## Subcarrier Assignment In Ofdm Signal

## 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

A power and subcarrier assignment algorithm is proposed in this paper for maximizing the energy efficiency in the single-relay multi-users orthogonal-frequency-division -multiplexing (OFDM) systems. Under the constraints of maximum total power and minimum transmission rate, we formulate a joint optimization scheme for subcarrier pairing and power allocation to maximize the energy efficiency. The Dinkelbach's method is used to depress the complexity and to transform the problem to a linear programming, then we use the dual decomposition approach solve the problem. In the premise of the system transmission rate, this algorithm uses the improved decode-and-forward (IDF) relay to maximize the system energy efficiency. Simulation results illustrate that, compared with the spectral-efficient maximization (SEM) algorithm, the energy-efficient maximization (EEM) algorithm proposed in this paper makes the energy efficiency not decline when the signal-to-noise radio (SNR) is at a high level. At the point where SNR is 10 dB and the number of subcarriers is 16, system energy efficiency is increased by 6.2% and 11.9% with the subcarrier pairing strategy and power allocation strategy respectively.

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