Near-Instantaneously Adaptive HSDPA-Style OFDM Versus MC-CDMA Transceivers for WIFI, WIMAX, and Next-Generation Cellular Systems

Burts-by-burst (BbB) adaptive high-speed downlink packet access (HSDPA) style multicarrier systems are reviewed, identifying their most critical design aspects. These systems exhibit numerous attractive features, rendering them eminently eligible for employment in next-generation wireless systems. It is argued that BbB-adaptive or symbol-by-symbol adaptive orthogonal frequency division multiplex (OFDM) modems counteract the near instantaneous channel quality variations and hence attain an increased throughput or robustness in comparison to their fixed-mode counterparts. Although they act quite differently, various diversity techniques, such as Rake receivers and space-time block coding (STBC) are also capable of mitigating the channel quality variations in their effort to reduce the bit error ratio (BER), provided that the individual antenna elements experience independent fading. By contrast, in the presence of correlated fading imposed by shadowing or time-variant multiuser interference, the benefits of space-time coding erode and it is unrealistic to expect that a fixed-mode space-time coded system remains capable of maintaining a near-constant BER

Multicarrier communication systems with low sensibility to nonlinear amplification

Actualment estem entrant a una nova era de la informació amb gran demanda de sistemes de comunicació sense fils. Nous serveis com dades i video requereixen transmissions fiables d'alta velocitat, fins i tot en escenaris d'alta mobilitat. A més a més, la dificultat d'assignar el limitat espectre radioelèctric juntament amb la necessitat d'incrementar el temps de vida de les bateries dels terminals mòbils, requereix el diseny de transceptors que usin la potència i l'ampla de banda disponibles de manera eficient. Les comunicacions multiportadora basades en OFDM són capaces de satisfer la majoria d'aquests requeriments. Però, entre altres reptes, reduir la sensibilitat a la amplificació no-lineal és un factor clau durant el diseny. En aquesta tesi doctoral s'analitza la sensibilitat dels sistemes multiportadora basats en OFDM a l'amplificació no-lineal i es consideren formes eficients per superar aquest problema. La tesi s'enfoca principalment al problema de reduir les fluctuacions de l'envolupant del senyal transmès. En aquest sentit es presenta també un estudi de les mètriques de l'envolupant del senyal, PAPR i CM. A més a més, basant-nos en l'anàlisis presentat es proposen noves tècniques per sistemes OFDM i MC-SS. Per MC-SS, també es tracta el diseny d'una tècnica de postprocessament en forma de detector multiusuari per canals no-lineals.Actualmente estamos entrando en una nueva era de la información donde se da una gran demanda de sistemas de comunicación inalámbricos. Nuevos servicios como datos y vídeo requieren transmisiones fiables de alta velocidad, incluso en escenarios de alta movilidad. Además, la dificultad de asignar el limitado espectro radioeléctrico junto con la necesidad de incrementar el tiempo de vida de las baterías de los terminales móviles, requiere el diseño de transceptores que usen eficientemente la potencia y el ancho de banda disponibles. Las comunicaciones multiportadora basadas en OFDM son capaces de satisfacer la mayoría de dichos requerimientos. Sin embargo, entre otros retos, reducir su sensibilidad a la amplificación no-lineal es un factor clave durante el diseño. En esta tesis se analiza la sensibilidad de los sistemas multiportadora basados en OFDM a la amplificación no-lineal y se consideran formas eficientes para superar dicho problema. La tesis se enfoca principalmente al problema de reducir las fluctuaciones de la envolvente. En este sentido también se presenta un estudio de las métricas de la señal, PAPR y CM. Además, basándonos en el análisis presentado se proponen nuevas técnicas para OFDM y MC-SS. Para MC-SS, también se trata el diseño de un detector multiusuario para canales no-lineales.We are now facing a new information age with high demand of wireless communication systems. New services such as data and video require achieving reliable high-speed transmissions even in high mobility scenarios. Moreover, the difficulty to allocate so many wireless communication systems in the limited frequency band in addition to the demand for long battery life requires designing spectrum and power efficient transceivers. Multicarrier communications based on OFDM are known to fulfill most of the requirements of such systems. However, among other challenges, reducing the sensitivity to nonlinear amplification has become a design key. In this thesis the sensitivity of OFDM-based multicarrier systems to nonlinear amplification is analyzed and efficient ways to overcome this problem are considered. The focus is mainly on the problem of reducing the envelope fluctuations. Therefore, a study of the signal metrics, namely PAPR and CM, is also presented. From the presented analysis, several new techniques for OFDM and MC-SS are proposed. For MC-SS, the design of a post-processing technique in the form of a multiuser detector for nonlinearly distorted MC-SS symbols is also addressed

High Capacity CDMA and Collaborative Techniques

The thesis investigates new approaches to increase the user capacity and improve the error performance of Code Division Multiple Access (CDMA) by employing adaptive interference cancellation and collaborative spreading and space diversity techniques. Collaborative Coding Multiple Access (CCMA) is also investigated as a separate technique and combined with CDMA. The advantages and shortcomings of CDMA and CCMA are analysed and new techniques for both the uplink and downlink are proposed and evaluated. Multiple access interference (MAI) problem in the uplink of CDMA is investigated first. The practical issues of multiuser detection (MUD) techniques are reviewed and a novel blind adaptive approach to interference cancellation (IC) is proposed. It exploits the constant modulus (CM) property of digital signals to blindly suppress interference during the despreading process and obtain amplitude estimation with minimum mean squared error for use in cancellation stages. Two new blind adaptive receiver designs employing successive and parallel interference cancellation architectures using the CM algorithm (CMA) referred to as ‘CMA-SIC’ and ‘BA-PIC’, respectively, are presented. These techniques have shown to offer near single user performance for large number of users. It is shown to increase the user capacity by approximately two fold compared with conventional IC receivers. The spectral efficiency analysis of the techniques based on output signal-to interference-and-noise ratio (SINR) also shows significant gain in data rate. Furthermore, an effective and low complexity blind adaptive subcarrier combining (BASC) technique using a simple gradient descent based algorithm is proposed for Multicarrier-CDMA. It suppresses MAI without any knowledge of channel amplitudes and allows large number of users compared with equal gain and maximum ratio combining techniques normally used in practice. New user collaborative schemes are proposed and analysed theoretically and by simulations in different channel conditions to achieve spatial diversity for uplink of CCMA and CDMA. First, a simple transmitter diversity and its equivalent user collaborative diversity techniques for CCMA are designed and analysed. Next, a new user collaborative scheme with successive interference cancellation for uplink of CDMA referred to as collaborative SIC (C-SIC) is investigated to reduce MAI and achieve improved diversity. To further improve the performance of C-SIC under high system loading conditions, Collaborative Blind Adaptive SIC (C-BASIC) scheme is proposed. It is shown to minimize the residual MAI, leading to improved user capacity and a more robust system. It is known that collaborative diversity schemes incur loss in throughput due to the need of orthogonal time/frequency slots for relaying source’s data. To address this problem, finally a novel near-unity-rate scheme also referred to as bandwidth efficient collaborative diversity (BECD) is proposed and evaluated for CDMA. Under this scheme, pairs of users share a single spreading sequence to exchange and forward their data employing a simple superposition or space-time encoding methods. At the receiver collaborative joint detection is performed to separate each paired users’ data. It is shown that the scheme can achieve full diversity gain at no extra bandwidth as inter-user channel SNR becomes high. A novel approach of ‘User Collaboration’ is introduced to increase the user capacity of CDMA for both the downlink and uplink. First, collaborative group spreading technique for the downlink of overloaded CDMA system is introduced. It allows the sharing of the same single spreading sequence for more than one user belonging to the same group. This technique is referred to as Collaborative Spreading CDMA downlink (CS-CDMA-DL). In this technique T-user collaborative coding is used for each group to form a composite codeword signal of the users and then a single orthogonal sequence is used for the group. At each user’s receiver, decoding of composite codeword is carried out to extract the user’s own information while maintaining a high SINR performance. To improve the bit error performance of CS-CDMA-DL in Rayleigh fading conditions, Collaborative Space-time Spreading (C-STS) technique is proposed by combining the collaborative coding multiple access and space-time coding principles. A new scheme for uplink of CDMA using the ‘User Collaboration’ approach, referred to as CS-CDMA-UL is presented next. When users’ channels are independent (uncorrelated), significantly higher user capacity can be achieved by grouping multiple users to share the same spreading sequence and performing MUD on per group basis followed by a low complexity ML decoding at the receiver. This approach has shown to support much higher number of users than the available sequences while also maintaining the low receiver complexity. For improved performance under highly correlated channel conditions, T-user collaborative coding is also investigated within the CS-CDMA-UL system

Wavelet-based multi-carrier code division multiple access systems

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Esquemas de pré-codificação IA com IB-DFE para sistemas MC-CDMA

Mestrado em Engenharia Eletrónica e TelecomunicaçõesTo achieve high bit rates, needed to meet the quality of service requirements of future multimedia applications, multi-carrier code division multiple access (MC-CDMA) has been considered as a candidate air-interface. Interference alignment (IA) is a promising technique that allows high capacity gains in interfering channels. On the other hand, iterative block decision feedback equalization (IB-DFE) based receivers can efficiently exploit the inherent space-frequency diversity of the MIMO MC-CDMA systems. In this thesis we proposed an IA precoding at the transmitter with IB-DFE based processing at the receiver for MC-CDMA systems. The IA precoding is applied at chip level instead of the data symbols level, as in the conventional IA based systems. The receiver is designed in two steps: first the equalizers based on zero forcing (ZF) or minimum mean square error (MMSE) are used to remove the aligned users´ interference. Then and after a whitening noise process, an IB-DFE based equalizer is designed to remove both the residual inter-user aligned and inter-carrier interferences. The results have shown that the obtained performance is very close to the one obtained by the optimal matched filter, with few iterations at the receiver side.Para atingir maiores ritmos de transmissão, as futures aplicações multimédia necessitam de atingir a qualidade de serviço necessária. Para isso, o multi-carrier code division multiple access (MC-CDMA) tem sido apontado como um forte candidato para interface ar dos futuros sistemas celulares. O Interference Alignment (IA) ou alinhamento de interferência é uma técnica promissora que permite ter altos ganhos de capacidade em canais com interferência. Por outro lado, temos receptores baseados no conceito iterative block decision feedback equalization(IB-DFE) que conseguem tirar partido, de uma forma eficiente, da inerente diversidade espaço-frequência dos sistemas MIMO MC-CDMA. Nesta dissertação é implementada uma pré-codificação baseada no conceito de IA considerando três transmissores (ou estações base) juntamente, com um processamento IB-DFE no receptor para sistemas MC-CDMA.A pré-codificação é aplicada ao nível de chip em vez de ser aplicado ao nível dos dados. O receptor é projectado em dois passos: em primeiro lugar equalizadores baseados em ZF ou em MMSE são utilizados para remover a interferência alinhada dos restantes utilizadores. De seguida, e após aplicar um processo de branqueamento do ruído ao sinal à saída do primeiro equalizador, um segundo equalizador baseado em IB-DFE é projectado para remover a interferência inter-utilizador residual e também a interferência residual entre portadoras. Os resultados obtidos mostraram-se satisfatórios na remoção da interferência obtendo-se um desempenho muito próximo do obtido considerando um filtro adaptado

Capacity, coding and interference cancellation in multiuser multicarrier wireless communications systems

Multicarrier modulation and multiuser systems have generated a great deal of research during the last decade. Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation generated with the inverse Discrete Fourier Transform, which has been adopted for standards in wireless and wire-line communications. Multiuser wireless systems using multicarrier modulation suffer from the effects of dispersive fading channels, which create multi-access, inter-symbol, and inter-carrier interference (MAI, ISI, ICI). Nevertheless, channel dispersion also provides diversity, which can be exploited and has the potential to increase robustness against fading. Multiuser multi-carrier systems can be implemented using Orthogonal Frequency Division Multiple Access (OFDMA), a flexible orthogonal multiplexing scheme that can implement time and frequency division multiplexing, and using multicarrier code division multiple access (MC-CDMA). Coding, interference cancellation, and resource sharing schemes to improve the performance of multiuser multicarrier systems on wireless channels were addressed in this dissertation. Performance of multiple access schemes applied to a downlink multiuser wireless system was studied from an information theory perspective and from a more practical perspective. For time, frequency, and code division, implemented using OFDMA and MC-CDMA, the system outage capacity region was calculated for a correlated fading channel. It was found that receiver complexity determines which scheme offers larger capacity regions, and that OFDMA results in a better compromise between complexity and performance than MC-CDMA. From the more practical perspective of bit error rate, the effects of channel coding and interleaving were investigated. Results in terms of coding bounds as well as simulation were obtained, showing that OFDMAbased orthogonal multiple access schemes are more sensitive to the effectiveness of the code to provide diversity than non-orthogonal, MC-CDMA-based schemes. While cellular multiuser schemes suffer mainly from MAI, OFDM-based broadcasting systems suffer from ICI, in particular when operating as a single frequency network (SFN). It was found that for SFN the performance of a conventional OFDM receiver rapidly degrades when transmitters have frequency synchronization errors. Several methods based on linear and decision-feedback ICI cancellation were proposed and evaluated, showing improved robustness against ICI. System function characterization of time-variant dispersive channels is important for understanding their effects on single carrier and multicarrier modulation. Using time-frequency duality it was shown that MC-CDMA and DS-CDMA are strictly dual on dispersive channels. This property was used to derive optimal matched filter structures, and to determine a criterion for the selection of spreading sequences for both DS and MC CDMA. The analysis of multiple antenna systems provided a unified framework for the study of DS-CDMA and MC-CDMA on time and frequency dispersive channels, which can also be used to compare their performance

Adaptive Communications for Next Generation Broadband Wireless Access Systems

Un dels aspectes claus en el disseny i gestió de les xarxes sense fils d'accés de banda ampla és l'ús eficient dels recursos radio. Des del punt de vista de l'operador, l'ample de banda és un bé escàs i preuat que s´ha d'explotar i gestionar de la forma més eficient possible tot garantint la qualitat del servei que es vol proporcionar. Per altra banda, des del punt de vista del usuari, la qualitat del servei ofert ha de ser comparable al de les xarxes fixes, requerint així un baix retard i una baixa pèrdua de paquets per cadascun dels fluxos de dades entre la xarxa i l'usuari. Durant els darrers anys s´han desenvolupat nombroses tècniques i algoritmes amb l'objectiu d'incrementar l'eficiència espectral. Entre aquestes tècniques destaca l'ús de múltiples antenes al transmissor i al receptor amb l'objectiu de transmetre diferents fluxos de dades simultaneament sense necessitat d'augmentar l'ample de banda. Per altra banda, la optimizació conjunta de la capa d'accés al medi i la capa física (fent ús de l'estat del canal per tal de gestionar de manera optima els recursos) també permet incrementar sensiblement l'eficiència espectral del sistema.L'objectiu d'aquesta tesi és l'estudi i desenvolupament de noves tècniques d'adaptació de l'enllaç i gestió dels recursos ràdio aplicades sobre sistemes d'accés ràdio de propera generació (Beyond 3G). Els estudis realitzats parteixen de la premissa que el transmisor coneix (parcialment) l'estat del canal i que la transmissió es realitza fent servir un esquema multiportadora amb múltiples antenes al transmisor i al receptor. En aquesta tesi es presenten dues línies d'investigació, la primera per casos d'una sola antenna a cada banda de l'enllaç, i la segona en cas de múltiples antenes. En el cas d'una sola antena al transmissor i al receptor, un nou esquema d'assignació de recursos ràdio i priorització dels paquets (scheduling) és proposat i analitzat integrant totes dues funcions sobre una mateixa entitat (cross-layer). L'esquema proposat té com a principal característica la seva baixa complexitat i que permet operar amb transmissions multimedia. Alhora, posteriors millores realitzades per l'autor sobre l'esquema proposat han permès també reduir els requeriments de senyalització i combinar de forma óptima usuaris d'alta i baixa mobilitat sobre el mateix accés ràdio, millorant encara més l'eficiència espectral del sistema. En cas d'enllaços amb múltiples antenes es proposa un nou esquema que combina la selecció del conjunt optim d'antenes transmissores amb la selecció de la codificació espai- (frequència-) temps. Finalment es donen una sèrie de recomanacions per tal de combinar totes dues línies d'investigació, així con un estat de l'art de les tècniques proposades per altres autors que combinen en part la gestió dels recursos ràdio i els esquemes de transmissió amb múltiples antenes.Uno de los aspectos claves en el diseño y gestión de las redes inalámbricas de banda ancha es el uso eficiente de los recursos radio. Desde el punto de vista del operador, el ancho de banda es un bien escaso y valioso que se debe explotar y gestionar de la forma más eficiente posible sin afectar a la calidad del servicio ofrecido. Por otro lado, desde el punto de vista del usuario, la calidad del servicio ha de ser comparable al ofrecido por las redes fijas, requiriendo así un bajo retardo y una baja tasa de perdida de paquetes para cada uno de los flujos de datos entre la red y el usuario. Durante los últimos años el número de técnicas y algoritmos que tratan de incrementar la eficiencia espectral en dichas redes es bastante amplio. Entre estas técnicas destaca el uso de múltiples antenas en el transmisor y en el receptor con el objetivo de poder transmitir simultáneamente diferentes flujos de datos sin necesidad de incrementar el ancho de banda. Por otro lado, la optimización conjunta de la capa de acceso al medio y la capa física (utilizando información de estado del canal para gestionar de manera óptima los recursos) también permite incrementar sensiblemente la eficiencia espectral del sistema.El objetivo de esta tesis es el estudio y desarrollo de nuevas técnicas de adaptación del enlace y la gestión de los recursos radio, y su posterior aplicación sobre los sistemas de acceso radio de próxima generación (Beyond 3G). Los estudios realizados parten de la premisa de que el transmisor conoce (parcialmente) el estado del canal a la vez que se considera que la transmisión se realiza sobre un sistema de transmisión multiportadora con múltiple antenas en el transmisor y el receptor. La tesis se centra sobre dos líneas de investigación, la primera para casos de una única antena en cada lado del enlace, y la segunda en caso de múltiples antenas en cada lado. Para el caso de una única antena en el transmisor y en el receptor, se ha desarrollado un nuevo esquema de asignación de los recursos radio así como de priorización de los paquetes de datos (scheduling) integrando ambas funciones sobre una misma entidad (cross-layer). El esquema propuesto tiene como principal característica su bajo coste computacional a la vez que se puede aplicar en caso de transmisiones multimedia. Posteriores mejoras realizadas por el autor sobre el esquema propuesto han permitido también reducir los requisitos de señalización así como combinar de forma óptima usuarios de alta y baja movilidad. Por otro lado, en caso de enlaces con múltiples antenas en transmisión y recepción, se presenta un nuevo esquema de adaptación en el cual se combina la selección de la(s) antena(s) transmisora(s) con la selección del esquema de codificación espacio-(frecuencia-) tiempo. Para finalizar, se dan una serie de recomendaciones con el objetivo de combinar ambas líneas de investigación, así como un estado del arte de las técnicas propuestas por otros autores que combinan en parte la gestión de los recursos radio y los esquemas de transmisión con múltiples antenas.In Broadband Wireless Access systems the efficient use of the resources is crucial from many points of views. From the operator point of view, the bandwidth is a scarce, valuable, and expensive resource which must be exploited in an efficient manner while the Quality of Service (QoS) provided to the users is guaranteed. On the other hand, a tight delay and link quality constraints are imposed on each data flow hence the user experiences the same quality as in fixed networks. During the last few years many techniques have been developed in order to increase the spectral efficiency and the throughput. Among them, the use of multiple antennas at the transmitter and the receiver (exploiting spatial multiplexing) with the joint optimization of the medium access control layer and the physical layer parameters.In this Ph.D. thesis, different adaptive techniques for B3G multicarrier wireless systems are developed and proposed focusing on the SS-MC-MA and the OFDM(A) (IEEE 802.16a/e/m standards) communication schemes. The research lines emphasize into the adaptation of the transmission having (Partial) knowledge of the Channel State Information for both; single antenna and multiple antenna links. For single antenna links, the implementation of a joint resource allocation and scheduling strategy by including adaptive modulation and coding is investigated. A low complexity resource allocation and scheduling algorithm is proposed with the objective to cope with real- and/or non-real- time requirements and constraints. A special attention is also devoted in reducing the required signalling. However, for multiple antenna links, the performance of a proposed adaptive transmit antenna selection scheme jointly with space-time block coding selection is investigated and compared with conventional structures. In this research line, mainly two optimizations criteria are proposed for spatial link adaptation, one based on the minimum error rate for fixed throughput, and the second focused on the maximisation of the rate for fixed error rate. Finally, some indications are given on how to include the spatial adaptation into the investigated and proposed resource allocation and scheduling process developed for single antenna transmission

Combination of OFDM and CDMA for high data rate UWB

For Wireless Personal Area Network (WPAN) systems, resource allocation between several users within a piconet and the coexistence of several piconets are very important points to take into consideration for the optimization of high data rate Ultra Wide Band (UWB) systems. To improve the performance of the Multi-Band OFDM (Orthogonal Frequency Division Multiplex) solution proposed by the Multi-Band OFDM Alliance (MBOA), the addition of a spreading component in the frequency domain is a good solution since it makes resource allocation easier and also offers better robustness against channel frequency selectivity and narrowband interference. The Spread Spectrum - Multi-Carrier - Multiple Access (SS-MC-MA) system proposed in this article offers not only the advantages of Multi-Carrier - Coded Division Multiple Access (MC-CDMA) brought by frequency spreading, but also a more effective dynamic resource allocation in a multi-user and multi-piconet context. These improvements are obtained without increasing the complexity of the radio-frequency part compared to the classical MBOA solution

Performance of a space-time coded multicarrier CDMA system in frequency-selective Rayleigh channel.

Ph. D. University of KwaZulu-Natal, Durban 2014.The increasing demand for wireless services requires fast and robust broadband wireless communication for efficient utilisation of the scarce electromagnetic spectrum. One of the promising techniques for future wireless communication is the deployment of multi-input multi-output (MIMO) antenna system with orthogonal frequency division multiplexing (OFDM) coupled with multiple-access techniques. The combination of these techniques guarantees a much more reliable and robust transmission over the hostile wireless channel. This thesis investigates the performance of a multi-antenna space-time coded (STC) multi-carrier code-division multiple-access (MC-CDMA) system in a frequency-selective channel using Gold codes as spreading sequences. Spreading codes are known to be central to the performance of spread spectrum systems, STC MC-CDMA systems inclusive. Initial phase of this research work investigates multiple-access performance of spreading codes for the communication system. The performance of different sets of Gold codes for increasing number of interfering users for up to a thousand users and eight different code lengths, ranging from 31 to 4095-chip Gold codes, were considered. Simulation results show that odd-degree Gold codes give better bit-error-rate performance than even-degree Gold codes. Whereas the odd-degree codes exhibited relatively marginal loss in performance when the system was loaded, their even-degree counterparts degraded rapidly in performance, resulting in early emergence of an error floor, culminating in premature system saturation. Furthermore in this thesis, software simulations were carried to investigate the performance of a direct-sequence (DS) CDMA system in a flat-fading Rayleigh channel, and a multi-carrier (MC) CDMA system in a frequency-selective channel using different sets of Gold. The results showed that in a flat-fading channel, the Gold codes provide a constant coding gain close to that obtainable in a Gaussian channel. The results also showed that the impact of longer spreading codes was more pronounced for the MC-CDMA system in a frequency-selective channel as indicated by significant lowering of error floors. Also, frequency diversity associated with the use of longer codes coupled with multi-carrier modulation makes the MC-CDMA system resilient to multi-path effects. Further still, this thesis investigated the performance of a space-time block-coded (STBC) CDMA system in a flat-fading channel. Results showed that at low signal-to-noise ratio, the coding gain provided by the codes surpasses the diversity advantage provided by the use of the multiple antennas. The results also showed that coding gain between no-diversity link and its Gold-coded counterpart is the same as that between the transmit-diversity link and its Gold–coded counterpart. The independence of the diversity advantage provided by multiple transmit antennas and the coding gain obtainable from the use of the spreading sequences enables the prediction of the performance of composite space-time block-coded CDMA systems. Performance of a STBC OFDM system as well as a STBC MC-CDMA system in frequency-selective channel was also investigated. Results showed that the combination of diversity gain from the use of multiple antennas, coupled with coding gain provided by the Gold codes of the CDMA system, plus the diversity gain resulting from frequency diversity of multi-carrier transmission and the spectrum-spreading by the CDMA makes the composite STBC MC-CDMA system resilient to channel fading. This fact is particularly the case for long codes. For example, with reference to the OFDM transmission, the results showed that a 511-chip Gold-coded STC MC-CDMA system provided a factor of about 3,786 reduction in error floor