En telecomunicaciones , la multiplexación por división de frecuencia ortogonal ( OFDM ) es un tipo de transmisión digital y un método de codificación de datos digitales en múltiples frecuencias portadoras . OFDM se ha convertido en un esquema popular para la comunicación digital de banda ancha , que se utiliza en aplicaciones tales como transmisión de audio y televisión digital, acceso a Internet DSL , redes inalámbricas , redes de líneas eléctricas y comunicaciones móviles 4G / 5G . [1]
OFDM es un esquema de multiplexación por división de frecuencia (FDM) que fue introducido por Robert W. Chang de Bell Labs en 1966. [2] [3] [4] En OFDM, múltiples señales subportadoras ortogonales estrechamente espaciadas con espectros superpuestos se transmiten para transportar datos en paralelo. [5] La demodulación se basa en algoritmos rápidos de transformada de Fourier . OFDM fue mejorado por Weinstein y Ebert en 1971 con la introducción de un intervalo de guarda , proporcionando una mejor ortogonalidad en los canales de transmisión afectados por la propagación por trayectos múltiples. [6] Cada subportadora (señal) se modula con un esquema de modulación convencional (como modulación de amplitud en cuadratura o modulación por desplazamiento de fase ) a una velocidad de símbolo baja . Esto mantiene velocidades de datos totales similares a los esquemas de modulación de portadora única convencionales en el mismo ancho de banda. [7]
La principal ventaja de OFDM sobre los esquemas de portadora única es su capacidad para hacer frente a condiciones de canal severas (por ejemplo, atenuación de altas frecuencias en un cable de cobre largo, interferencia de banda estrecha y desvanecimiento selectivo de frecuencia debido a trayectos múltiples ) sin filtros de ecualización complejos. La ecualización de canal se simplifica porque OFDM puede verse como que usa muchas señales de banda estrecha de modulación lenta en lugar de una señal de banda ancha de modulación rápida . La baja tasa de símbolos hace que el uso de un intervalo de guarda entre símbolos sea asequible, lo que hace posible eliminar la interferencia entre símbolos (ISI) y usar ecos y propagación del tiempo (en la televisión analógica visible como imagen fantasma y borrosa, respectivamente) para lograr una ganancia de diversidad . es decir, una mejora de la relación señal / ruido . Este mecanismo también facilita el diseño de redes de frecuencia única (SFN) en las que varios transmisores adyacentes envían la misma señal simultáneamente a la misma frecuencia, ya que las señales de varios transmisores distantes se pueden volver a combinar de manera constructiva, evitando la interferencia de un sistema tradicional de una sola portadora. .
En la multiplexación por división de frecuencia ortogonal codificada (COFDM), la corrección de errores hacia adelante (codificación convolucional) y el entrelazado de tiempo / frecuencia se aplican a la señal que se transmite. Esto se hace para superar errores en los canales de comunicaciones móviles afectados por la propagación por trayectos múltiples y los efectos Doppler . El COFDM fue introducido por Alard en 1986 [8] [9] [10] para la radiodifusión de audio digital para el proyecto Eureka 147. En la práctica, el OFDM se ha utilizado en combinación con dicha codificación y entrelazado, por lo que los términos COFDM y OFDM se aplican conjuntamente a aplicaciones comunes. [11] [12]
Ejemplo de aplicaciones
La siguiente lista es un resumen de los estándares y productos existentes basados en OFDM. Para obtener más detalles, consulte la sección Uso al final del artículo.
Versión con cable principalmente conocida como transmisión discreta multitono (DMT)
- Acceso de banda ancha ADSL y VDSL a través de cableado de cobre POTS
- DVB-C 2, una versión mejorada del estándar de televisión por cable digital DVB-C
- Comunicación por línea eléctrica (PLC)
- ITU-T G.hn , un estándar que proporciona redes de área local de alta velocidad del cableado doméstico existente (líneas eléctricas, líneas telefónicas y cables coaxiales) [13]
- Módems de línea telefónica TrailBlazer
- Redes domésticas multimedia sobre Coax Alliance (MoCA)
- Entrega de banda ancha DOCSIS 3.1
Inalámbrica
- Las interfaces de radio de LAN inalámbrica (WLAN) IEEE 802.11a , g , n , ac , ah e HIPERLAN / 2
- Los sistemas de radio digital DAB / EUREKA 147 , DAB + , Digital Radio Mondiale , HD Radio , T-DMB e ISDB-TSB
- Los sistemas de televisión digital terrestre DVB-T e ISDB-T
- Los sistemas de TV móvil terrestre DVB-H , T-DMB , ISDB-T y MediaFLO forward link
- La implementación de la red de área personal inalámbrica (PAN) de banda ultra ancha (UWB) IEEE 802.15.3a sugerida por WiMedia Alliance
La tecnología de acceso múltiple basada en OFDM OFDMA también se utiliza en varias redes celulares 4G y pre-4G , estándares de banda ancha móvil y la próxima generación de WLAN:
- El modo de movilidad del estándar inalámbrico MAN / acceso inalámbrico de banda ancha (BWA) IEEE 802.16e (o Mobile- WiMAX )
- El estándar de acceso inalámbrico de banda ancha móvil (MBWA) IEEE 802.20
- El enlace descendente del estándar de banda ancha móvil 3GPP Long Term Evolution (LTE) de cuarta generación. La interfaz de radio se llamaba anteriormente Acceso de paquetes OFDM de alta velocidad (HSOPA), ahora se llama Acceso de radio terrestre UMTS evolucionado (E-UTRA)
- WLAN IEEE 802.11ax
Caracteristicas clave
Las ventajas y desventajas que se enumeran a continuación se analizan con más detalle en la sección Características y principios de funcionamiento a continuación.
Resumen de ventajas
- Alta eficiencia espectral en comparación con otros esquemas de modulación de doble banda lateral , espectro ensanchado, etc.
- Puede adaptarse fácilmente a condiciones de canal severas sin una ecualización compleja en el dominio del tiempo.
- Robusto contra la interferencia cocanal de banda estrecha
- Robusto contra la interferencia entre símbolos (ISI) y el desvanecimiento causado por la propagación por trayectos múltiples
- Implementación eficiente usando transformada rápida de Fourier
- Baja sensibilidad a los errores de sincronización horaria.
- No se requieren filtros de receptor de subcanal sintonizados (a diferencia del FDM convencional )
- Facilita las redes de frecuencia única (SFN) (es decir, la macrodiversidad del transmisor )
Resumen de desventajas
- Sensible al desplazamiento Doppler
- Sensible a los problemas de sincronización de frecuencia
- Alta relación de potencia pico a promedio (PAPR), que requiere un circuito de transmisor lineal, que adolece de una baja eficiencia energética
- Pérdida de eficiencia causada por prefijo cíclico / intervalo de guarda
Características y principios de funcionamiento.
Ortogonalidad
Conceptualmente, OFDM es un método especializado de multiplexación por división de frecuencia (FDM), con la restricción adicional de que todas las señales de subportadora dentro de un canal de comunicación son ortogonales entre sí.
En OFDM, las frecuencias de las subportadoras se eligen de modo que las subportadoras sean ortogonales entre sí, lo que significa que se elimina la diafonía entre los subcanales y no se requieren bandas de protección entre portadoras. Esto simplifica enormemente el diseño tanto del transmisor como del receptor ; a diferencia del FDM convencional, no se requiere un filtro separado para cada subcanal.
La ortogonalidad requiere que el espaciado de subportadoras sea Hertz , donde T U segundos es la duración útil del símbolo (el tamaño de la ventana del lado del receptor) y k es un número entero positivo, típicamente igual a 1. Esto estipula que cada frecuencia portadora experimenta k ciclos más completos por período de símbolo que la portadora anterior. . Por lo tanto, con N subportadoras, el ancho de banda de paso total será B ≈ N · Δ f (Hz).
La ortogonalidad también permite una alta eficiencia espectral , con una tasa de símbolo total cercana a la tasa de Nyquist para la señal de banda base equivalente (es decir, cerca de la mitad de la tasa de Nyquist para la señal de banda de paso física de doble banda lateral). Se puede utilizar casi toda la banda de frecuencia disponible. OFDM generalmente tiene un espectro casi "blanco", lo que le confiere propiedades de interferencia electromagnética benignas con respecto a otros usuarios de canal común.
- Un ejemplo simple: una duración útil de símbolo T U = 1 ms requeriría un espaciado de subportadoras de (o un múltiplo entero de eso) para ortogonalidad. N = 1000 subportadoras daría como resultado un ancho de banda de paso total de N Δf = 1 MHz. Para este tiempo de símbolo, el ancho de banda requerido en teoría según Nyquist es (la mitad del ancho de banda alcanzado requerido por nuestro esquema), donde R es la tasa de bits y donde N = 1,000 muestras por símbolo por FFT. Si se aplica un intervalo de guarda (ver más abajo), el requisito de ancho de banda de Nyquist sería aún menor. La FFT daría como resultado N = 1000 muestras por símbolo. Si no se aplica un intervalo de guarda, esto daría como resultado una señal de valor complejo de banda base con una frecuencia de muestreo de 1 MHz, lo que requeriría un ancho de banda de banda base de 0,5 MHz según Nyquist. Sin embargo, la señal de RF de banda de paso se produce multiplicando la señal de banda base con una forma de onda portadora (es decir, modulación de amplitud en cuadratura de doble banda lateral) que da como resultado un ancho de banda de banda de paso de 1 MHz. Un esquema de modulación de banda lateral única (SSB) o de banda lateral vestigial (VSB) alcanzaría casi la mitad de ese ancho de banda para la misma velocidad de símbolos (es decir, el doble de eficiencia espectral para la misma longitud de alfabeto de símbolos). Sin embargo, es más sensible a la interferencia por trayectos múltiples.
OFDM requiere una sincronización de frecuencia muy precisa entre el receptor y el transmisor; con la desviación de frecuencia, las subportadoras ya no serán ortogonales, lo que provocará interferencia entre portadoras (ICI) (es decir, diafonía entre las subportadoras). Los desplazamientos de frecuencia suelen ser causados por osciladores de transmisor y receptor no coincidentes, o por desplazamiento Doppler debido al movimiento. Si bien el receptor solo puede compensar el desplazamiento Doppler, la situación empeora cuando se combina con trayectos múltiples , ya que aparecerán reflejos en varios desplazamientos de frecuencia, lo que es mucho más difícil de corregir. Este efecto normalmente empeora a medida que aumenta la velocidad, [14] y es un factor importante que limita el uso de OFDM en vehículos de alta velocidad. Para mitigar la ICI en tales escenarios, se puede dar forma a cada subportadora para minimizar la interferencia que resulta en una superposición de subportadoras no ortogonales. [15] Por ejemplo, un esquema de baja complejidad denominado WCP-OFDM ( Multiplexación por división de frecuencia ortogonal de prefijo cíclico ponderado ) consiste en utilizar filtros cortos en la salida del transmisor para realizar una formación de pulso potencialmente no rectangular y una reconstrucción perfecta utilizando un solo toque por ecualización de subportadora. [16] Otras técnicas de supresión de ICI suelen aumentar drásticamente la complejidad del receptor. [17]
Implementación usando el algoritmo FFT
La ortogonalidad permite una implementación eficiente del modulador y demodulador utilizando el algoritmo FFT en el lado del receptor y FFT inversa en el lado del emisor. Aunque los principios y algunos de los beneficios se conocen desde la década de 1960, OFDM es popular para las comunicaciones de banda ancha en la actualidad por medio de componentes de procesamiento de señales digitales de bajo costo que pueden calcular la FFT de manera eficiente.
El tiempo para calcular la FFT inversa o la transformada FFT debe tomar menos que el tiempo para cada símbolo, [18] : 84 que, por ejemplo, para DVB-T (FFT 8k) significa que el cálculo debe realizarse en 896 µs o menos .
Para una FFT de 8 192 puntos, esto puede aproximarse a: [18] [ aclaración necesaria ]
- [18]
- MIPS = Millones de instrucciones por segundo
La demanda computacional escala aproximadamente linealmente con el tamaño de la FFT, por lo que una FFT de tamaño doble necesita el doble de tiempo y viceversa. [18] : 83 Como comparación, una CPU Intel Pentium III a 1.266 GHz es capaz de calcular una FFT de 8192 puntos en 576 µs usando FFTW . [19] Intel Pentium M a 1.6 GHz lo hace en 387 µs. [20] Intel Core Duo a 3,0 GHz lo hace en 96,8 µs . [21]
Guard interval for elimination of intersymbol interference
One key principle of OFDM is that since low symbol rate modulation schemes (i.e., where the symbols are relatively long compared to the channel time characteristics) suffer less from intersymbol interference caused by multipath propagation, it is advantageous to transmit a number of low-rate streams in parallel instead of a single high-rate stream. Since the duration of each symbol is long, it is feasible to insert a guard interval between the OFDM symbols, thus eliminating the intersymbol interference.
The guard interval also eliminates the need for a pulse-shaping filter, and it reduces the sensitivity to time synchronization problems.
- A simple example: If one sends a million symbols per second using conventional single-carrier modulation over a wireless channel, then the duration of each symbol would be one microsecond or less. This imposes severe constraints on synchronization and necessitates the removal of multipath interference. If the same million symbols per second are spread among one thousand sub-channels, the duration of each symbol can be longer by a factor of a thousand (i.e., one millisecond) for orthogonality with approximately the same bandwidth. Assume that a guard interval of 1/8 of the symbol length is inserted between each symbol. Intersymbol interference can be avoided if the multipath time-spreading (the time between the reception of the first and the last echo) is shorter than the guard interval (i.e., 125 microseconds). This corresponds to a maximum difference of 37.5 kilometers between the lengths of the paths.
The cyclic prefix, which is transmitted during the guard interval, consists of the end of the OFDM symbol copied into the guard interval, and the guard interval is transmitted followed by the OFDM symbol. The reason that the guard interval consists of a copy of the end of the OFDM symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of the multipaths when it performs OFDM demodulation with the FFT.
In some standards such as Ultrawideband, in the interest of transmitted power, cyclic prefix is skipped and nothing is sent during the guard interval. The receiver will then have to mimic the cyclic prefix functionality by copying the end part of the OFDM symbol and adding it to the beginning portion.
Simplified equalization
The effects of frequency-selective channel conditions, for example fading caused by multipath propagation, can be considered as constant (flat) over an OFDM sub-channel if the sub-channel is sufficiently narrow-banded (i.e., if the number of sub-channels is sufficiently large). This makes frequency domain equalization possible at the receiver, which is far simpler than the time-domain equalization used in conventional single-carrier modulation. In OFDM, the equalizer only has to multiply each detected subcarrier (each Fourier coefficient) in each OFDM symbol by a constant complex number, or a rarely changed value. On a fundamental level, simpler digital equalizers are better because they require fewer operations, which translates to fewer round-off errors in the equalizer. Those round-off errors can be viewed as numerical noise and are inevitable.
- Our example: The OFDM equalization in the above numerical example would require one complex valued multiplication per subcarrier and symbol (i.e., complex multiplications per OFDM symbol; i.e., one million multiplications per second, at the receiver). The FFT algorithm requires [this is imprecise: over half of these complex multiplications are trivial, i.e. = to 1 and are not implemented in software or HW]. complex-valued multiplications per OFDM symbol (i.e., 10 million multiplications per second), at both the receiver and transmitter side. This should be compared with the corresponding one million symbols/second single-carrier modulation case mentioned in the example, where the equalization of 125 microseconds time-spreading using a FIR filter would require, in a naive implementation, 125 multiplications per symbol (i.e., 125 million multiplications per second). FFT techniques can be used to reduce the number of multiplications for an FIR filter-based time-domain equalizer to a number comparable with OFDM, at the cost of delay between reception and decoding which also becomes comparable with OFDM.
If differential modulation such as DPSK or DQPSK is applied to each subcarrier, equalization can be completely omitted, since these non-coherent schemes are insensitive to slowly changing amplitude and phase distortion.
In a sense, improvements in FIR equalization using FFTs or partial FFTs leads mathematically closer to OFDM,[citation needed] but the OFDM technique is easier to understand and implement, and the sub-channels can be independently adapted in other ways than varying equalization coefficients, such as switching between different QAM constellation patterns and error-correction schemes to match individual sub-channel noise and interference characteristics.[clarification needed]
Some of the subcarriers in some of the OFDM symbols may carry pilot signals for measurement of the channel conditions[22][23] (i.e., the equalizer gain and phase shift for each subcarrier). Pilot signals and training symbols (preambles) may also be used for time synchronization (to avoid intersymbol interference, ISI) and frequency synchronization (to avoid inter-carrier interference, ICI, caused by Doppler shift).
OFDM was initially used for wired and stationary wireless communications. However, with an increasing number of applications operating in highly mobile environments, the effect of dispersive fading caused by a combination of multi-path propagation and doppler shift is more significant. Over the last decade, research has been done on how to equalize OFDM transmission over doubly selective channels.[24][25][26]
Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (forward error correction), and almost always uses frequency and/or time interleaving.
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel conditions such as fading. For example, when a part of the channel bandwidth fades, frequency interleaving ensures that the bit errors that would result from those subcarriers in the faded part of the bandwidth are spread out in the bit-stream rather than being concentrated. Similarly, time interleaving ensures that bits that are originally close together in the bit-stream are transmitted far apart in time, thus mitigating against severe fading as would happen when travelling at high speed.
However, time interleaving is of little benefit in slowly fading channels, such as for stationary reception, and frequency interleaving offers little to no benefit for narrowband channels that suffer from flat-fading (where the whole channel bandwidth fades at the same time).
The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-stream that is presented to the error correction decoder, because when such decoders are presented with a high concentration of errors the decoder is unable to correct all the bit errors, and a burst of uncorrected errors occurs. A similar design of audio data encoding makes compact disc (CD) playback robust.
A classical type of error correction coding used with OFDM-based systems is convolutional coding, often concatenated with Reed-Solomon coding. Usually, additional interleaving (on top of the time and frequency interleaving mentioned above) in between the two layers of coding is implemented. The choice for Reed-Solomon coding as the outer error correction code is based on the observation that the Viterbi decoder used for inner convolutional decoding produces short error bursts when there is a high concentration of errors, and Reed-Solomon codes are inherently well suited to correcting bursts of errors.
Newer systems, however, usually now adopt near-optimal types of error correction codes that use the turbo decoding principle, where the decoder iterates towards the desired solution. Examples of such error correction coding types include turbo codes and LDPC codes, which perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel. Some systems that have implemented these codes have concatenated them with either Reed-Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to improve upon an error floor inherent to these codes at high signal-to-noise ratios.[27]
Adaptive transmission
The resilience to severe channel conditions can be further enhanced if information about the channel is sent over a return-channel. Based on this feedback information, adaptive modulation, channel coding and power allocation may be applied across all subcarriers, or individually to each subcarrier. In the latter case, if a particular range of frequencies suffers from interference or attenuation, the carriers within that range can be disabled or made to run slower by applying more robust modulation or error coding to those subcarriers.
The term discrete multitone modulation (DMT) denotes OFDM-based communication systems that adapt the transmission to the channel conditions individually for each subcarrier, by means of so-called bit-loading. Examples are ADSL and VDSL.
The upstream and downstream speeds can be varied by allocating either more or fewer carriers for each purpose. Some forms of rate-adaptive DSL use this feature in real time, so that the bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever subscriber needs it most.
OFDM extended with multiple access
OFDM in its primary form is considered as a digital modulation technique, and not a multi-user channel access method, since it is used for transferring one bit stream over one communication channel using one sequence of OFDM symbols. However, OFDM can be combined with multiple access using time, frequency or coding separation of the users.
In orthogonal frequency-division multiple access (OFDMA), frequency-division multiple access is achieved by assigning different OFDM sub-channels to different users. OFDMA supports differentiated quality of service by assigning different number of subcarriers to different users in a similar fashion as in CDMA, and thus complex packet scheduling or Media Access Control schemes can be avoided. OFDMA is used in:
- the mobility mode of the IEEE 802.16 Wireless MAN standard, commonly referred to as WiMAX,
- the IEEE 802.20 mobile Wireless MAN standard, commonly referred to as MBWA,
- the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard downlink. The radio interface was formerly named High Speed OFDM Packet Access (HSOPA), now named Evolved UMTS Terrestrial Radio Access (E-UTRA).
- the 3GPP 5G NR (New Radio) fifth generation mobile network standard downlink and uplink. 5G NR is the successor to LTE.
- the now defunct Qualcomm/3GPP2 Ultra Mobile Broadband (UMB) project, intended as a successor of CDMA2000, but replaced by LTE.
OFDMA is also a candidate access method for the IEEE 802.22 Wireless Regional Area Networks (WRAN). The project aims at designing the first cognitive radio-based standard operating in the VHF-low UHF spectrum (TV spectrum).
- the most recent amendment of 802.11 standard, namely 802.11ax, includes OFDMA for high efficiency and simultaneous communication.
In multi-carrier code division multiple access (MC-CDMA), also known as OFDM-CDMA, OFDM is combined with CDMA spread spectrum communication for coding separation of the users. Co-channel interference can be mitigated, meaning that manual fixed channel allocation (FCA) frequency planning is simplified, or complex dynamic channel allocation (DCA) schemes are avoided.
Space diversity
In OFDM-based wide-area broadcasting, receivers can benefit from receiving signals from several spatially dispersed transmitters simultaneously, since transmitters will only destructively interfere with each other on a limited number of subcarriers, whereas in general they will actually reinforce coverage over a wide area. This is very beneficial in many countries, as it permits the operation of national single-frequency networks (SFN), where many transmitters send the same signal simultaneously over the same channel frequency. SFNs use the available spectrum more effectively than conventional multi-frequency broadcast networks (MFN), where program content is replicated on different carrier frequencies. SFNs also result in a diversity gain in receivers situated midway between the transmitters. The coverage area is increased and the outage probability decreased in comparison to an MFN, due to increased received signal strength averaged over all subcarriers.
Although the guard interval only contains redundant data, which means that it reduces the capacity, some OFDM-based systems, such as some of the broadcasting systems, deliberately use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN, and longer guard intervals allow larger SFN cell-sizes. A rule of thumb for the maximum distance between transmitters in an SFN is equal to the distance a signal travels during the guard interval — for instance, a guard interval of 200 microseconds would allow transmitters to be spaced 60 km apart.
A single frequency network is a form of transmitter macrodiversity. The concept can be further used in dynamic single-frequency networks (DSFN), where the SFN grouping is changed from timeslot to timeslot.
OFDM may be combined with other forms of space diversity, for example antenna arrays and MIMO channels. This is done in the IEEE 802.11 Wireless LAN standards.
Linear transmitter power amplifier
An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent phases of the subcarriers mean that they will often combine constructively. Handling this high PAPR requires:
- A high-resolution digital-to-analog converter (DAC) in the transmitter
- A high-resolution analog-to-digital converter (ADC) in the receiver
- A linear signal chain
Any non-linearity in the signal chain will cause intermodulation distortion that
- Raises the noise floor
- May cause inter-carrier interference
- Generates out-of-band spurious radiation
The linearity requirement is demanding, especially for transmitter RF output circuitry where amplifiers are often designed to be non-linear in order to minimise power consumption. In practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a judicious trade-off against the above consequences. However, the transmitter output filter which is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that were clipped, so clipping is not an effective way to reduce PAPR.
Although the spectral efficiency of OFDM is attractive for both terrestrial and space communications, the high PAPR requirements have so far limited OFDM applications to terrestrial systems.
The crest factor CF (in dB) for an OFDM system with n uncorrelated subcarriers is[28]
where CFc is the crest factor (in dB) for each subcarrier. (CFc is 3.01 dB for the sine waves used for BPSK and QPSK modulation).
For example, the DVB-T signal in 2K mode is composed of 1705 subcarriers that are each QPSK-modulated, giving a crest factor of 35.32 dB.[28]
Many PAPR (or crest factor) reduction techniques have been developed, for instance, based on intertaive clipping.[29]
The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB.[30] As a comparison, each extra bit per sample increases the dynamic range by 6 dB.
Comparación de eficiencia entre portadora única y multicarrier
The performance of any communication system can be measured in terms of its power efficiency and bandwidth efficiency. The power efficiency describes the ability of communication system to preserve bit error rate (BER) of the transmitted signal at low power levels. Bandwidth efficiency reflects how efficiently the allocated bandwidth is used and is defined as the throughput data rate per hertz in a given bandwidth. If the large number of subcarriers are used, the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel is defined as[31]
where is the symbol rate in giga-symbols per second (Gsps), is the bandwidth of OFDM signal, and the factor of 2 is due to the two polarization states in the fiber.
There is saving of bandwidth by using multicarrier modulation with orthogonal frequency division multiplexing. So the bandwidth for multicarrier system is less in comparison with single carrier system and hence bandwidth efficiency of multicarrier system is larger than single carrier system.
S.no. | Transmission type | M in M-QAM | No. of subcarriers | Bit rate | Fiber length | Power at the receiver (at BER of 10−9) | Bandwidth efficiency |
---|---|---|---|---|---|---|---|
1. | Single carrier | 64 | 1 | 10 Gbit/s | 20 km | −37.3 dBm | 6.0000 |
2. | Multicarrier | 64 | 128 | 10 Gbit/s | 20 km | −36.3 dBm | 10.6022 |
There is only 1 dBm increase in receiver power, but we get 76.7% improvement in bandwidth efficiency with using multicarrier transmission technique.
Modelo de sistema idealizado
This section describes a simple idealized OFDM system model suitable for a time-invariant AWGN channel.
Transmitter
An OFDM carrier signal is the sum of a number of orthogonal subcarriers, with baseband data on each subcarrier being independently modulated commonly using some type of quadrature amplitude modulation (QAM) or phase-shift keying (PSK). This composite baseband signal is typically used to modulate a main RF carrier.
is a serial stream of binary digits. By inverse multiplexing, these are first demultiplexed into parallel streams, and each one mapped to a (possibly complex) symbol stream using some modulation constellation (QAM, PSK, etc.). Note that the constellations may be different, so some streams may carry a higher bit-rate than others.
An inverse FFT is computed on each set of symbols, giving a set of complex time-domain samples. These samples are then quadrature-mixed to passband in the standard way. The real and imaginary components are first converted to the analogue domain using digital-to-analogue converters (DACs); the analogue signals are then used to modulate cosine and sine waves at the carrier frequency, , respectively. These signals are then summed to give the transmission signal, .
Receiver
The receiver picks up the signal , which is then quadrature-mixed down to baseband using cosine and sine waves at the carrier frequency. This also creates signals centered on , so low-pass filters are used to reject these. The baseband signals are then sampled and digitised using analog-to-digital converters (ADCs), and a forward FFT is used to convert back to the frequency domain.
This returns parallel streams, each of which is converted to a binary stream using an appropriate symbol detector. These streams are then re-combined into a serial stream, , which is an estimate of the original binary stream at the transmitter.
Descripción matemática
If subcarriers are used, and each subcarrier is modulated using alternative symbols, the OFDM symbol alphabet consists of combined symbols.
The low-pass equivalent OFDM signal is expressed as:
where are the data symbols, is the number of subcarriers, and is the OFDM symbol time. The subcarrier spacing of makes them orthogonal over each symbol period; this property is expressed as:
where denotes the complex conjugate operator and is the Kronecker delta.
To avoid intersymbol interference in multipath fading channels, a guard interval of length is inserted prior to the OFDM block. During this interval, a cyclic prefix is transmitted such that the signal in the interval equals the signal in the interval . The OFDM signal with cyclic prefix is thus:
The low-pass signal above can be either real or complex-valued. Real-valued low-pass equivalent signals are typically transmitted at baseband—wireline applications such as DSL use this approach. For wireless applications, the low-pass signal is typically complex-valued; in which case, the transmitted signal is up-converted to a carrier frequency . In general, the transmitted signal can be represented as:
Uso
OFDM is used in:
- Digital Radio Mondiale (DRM)
- Digital Audio Broadcasting (DAB)
- Digital television DVB-T/T2 (terrestrial), DVB-H (handheld), DMB-T/H, DVB-C2 (cable)
- Wireless LAN IEEE 802.11a, IEEE 802.11g, IEEE 802.11n, IEEE 802.11ac, and IEEE 802.11ad
- WiMAX
- Li-Fi
- ADSL (G.dmt/ITU G.992.1)
- LTE and LTE Advanced 4G mobile networks
- DECT cordless phones
- Modern narrow and broadband power line communications[32]
OFDM system comparison table
Key features of some common OFDM-based systems are presented in the following table.
Standard name | DAB Eureka 147 | DVB-T | DVB-H | DMB-T/H | DVB-T2 | IEEE 802.11a |
---|---|---|---|---|---|---|
Ratified year | 1995 | 1997 | 2004 | 2006 | 2007 | 1999 |
Frequency range of today's equipment | 174–240 MHz 1.452–1.492 GHz | 470–862 MHz 174–230 MHz | 470–862 MHz | 470–862 MHz | 4,915–6,100 MHz | |
Channel spacing, B (MHz) | 1.712 | 6, 7, 8 | 5, 6, 7, 8 | 8 | 1.7, 5, 6, 7, 8, 10 | 20 |
FFT size, k = 1,024 | Mode I: 2k Mode II: 512 Mode III: 256 Mode IV: 1k | 2k, 8k | 2k, 4k, 8k | 1 (single-carrier) 4k (multi-carrier) | 1k, 2k, 4k, 8k, 16k, 32k | 64 |
Number of non-silent subcarriers, N | Mode I: 1,536 Mode II: 384 Mode III: 192 Mode IV: 768 | 2K mode: 1,705 8K mode: 6,817 | 1,705, 3,409, 6,817 | 1 (single-carrier) 3,780 (multi-carrier) | 853–27,841 (1K normal to 32K extended carrier mode) | 52 |
Subcarrier modulation scheme | π⁄4-DQPSK | QPSK,[33] 16QAM or 64QAM | QPSK,[33] 16QAM or 64QAM | 4QAM,[33] 4QAM-NR,[34] 16QAM, 32QAM and 64QAM. | QPSK, 16QAM, 64QAM, 256QAM | BPSK, QPSK,[33] 16QAM or 64QAM |
Useful symbol length, TU (μs) | Mode I: 1,000 Mode II: 250 Mode III: 125 Mode IV: 500 | 2K mode: 224 8K mode: 896 | 224, 448, 896 | 500 (multi-carrier) | 112–3,584 (1K to 32K mode on 8 MHz channel) | 3.2 |
Additional guard interval, TG (fraction of TU) | 24.6% (all modes) | 1⁄4, 1⁄8, 1⁄16, 1⁄32 | 1⁄4, 1⁄8, 1⁄16, 1⁄32 | 1⁄4, 1⁄6, 1⁄9 | 1/128, 1/32, 1/16, 19/256, 1/8, 19/128, 1/4. (For 32k mode maximum 1/8) | 1⁄4 |
Subcarrier spacing (Hz) | Mode I: 1,000 Mode II: 4,000 Mode III: 8,000 Mode IV: 2,000 | 2K mode: 4,464 8K mode: 1,116 | 4,464, 2,232, 1,116 | 8 M (single-carrier) 2,000 (multi-carrier) | 279–8,929 (32K down to 1K mode) | 312.5 K |
Net bit rate, R (Mbit/s) | 0.576–1.152 | 4.98–31.67 (typically 24.13) | 3.7–23.8 | 4.81–32.49 | Typically 35.4 | 6–54 |
Link spectral efficiency R/B (bit/s·Hz) | 0.34–0.67 | 0.62–4.0 (typ. 3.0) | 0.62–4.0 | 0.60–4.1 | 0.87–6.65 | 0.30–2.7 |
Inner FEC | Conv. coding with equal error protection code rates: 1⁄4, 3⁄8, 4⁄9, 1⁄2, 4⁄7, 2⁄3, 3⁄4, 4⁄5 Unequal error protection with av. code rates of: | Conv. coding with code rates: 1⁄2, 2⁄3, 3⁄4, 5⁄6, or 7⁄8 | Conv. coding with code rates: 1⁄2, 2⁄3, 3⁄4, 5⁄6, or 7⁄8 | LDPC with code rates: 0.4, 0.6, or 0.8 | LDPC: 1⁄2, 3⁄5, 2⁄3, 3⁄4, 4⁄5, 5⁄6 | Conv. coding with code rates: 1⁄2, 2⁄3, or 3⁄4 |
Outer FEC (if any) | Optional RS (120, 110, t = 5) | RS (204, 188, t = 8) | RS (204, 188, t = 8) + MPE-FEC | BCH code (762, 752) | BCH code | |
Maximum travelling speed (km/h) | 200–600 | 53–185, depending upon transmission frequency | ||||
Time interleaving depth (ms) | 384 | 0.6–3.5 | 0.6–3.5 | 200–500 | Up to 250 (500 with extension frame) | |
Adaptive transmission, if any | None | None | None | None | ||
Multiple access method (if any) | None | None | None | None | ||
Typical source coding | 192 kbit/s MPEG2 Audio layer 2 | 2–18 Mbit/s Standard - HDTV H.264 or MPEG2 | H.264 | Not defined (Video: MPEG-2, H.264 and/or AVS Audio: MP2 or AC-3) | H.264 or MPEG2 (Audio: AAC HE, Dolby Digital AC-3 (A52), MPEG-2 AL 2.) |
ADSL
OFDM is used in ADSL connections that follow the ANSI T1.413 and G.dmt (ITU G.992.1) standards, where it is called discrete multitone modulation (DMT).[35] DSL achieves high-speed data connections on existing copper wires. OFDM is also used in the successor standards ADSL2, ADSL2+, VDSL, VDSL2, and G.fast. ADSL2 uses variable subcarrier modulation, ranging from BPSK to 32768QAM (in ADSL terminology this is referred to as bit-loading, or bit per tone, 1 to 15 bits per subcarrier).
Long copper wires suffer from attenuation at high frequencies. The fact that OFDM can cope with this frequency selective attenuation and with narrow-band interference are the main reasons it is frequently used in applications such as ADSL modems.
Powerline Technology
OFDM is used by many powerline devices to extend digital connections through power wiring. Adaptive modulation is particularly important with such a noisy channel as electrical wiring. Some medium speed smart metering modems, "Prime" and "G3" use OFDM at modest frequencies (30–100 kHz) with modest numbers of channels (several hundred) in order to overcome the intersymbol interference in the power line environment.[36] The IEEE 1901 standards include two incompatible physical layers that both use OFDM.[37] The ITU-T G.hn standard, which provides high-speed local area networking over existing home wiring (power lines, phone lines and coaxial cables) is based on a PHY layer that specifies OFDM with adaptive modulation and a Low-Density Parity-Check (LDPC) FEC code.[32]
Wireless local area networks (LAN) and metropolitan area networks (MAN)
OFDM is extensively used in wireless LAN and MAN applications, including IEEE 802.11a/g/n and WiMAX.
IEEE 802.11a/g/n, operating in the 2.4 and 5 GHz bands, specifies per-stream airside data rates ranging from 6 to 54 Mbit/s. If both devices can use "HT mode" (added with 802.11n), the top 20 MHz per-stream rate is increased to 72.2 Mbit/s, with the option of data rates between 13.5 and 150 Mbit/s using a 40 MHz channel. Four different modulation schemes are used: BPSK, QPSK, 16-QAM, and 64-QAM, along with a set of error correcting rates (1/2–5/6). The multitude of choices allows the system to adapt the optimum data rate for the current signal conditions.
Wireless personal area networks (PAN)
OFDM is also now being used in the WiMedia/Ecma-368 standard for high-speed wireless personal area networks in the 3.1–10.6 GHz ultrawideband spectrum (see MultiBand-OFDM).
Terrestrial digital radio and television broadcasting
Much of Europe and Asia has adopted OFDM for terrestrial broadcasting of digital television (DVB-T, DVB-H and T-DMB) and radio (EUREKA 147 DAB, Digital Radio Mondiale, HD Radio and T-DMB).
DVB-T
By Directive of the European Commission, all television services transmitted to viewers in the European Community must use a transmission system that has been standardized by a recognized European standardization body,[38] and such a standard has been developed and codified by the DVB Project, Digital Video Broadcasting (DVB); Framing structure, channel coding and modulation for digital terrestrial television.[39] Customarily referred to as DVB-T, the standard calls for the exclusive use of COFDM for modulation. DVB-T is now widely used in Europe and elsewhere for terrestrial digital TV.
SDARS
The ground segments of the Digital Audio Radio Service (SDARS) systems used by XM Satellite Radio and Sirius Satellite Radio are transmitted using Coded OFDM (COFDM).[40] The word "coded" comes from the use of forward error correction (FEC).[5]
COFDM vs VSB
The question of the relative technical merits of COFDM versus 8VSB for terrestrial digital television has been a subject of some controversy, especially between European and North American technologists and regulators. The United States has rejected several proposals to adopt the COFDM-based DVB-T system for its digital television services, and has instead opted for 8VSB (vestigial sideband modulation) operation.
One of the major benefits provided by COFDM is in rendering radio broadcasts relatively immune to multipath distortion and signal fading due to atmospheric conditions or passing aircraft. Proponents of COFDM argue it resists multipath far better than 8VSB. Early 8VSB DTV (digital television) receivers often had difficulty receiving a signal. Also, COFDM allows single-frequency networks, which is not possible with 8VSB.
However, newer 8VSB receivers are far better at dealing with multipath, hence the difference in performance may diminish with advances in equalizer design.[citation needed]
Digital radio
COFDM is also used for other radio standards, for Digital Audio Broadcasting (DAB), the standard for digital audio broadcasting at VHF frequencies, for Digital Radio Mondiale (DRM), the standard for digital broadcasting at shortwave and medium wave frequencies (below 30 MHz) and for DRM+ a more recently introduced standard for digital audio broadcasting at VHF frequencies. (30 to 174 MHz)
The USA again uses an alternate standard, a proprietary system developed by iBiquity dubbed HD Radio. However, it uses COFDM as the underlying broadcast technology to add digital audio to AM (medium wave) and FM broadcasts.
Both Digital Radio Mondiale and HD Radio are classified as in-band on-channel systems, unlike Eureka 147 (DAB: Digital Audio Broadcasting) which uses separate VHF or UHF frequency bands instead.
BST-OFDM used in ISDB
The band-segmented transmission orthogonal frequency division multiplexing (BST-OFDM) system proposed for Japan (in the ISDB-T, ISDB-TSB, and ISDB-C broadcasting systems) improves upon COFDM by exploiting the fact that some OFDM carriers may be modulated differently from others within the same multiplex. Some forms of COFDM already offer this kind of hierarchical modulation, though BST-OFDM is intended to make it more flexible. The 6 MHz television channel may therefore be "segmented", with different segments being modulated differently and used for different services.
It is possible, for example, to send an audio service on a segment that includes a segment composed of a number of carriers, a data service on another segment and a television service on yet another segment—all within the same 6 MHz television channel. Furthermore, these may be modulated with different parameters so that, for example, the audio and data services could be optimized for mobile reception, while the television service is optimized for stationary reception in a high-multipath environment.
Ultra-wideband
Ultra-wideband (UWB) wireless personal area network technology may also use OFDM, such as in Multiband OFDM (MB-OFDM). This UWB specification is advocated by the WiMedia Alliance (formerly by both the Multiband OFDM Alliance [MBOA] and the WiMedia Alliance, but the two have now merged), and is one of the competing UWB radio interfaces.
FLASH-OFDM
Fast low-latency access with seamless handoff orthogonal frequency division multiplexing (Flash-OFDM), also referred to as F-OFDM, was based on OFDM and also specified higher protocol layers. It was developed by Flarion, and purchased by Qualcomm in January 2006.[41][42] Flash-OFDM was marketed as a packet-switched cellular bearer, to compete with GSM and 3G networks. As an example, 450 MHz frequency bands previously used by NMT-450 and C-Net C450 (both 1G analogue networks, now mostly decommissioned) in Europe are being licensed to Flash-OFDM operators.[citation needed]
In Finland, the license holder Digita began deployment of a nationwide "@450" wireless network in parts of the country since April 2007. It was purchased by Datame in 2011.[43] In February 2012 Datame announced they would upgrade the 450 MHz network to competing CDMA2000 technology.[44]
Slovak Telekom in Slovakia offers Flash-OFDM connections[45] with a maximum downstream speed of 5.3 Mbit/s, and a maximum upstream speed of 1.8 Mbit/s, with a coverage of over 70 percent of Slovak population.[citation needed] The Flash-OFDM network was switched off in the majority of Slovakia on 30 September 2015.[46]
T-Mobile Germany used Flash-OFDM to backhaul Wi-Fi HotSpots on the Deutsche Bahn's ICE high speed trains between 2005 and 2015, until switching over to UMTS and LTE.[47]
American wireless carrier Nextel Communications field tested wireless broadband network technologies including Flash-OFDM in 2005.[48] Sprint purchased the carrier in 2006 and decided to deploy the mobile version of WiMAX, which is based on Scalable Orthogonal Frequency Division Multiple Access (SOFDMA) technology.[49]
Citizens Telephone Cooperative launched a mobile broadband service based on Flash-OFDM technology to subscribers in parts of Virginia in March 2006. The maximum speed available was 1.5 Mbit/s.[50] The service was discontinued on April 30, 2009.[51]
Vector OFDM (VOFDM)
VOFDM was proposed by Xiang-Gen Xia in 2000 (Proceedings of ICC 2000, New Orleans, and IEEE Trans. on Communications, Aug. 2001) for single transmit antenna systems. VOFDM replaces each scalar value in the conventional OFDM by a vector value and is a bridge between OFDM and the single carrier frequency domain equalizer (SC-FDE). When the vector size is , it is OFDM and when the vector size is at least the channel length and the FFT size is , it is SC-FDE.
In VOFDM, assume is the vector size, and each scalar-valued signal in OFDM is replaced by a vector-valued signal of vector size , . One takes the -point IFFT of , component-wisely and gets another vector sequence of the same vector size , . Then, one adds a vector CP of length to this vector sequence as
.
This vector sequence is converted to a scalar sequence by sequentializing all the vectors of size , which is transmitted at a transmit antenna sequentially.
At the receiver, the received scalar sequence is first converted to the vector sequence of vector size . When the CP length satisfies , then, after the vector CP is removed from the vector sequence and the -point FFT is implemented component-wisely to the vector sequence of length , one obtains
where are additive white noise and and is the following polyphase matrix of the ISI channel :
,
where is the th polyphase component of the channel . From (1), one can see that the original ISI channel is converted to many vector subchannels of vector size . There is no ISI across these vector subchannels but there is ISI inside each vector subchannel. In each vector subchannel, at most many symbols are interfered each other. Clearly, when the vector size , the above VOFDM returns to OFDM and when and , it becomes the SC-FDE. The vector size is a parameter that one can choose freely and properly in practice and controls the ISI level. There may be a tradeoff between vector size , demodulation complexity at the receiver, and FFT size, for a given channel bandwidth.
Note that there exist many other different generalizations/forms of OFDM, to see their essential differences, it is critical to see their corresponding received signal equations to demodulate. The above VOFDM is the earliest and the only one that achieves the received signal equation (1) and/or its equivalent form, although it may have different implementations at transmitter vs. different IFFT algorithms. It has been shown (Yabo Li et. al., IEEE Trans. on Signal Processing, Oct. 2012) that applying the MMSE linear receiver to each vector subchannel (1), it achieves multipath diversity.
Wavelet-OFDM
OFDM has become an interesting technique for power line communications (PLC). In this area of research, a wavelet transform is introduced to replace the DFT as the method of creating orthogonal frequencies. This is due to the advantages wavelets offer, which are particularly useful on noisy power lines.[52]
Instead of using an IDFT to create the sender signal, the wavelet OFDM uses a synthesis bank consisting of a -band transmultiplexer followed by the transform function
On the receiver side, an analysis bank is used to demodulate the signal again. This bank contains an inverse transform
followed by another -band transmultiplexer. The relationship between both transform functions is
An example of W-OFDM uses the Perfect Reconstruction Cosine Modulated Filter Bank (PR-CMFB) and Extended Lapped Transform (ELT) is used for the wavelet TF. Thus, and are given as
These two functions are their respective inverses, and can be used to modulate and demodulate a given input sequence. Just as in the case of DFT, the wavelet transform creates orthogonal waves with , , ..., . The orthogonality ensures that they do not interfere with each other and can be sent simultaneously. At the receiver, , , ..., are used to reconstruct the data sequence once more.
Advantages over standard OFDM
W-OFDM is an evolution of the standard OFDM, with certain advantages.
Mainly, the sidelobe levels of W-OFDM are lower. This results in less ICI, as well as greater robustness to narrowband interference. These two properties are especially useful in PLC, where most of the lines aren't shielded against EM-noise, which creates noisy channels and noise spikes.
A comparison between the two modulation techniques also reveals that the complexity of both algorithms remains approximately the same.[52]
Historia
- 1957: Kineplex, multi-carrier HF modem (R.R. Mosier & R.G. Clabaugh)
- 1966: Chang, Bell Labs: OFDM paper[3] and patent[4]
- 1971: Weinstein & Ebert proposed use of FFT and guard interval[6]
- 1985: Cimini described use of OFDM for mobile communications
- 1985: Telebit Trailblazer Modem introduced a 512 carrier Packet Ensemble Protocol (18 432 bit/s)
- 1987: Alard & Lasalle: COFDM for digital broadcasting[9]
- 1988: In September TH-CSF LER, first experimental Digital TV link in OFDM, Paris area
- 1989: OFDM international patent application PCT/FR 89/00546, filed in the name of THOMSON-CSF, Fouche, de Couasnon, Travert, Monnier and all[53]
- October 1990: TH-CSF LER, first OFDM equipment field test, 34 Mbit/s in an 8 MHz channel, experiments in Paris area
- December 1990: TH-CSF LER, first OFDM test bed comparison with VSB in Princeton USA
- September 1992: TH-CSF LER, second generation equipment field test, 70 Mbit/s in an 8 MHz channel, twin polarisations. Wuppertal, Germany
- October 1992: TH-CSF LER, second generation field test and test bed with BBC, near London, UK
- 1993: TH-CSF show in Montreux SW, 4 TV channel and one HDTV channel in a single 8 MHz channel
- 1993: Morris: Experimental 150 Mbit/s OFDM wireless LAN
- 1995: ETSI Digital Audio Broadcasting standard EUreka: first OFDM-based standard
- 1997: ETSI DVB-T standard
- 1998: Magic WAND project demonstrates OFDM modems for wireless LAN
- 1999: IEEE 802.11a wireless LAN standard (Wi-Fi)[54]
- 2000: Proprietary fixed wireless access (V-OFDM, FLASH-OFDM, etc.)
- May 2001: The FCC allows OFDM in the 2.4GHz license exempt band. [55]
- 2002: IEEE 802.11g standard for wireless LAN[56]
- 2004: IEEE 802.16 standard for wireless MAN (WiMAX)[57]
- 2004: ETSI DVB-H standard
- 2004: Candidate for IEEE 802.15.3a standard for wireless PAN (MB-OFDM)
- 2004: Candidate for IEEE 802.11n standard for next generation wireless LAN
- 2005: OFDMA is candidate for the 3GPP Long Term Evolution (LTE) air interface E-UTRA downlink.
- 2007: The first complete LTE air interface implementation was demonstrated, including OFDM-MIMO, SC-FDMA and multi-user MIMO uplink[58]
Ver también
- ATSC standards
- Carrier interferometry
- N-OFDM
- Single-carrier FDMA (SC-FDMA)
- Single-carrier frequency-domain-equalization (SC-FDE)
- Orthogonal Time Frequency and Space (OTFS)
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- ^ "Nextel Flash-OFDM: The Best Network You May Never Use". PC Magazine. March 2, 2005. Retrieved July 23, 2011.
- ^ Sascha Segan (August 8, 2006). "Sprint Nextel Goes To The WiMax". PC Magazine. Archived from the original on 2018-11-30. Retrieved July 23, 2011.
- ^ "Citizens Offers First "Truly Mobile" Wireless Internet in Christiansburg and other parts of the New River Valley" (PDF). News release. Citizens Wireless. March 28, 2006. Retrieved July 23, 2011.
- ^ "Thank you for supporting Citizens Mobile Broadband". Citizens Wireless. 2009. Archived from the original on July 18, 2011. Retrieved July 23, 2011.
- ^ a b S. Galli; H. Koga; N. Nodokama (May 2008). Advanced Signal Processing for PLCs: Wavelet-OFDM. 2008 IEEE International Symposium on Power Line Communications and Its Applications. pp. 187–192. doi:10.1109/ISPLC.2008.4510421. ISBN 978-1-4244-1975-3.
- ^ "Archived copy". Archived from the original on 2007-12-15. Retrieved 2019-12-13.CS1 maint: archived copy as title (link)
- ^ "IEEE 802.11a-1999 - IEEE Standard for Telecommunications and Information Exchange Between Systems - LAN/MAN Specific Requirements - Part 11: Wireless Medium Access Control (MAC) and physical layer (PHY) specifications: High Speed Physical Layer in the 5 GHz band". standards.ieee.org. Retrieved 2020-12-12.
- ^ https://www.researchgate.net/publication/228163323_Spectrum_Rights_in_the_Telecosm_to_Come
- ^ "IEEE 802.11g-2003 - IEEE Standard for Information technology-- Local and metropolitan area networks-- Specific requirements-- Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: Further Higher Data Rate Extension in the 2.4 GHz Band". standards.ieee.org. Retrieved 2020-12-12.
- ^ "IEEE Standard 802.16 for Global Broadband Wireless Access" (PDF). 2002-10-21.
- ^ "Nortel 3G World Congress Press Release". Archived from the original on 2007-09-29. Retrieved 2008-01-29.
Otras lecturas
- Bank, M. (2007). "System free of channel problems inherent in changing mobile communication systems". Electronics Letters. 43 (7): 401–402. doi:10.1049/el:20070014.
- M. Bank, B. Hill, Miriam Bank. A wireless mobile communication system without pilot signals Patent PCT/Il N 2006000926, Patent PCT International Application N0 PCT/IL 2006000926. Patent No. 7,986,740, Issue date: 26 July 2011
enlaces externos
- Numerous useful links and resources for OFDM - WCSP Group - University of South Florida (USF)
- WiMAX Forum, WiMAX, the framework standard for 4G mobile personal broadband
- Stott, 1997 [1] Technical presentation by J H Stott of the BBC's R&D division, delivered at the 20 International Television Symposium in 1997; this URL accessed 24 January 2006.
- Page on Orthogonal Frequency Division Multiplexing at https://web.archive.org/web/20090325005048/http://www.iss.rwth-aachen.de/Projekte/Theo/OFDM/node6.html accessed on 24 September 2007.
- A tutorial on the significance of Cyclic Prefix (CP) in OFDM Systems.
- Siemens demos 360 Mbit/s wireless
- An Introduction to Orthogonal Frequency Division Multiplex Technology
- Short Introduction to OFDM - Tutorial written by Prof. Debbah, head of the Alcatel-Lucent Chair on flexible radio.
- Short free tutorial on COFDM by Mark Massel formerly at STMicroelectronics and in the digital TV industry for many years.
- A popular book on both COFDM and US ATSC by Mark Massel
- OFDM transmission step-by-step – online experiment
- Simulation of optical OFDM systems