# Subcarrier Assignment In Ofdm Tutorial

## Construction

creates a modulator System object, , that modulates the input signal using the orthogonal frequency division modulation (OFDM) method.

creates a OFDM modulator object, , with each specified property set to the specified value. You can specify additional name-value pair arguments in any order as (,,...,,).

creates an OFDM modulator object, , whose properties are determined by the corresponding OFDM demodulator object, .

## Algorithms

Orthogonal frequency division modulation (OFDM) divides a high-rate transmit data stream into *N* lower-rate streams, each of which has a symbol duration larger than the channel delay spread. This serves to mitigate intersymbol interference (ISI). The individual substreams are sent over *N* parallel subchannels which are orthogonal to each other. Through the use of an inverse fast Fourier transform (IFFT), OFDM can be transmitted using a single radio. Specifically, the OFDM Modulator System object modulates an input signal using orthogonal frequency division modulation. The output is a baseband representation of the modulated signal:

where {*X*_{k}} are data symbols, *N* is the number of subcarriers, and *T* is the OFDM symbol time. The subcarrier spacing of Δ*f* = 1/*T* makes them orthogonal over each symbol period. This is expressed as:

*X*

_{k}, are usually complex and can be from any modulation alphabet, e.g., QPSK, 16-QAM, or 64-QAM.

The figure shows an OFDM modulator. It consists of a bank of *N* complex modulators, where each corresponds to one OFDM subcarrier.

### Guard Bands and Intervals

There are three types of OFDM subcarriers: data, pilot, and null. Data subcarriers are used for transmitting data while pilot subcarriers are used for channel estimation. There is no transmission on null subcarriers, which provide a DC null and provide buffers between OFDM resource blocks. These buffers are referred to as guard bands whose purpose is to prevent inter-symbol interference. The allocation of nulls and guard bands vary depending upon the applicable standard, e.g., 802.11n differs from LTE. Consequently, the OFDM modulator object allows the user to assign subcarrier indices.

Analogous to the concept of guard bands, the OFDM modulator object supports guard intervals which are used to provide temporal separation between OFDM symbols so that the signal does not lose orthogonality due to time-dispersive channels. As long as the guard interval is longer than the delay spread, each symbol does not interfere with other symbols. Guard intervals are created by using cyclic prefixes in which the last part of an OFDM symbol is copied and inserted as the first part of the OFDM symbol. The benefit of cyclic prefix insertion is maintained as long as the span of the time dispersion does not exceed the duration of the cyclic prefix. The OFDM modulator object enables the setting of the cyclic prefix length. The drawback in using a cyclic prefix is the penalty from increased overhead.

### Raised Cosine Windowing

While the cyclic prefix creates guard period in time domain to preserve orthogonality, an OFDM symbol rarely begins with the same amplitude and phase exhibited at the end of the prior OFDM symbol. This causes spectral regrowth, which is the spreading of signal bandwidth due to intermodulation distortion. To limit this spectral regrowth, it is desired to create a smooth transition between the last sample of a symbol and the first sample of the next symbol. This can be done by using a cyclic suffix and raised cosine windowing.

To create the cyclic suffix, the first *N*_{WIN} samples of a given symbol are appended to the end of that symbol. However, in order to comply with the 802.11g standard, for example, the length of a symbol cannot be arbitrarily lengthened. Instead, the cyclic suffix must overlap in time and is effectively summed with the cyclic prefix of the following symbol. This overlapped segment is where windowing is applied. Two windows are applied, one of which is the mathematical inverse of the other. The first raised cosine window is applied to the cyclic suffix of symbol *k*, and decreases from 1 to 0 over its duration. The second raised cosine window is applied to the cyclic prefix of symbol *k*+1, and increases from 0 to 1 over its duration. This provides a smooth transition from one symbol to the next.

The raised cosine window, *w(t)*, in the time domain can be expressed as:

where

*T*represents the OFDM symbol duration including the guard interval.*T*_{W}represents the duration of the window.

Adjust the length of the cyclic suffix via the window length setting property, with suffix lengths set between 1 and the minimum cyclic prefix length. While windowing improves spectral regrowth, it does so at the expense of multipath fading immunity. This occurs because redundancy in the guard band is reduced because the guard band sample values are compromised by the smoothing.

The following figures display the application of raised cosine windowing.

## Selected Bibliography

[1] Dahlman, E., S. Parkvall, and J. Skold. *4G LTE/LTE-Advanced for Mobile Broadband*.London: Elsevier Ltd., 2011.

[2] Andrews, J. G., A. Ghosh, and R. Muhamed. *Fundamentals of WiMAX*.Upper Saddle River, NJ: Prentice Hall, 2007.

[3] Agilent Technologies, Inc., “OFDM Raised Cosine Windowing”, http://wireless.agilent.com/rfcomms/n4010a/n4010aWLAN/onlineguide/ofdm_raised_cosine_windowing.htm.

[4] Montreuil, L., R. Prodan, and T. Kolze. “OFDM TX Symbol Shaping 802.3bn”, http://www.ieee802.org/3/bn/public/jan13/montreuil_01a_0113.pdf.Broadcom, 2013.

[5] “IEEE Standard 802.16^{TM}-2009,” New York: IEEE, 2009.

#### Introduced in R2014a

**Orthogonal frequency-division multiple access** (**OFDMA**) is a multi-user version of the popular orthogonal frequency-division multiplexing (OFDM) digital modulation scheme. Multiple access is achieved in OFDMA by assigning subsets of subcarriers to individual users. This allows simultaneous low-data-rate transmission from several users.

## Key features[edit]

The advantages and disadvantages summarized below are further discussed in the Characteristics and principles of operation section. See also the list of OFDM key features.

### Claimed advantages over OFDM with time-domain statistical multiplexing[edit]

- Allows simultaneous low-data-rate transmission from several users.
- Pulsed carrier can be avoided.
- Lower maximal transmission power for low-data-rate users.
- Shorter delay and constant delay.
- Contention-based multiple access (collision avoidance) is simplified.
- Further improves OFDM robustness to fading and interference.
- Combat narrow-band interference.

### Claimed OFDMA advantages[edit]

- Flexibility of deployment across various frequency bands with little needed modification to the air interface.
^{[1]} - Averaging interferences from neighboring cells, by using different basic carrier permutations between users in different cells.
- Interferences within the cell are averaged by using allocation with cyclic permutations.
- Enables single-frequency network coverage, where coverage problem exists and gives excellent coverage.
- Offers frequency diversity by spreading the carriers all over the used spectrum.
- Allows per-channel or per-subchannel power.

### Recognised disadvantages of OFDMA[edit]

- Higher sensitivity to frequency offsets and phase noise.
^{[1]} - Asynchronous data communication services such as web access are characterised by short communication bursts at high data rate. Few users in a base station cell are transferring data simultaneously at low constant data rate.
- The complex OFDM electronics, including the FFT algorithm and forward error correction, are constantly active independent of the data rate, which is inefficient from power-consumption point of view, while OFDM combined with data packet scheduling may allow FFT algorithm to hibernate during certain time intervals.
- The OFDM diversity gain and resistance to frequency-selective fading may partly be lost if very few sub-carriers are assigned to each user, and if the same carrier is used in every OFDM symbol. Adaptive sub-carrier assignment based on fast feedback information about the channel, or sub-carrier frequency hopping, is therefore desirable.
- Dealing with co-channel interference from nearby cells is more complex in OFDM than in CDMA. It would require dynamic channel allocation with advanced coordination among adjacent base stations.
- The fast channel feedback information and adaptive sub-carrier assignment is more complex than CDMA fast power control.

## Characteristics and principles of operation[edit]

Based on feedback information about the channel conditions, adaptive user-to-subcarrier assignment can be achieved.^{[2]} If the assignment is done sufficiently fast, this further improves the OFDM robustness to fast fading and narrow-band cochannel interference, and makes it possible to achieve even better system spectral efficiency.

Different numbers of sub-carriers can be assigned to different users, in view to support differentiated Quality of Service (QoS), i.e. to control the data rate and error probability individually for each user.

OFDMA can be seen as an alternative to combining OFDM with time-division multiple access (TDMA) or time-domain statistical multiplexing communication. Low-data-rate users can send continuously with low transmission power instead of using a "pulsed" high-power carrier. Constant delay, and shorter delay, can be achieved.

OFDMA can also be described as a combination of frequency-domain and time-domain multiple access, where the resources are partitioned in the time–frequency space, and slots are assigned along the OFDM symbol index, as well as OFDM sub-carrier index.

OFDMA is considered as highly suitable for broadband wireless networks, due to advantages including scalability and use of multiple antennas (MIMO)-friendliness, and ability to take advantage of channel frequency selectivity.^{[1]}

In spectrum sensing cognitive radio, OFDMA is a possible approach to filling free radio frequency bands adaptively. Timo A. Weiss and Friedrich K. Jondral of the University of Karlsruhe proposed a spectrum pooling system in which free bands sensed by nodes were immediately filled by OFDMA subbands.

## Usage[edit]

OFDMA is used in:

- the mobility mode of the IEEE 802.16 Wireless MAN standard, commonly referred to as WiMAX,
- the wireless LAN (WLAN) standard IEEE 802.11ax,
- the IEEE 802.20 mobile Wireless MAN standard, commonly referred to as MBWA,
- MoCA 2.0,
- the downlink of the 3GPPLong-Term Evolution (LTE) fourth-generation mobile broadband standard. The radio interface was formerly named
*High Speed OFDM Packet Access*(HSOPA), now named Evolved UMTS Terrestrial Radio Access (E-UTRA). - the Qualcomm Flarion Technologies Mobile Flash-OFDM
- the now defunct Qualcomm/3GPP2Ultra 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).

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