**4. Subcarrier permutations**

To create an OFDM symbol in the frequency domain, the mapping of the physical resources (subcarriers) to the logical channels (sub-channels) has to be done. This is not only aimed at assigning the right modulated signals with the right transmission blocks but also meant at reducing sub-channel sensitivity with regards to spectral fading. Permutation scheme is used to carry out this mapping . This ensures a sub-channel can use its assigned subcarrier only for a finite number of symbols and then permutated to another subcarrier. In general 802.16\* suite of standards define a number permutation schemes for varied requirements ideally to introduce a robustness that minimizes interference. These schemes could be [2, 3]:


Distributed permutations use the full spectral diversity of the subcarriers for the permutation of a sub-channel while adjacent permutations assign adjacent sub carriers to a sub-channel. The distributed mode is ideal for optimizing a network towards a more robust spectral sensitivity. On the other hand the adjacent sub carriers allow faster system feedback and permutation processing thus better suited for fixed/ portable devices with increased throughput [7].

#### **4.1 Segmentation and sub-channelization**

A sub-channel is a logical transmission resource of a collection of physical subcarriers. A permutation scheme defines the number and pattern for mapping the subcarriers to the subchannels. A sub-channel is constant in time over a transmission block and maybe allocated to different connections over time. However, subcarriers of a sub-channel do not have to be adjacent. Certain factors such as size of data block to be transmitted, the modulation scheme and the coding rate may determine the amount of sub-channels allocated to a specified data block. It's important to note that a particular data region of users always uses the same burst profile . A burst profile is defined by a chosen modulation scheme, coding rate and FEC type while a data region of users refers to the contiguous set of sub-channels assigned to a user(s) in frequency and time [8,9].

An optional alternative to sub-channelization is segmentation shown in Fig. 7 that aims to divide a transmission channel into groups of sub-channels with the following properties:


#### **4.2 FUSC permutation**

In the Fully Used Sub-Channelization permutation shown in Fig. 8, all subcarriers are used in all the sub-channels distributed evenly across the entire frequency band. FUSC is only permutated in the Downlink (DL). The set of Pilot subcarriers, which are assigned first, is divided into two constant and two variables sets. The difference in both sets lies in the indexing of the pilot subscribers. With the variable set the index changes from one OFDM symbol to the next, while the index stays constant with the constant set. The variable sets allows for accurate estimation of channel response at the receiver especially in channels with larger delay spread or small coherence bandwidth. In cases where FUSC is implemented with transmit diversity, say of order n, then each antenna is allocated an nth each of the variable and constant sets of pilot subscribers [4, 9).

Fig. 8. FUSC Permutation

It's instructive to note that each sub-channel has a max of 48 subcarriers across all FFT sizes as shown in Table 2. The 802.16d does NOT support FUSC/PUSC and thus the 256 FFT size is not ignored in the presentation.


Table 2. Parameters of FUSC Permutation

## **4.3 PUSC permutation**

Partially Used Sub-Channelization is based on the concept of segmentation with subcarriers allocated to a segment first then to the sub-channel belonging to the dedicated segment. PUSC is similar to FUSC but with the extra advantage of permutation both in the UL and DL. The subcarriers are first subdivided into groups of 6 then clustered, save for the null subcarrier. The clusters consist of fourteen adjacent subcarriers spanned over two OFDM symbols. Permutations are thus done within groups independently of the others [12].

In the DL, each cluster's subcarriers are divided into 24 data subcarriers and 4 pilot subcarriers . The clusters are then pseudo-randomly renumbered using a scheme that redistributes the logical identity of the clusters, then divided into six groups, with the first one-sixth of the clusters belonging to group 0, and so on. A sub-channel is created using two clusters from the same group [9]. The segmentation can be done to allocate all or a subset of the six groups to a given transmitter. If this is done over sectors of a BS a better frequency reuse can be achieved.

In the UL, the subcarriers are first divided into various tiles, consisting of 4 subcarriers over three OFDM symbols. The subcarriers within a tile are divided into eight data subcarriers and four pilot subcarriers


Table 3. PUSC Permutation - DL

#### **4.4 AMC permutation**

Advanced Modulation and Coding uses adjacent subcarriers to build a sub-channel. As in the TUSC scheme, it is mainly utilized in the AAS networks. In spite of some loss of frequency diversity, exploitation of multiuser diversity is easier and robust. Multiuser diversity provides significant improvement in overall system capacity and throughput, since a sub-channel at any given time is allocated to the user with the highest SNR/ capacity in that sub-channel [12].

The wireless channel is dynamic and diverse users get allocated on the sub-channel at different instants in time uncorrelated channel conditions. In AMC permutation, nine adjacent subcarriers with eight data subcarriers and one pilot subcarrier are used to form a bin, as shown in Fig. 9. An AMC sub-channel consists of six contiguous bins from within the same band where four adjacent bins in the frequency domain constitute a band . An AMC subchannel thus consists of one bin over six consecutive symbols, two consecutive bins over three consecutive symbols or three consecutive bins over two consecutive symbols [9, 10].

Fig. 9. AMC Permutation
