPSK ZGI CO-OFDM signals over 4160 km.

Ultrafast and low overhead training symbol based channel estimation in coherent M-QAM single-carrier transmission systems

We propose a training symbol based channel estimation (TS-EST) algorithm that estimates the 2 × 2 Jones channel matrix. The estimated matrix entries are then used as the initial center taps of the 2 × 2 butterfly equalizer. Employing very few training symbols for TS-EST, ultrafast polarization tracking is achieved and tap update can be initially pursued using the decision-directed least mean squares (DD-LMS) algorithm to mitigate residual intersymbol interference (ISI). We experimentally verify the proposed TS-EST algorithm for 112 Gbps PDM-QPSK and 224 Gbps PDM-16QAM systems using 10 and 40 training symbols for TS-EST, respectively. Steady-state and transient bit error rates (BERs) achieved using the TS-EST algorithm are compared to those obtained using the constant modulus algorithm (CMA) and the training symbol least mean squares (TS-LMS) algorithm and results show that the proposed TS-EST algorithm provides the same steady-state BER with a superior convergence speed. Also, the tolerance of the proposed TS-EST algorithm to laser phase noise and fiber nonlinearity is experimentally verified. Finally, we show by simulation that the superior tracking speed of the TS-EST algorithm allows not only for initial polarization tracking but also for tracking fast polarization transients if four training symbols are periodically sent during steady-state operation with an overhead as low as 0.57%.

16-QAM 신호에 대한 이중 구조 CR-CMA 적응 등화기의 성능

In this paper, the concerned existing blind equalizer convergence rate and residual inter-symbol interference using constellation reduced and cost function by separation the real part and an imaginary part, the dual structure CR-CMA(constellation Reduction CMA). The CMA methed compensates amplitude but does no compensate phase, On the other hand, The CMA method compensates both the amplitude and the phase but it has the convergence rate problem, and the MCMA method is a way to solve the phase problem of CMA method compensates both the amplitude and the phase after respectively calculating the real part and imaginary part components. Proposal a new method that the dual structure of CR-CMA, the cost function and error function and respectively calculating the real part and imaginary part components can advantages by improving the CMA and the MCMA algorithms so that the amplitude and phase retrieval and constellation reduce the residual ISI and faster convergence rate and performance is good SER (Symbol Error Ratio) was confirmed by computer simulations.

LTE uplink MIMO receiver with low complexity interference cancellation

In LTE/LTE-A uplink receiver, frequency domain equalizers (FDE) are adopted to achieve good performance. However, in multi-tap channels, the residual inter-symbol and inter-antenna interference still exist after FDE and degrade the performance. Conventional interference cancellation schemes can minimize this interference by using frequency domain interference cancellation. However, those schemes have high complexity and large feedback latency, especially when adopting a large number of iterations. These result in low throughput and require a large amount of resource in software defined radio implementation. In this paper, we propose a novel low complexity interference cancellation scheme to minimize the residual interference in LTE/LTE-A uplink. Our proposed scheme can bring about 2 dB gains in different channels, but only adds up to 7.2 % complexity to the receiver. The scheme is further implemented on Xilinx FPGA. Compared to other conventional interference cancellation schemes, our scheme has less complexity, less data to store, and shorter feedback latency.

Performance analysis of the bit-interleaved coded modulation using turbo equalization with single carrier frequency domain equalization over fast fading channels

The performance of the bit-interleaved coded modulation using turbo equalization with single carrier frequency domain equalization (BICM TE-SC-FDE) over frequency-selective fading channels with the residual inter-symbol interference (ISI) is investigated. We focus on the impact of the residual ISI on the convergence behavior using the extrinsic information transfer (EXIT) chart. We first exhibit that the residual ISI impacts not only the error floor but also the convergence behavior of the BICM TE-SC-FDE. Then, we show that the Gaussian assumption of the soft information within the TE-SC-FDE, with or without the residual ISI, can accurately track the flow of the extrinsic information in the iterative procedure. We exhibit through simulation the accuracy of the EXIT chart in predicting the transfer function of the equalizer. We show that the product of the transmit block length and Doppler spread is a key parameter affecting the convergence behavior of the TE-SC-FDE with the residual ISI. The accuracy of our EXIT chart prediction is verified by simulation.