Naveen M B, Nidhish N, Prasanna M, Varun V
WiMAX is defined as Worldwide Interoperability
for Microwave Access by the WiMAX Forum. The WiMAX Forum
has more than 522 members comprising the major communication players, component
and equipment companies in the communications field including Accenture, Agilent, Acer, Intel,
Fujitsu, Motorola, Samsung, Sprint and AT&T. The WiMAX forum was formed in April 2001 to promote conformance and
interoperability of the IEEE 802.16 standard, officially known as
It should be noted that, WiMAX is not a technology that is used but is more specifically a Certification or an Approval stamp given to devices that are in conformity with certain standards of the IEEE 802.16 family of standards. WiMAX supports data rate of up to 75 Mbps and provides a range of about 50 kms for LOS propagation.
Wi-Fi devices operate in the unlicensed ISM band (Industrial Scientific and Medical Band) centered at 2.4GHz. This frequency band is also used by other devices. Hence the Wi-Fi devices are allocated a maximum power limit by FCC which limits their range or coverage. WiMAX was designed keeping in mind a WMAN. It is allocated a licensed frequency band and hence interference from other devices is relatively less. Correspondingly the range for WiMAX is more.
Further, in Wi-Fi, the media access controller ("MAC") uses CSMACA (Carrier Sense Multiple Access Collision Avoidance) scheme. In this media access scheme, a station first senses the medium, if it finds the medium busy; it backs off, waits for a random period of time and tries accessing the medium again. A packet is allowed up to maximum of about 10 retransmission attempts before it is dropped. Thus all subscriber stations that wish to pass data through a wireless “access point” (AP) are competing for the AP's attention on a random interrupt basis. This can cause distant nodes from the AP to be repeatedly interrupted by closer nodes, greatly reducing their throughput. This makes delay sensitive services such as Voice over IP (VoIP) or IPTV, which depend on a predetermined type of "quality of service" (QoS), difficult to maintain for large numbers of users. In contrast, the 802.16 MAC uses a scheduling algorithm, where the subscriber station only has to compete once (for initial entry into the network). After that it is allocated a time slot by the base station. The time slot can enlarge and contract, but it remains assigned to the subscriber station, meaning that other subscribers cannot use it. This scheduling algorithm is stable under overload and over-subscription (unlike 802.11). It can also be more bandwidth efficient. The scheduling algorithm also allows the base station to control Quality of Service parameters by balancing the time-slot assignments among the application needs of the subscriber stations.
Another limitation of Wi-Fi is that the devices need to be in Line Of Sight of each other. However WiMAX provides connectivity between network endpoints without the need for direct line of sight in favorable circumstances. It relies upon clever use of multi-path signals using Cyclic Prefix.
The most basic use of WiMAX is to provide Wireless broadband services at all times and at all places. It provides fixed and wireless connectivity to all devices in a cell range of 3 to 10 kilometers.
disasters like tsunami in
Figure 1: Typical Network using WiMAX 
The above figure shows typical applications supported by WiMAX. The products incorporated in the WiMAX family range from Mobile phones, Laptops, PDAs and many more. Some of the products having WiMAX technology built in within them are as shown below.
Figure 2: Typical products that use WiMAX technology 
(a) PDA and (b) Mobile WiMAX Measurement.
Unlike Wi-Fi which is operated in an Unlicensed Band, WiMAX is allotted fixed licensed bands for its operation by the FCC. Originally WiMAX was allocated the frequency band in the range of 10 to 66 GHz (802.16a). However, in 2004 it was further updated to 2 to 11 GHz (802.16d). 802.16e is the standard that is currently worked upon. It uses scalable OFDMA that allows multiple channels of different bandwidths and hence different number of sub carriers.
The features proposed by WiMAX Forum, the standardizing body for WiMAX, are as follows:
The standard documents can be found at http://www.ieee802.org/16/published.html viz. 1. IEEE Std 802.16-2004
2. IEEE Std 802.16e-2005
The details on the Physical layer can be found in Chapter 8 of the relevant document.
The frame structure in TDD WiMAX is as shown below:
Figure 3: Frame format 
The Downlink (DL) frame consists of transmission from the Base Station (BS) to the Mobile Stations (MS). The first symbol in the Downlink is the preamble. Preamble is chosen based on the segment number and the Cell ID. The data and control information are identified as “bursts”. The first burst is a control burst named the Frame Control Header (FCH). FCH gives information about Downlink MAP (DL-MAP). The DL-MAP gives information about the data bursts. So, every mobile station has to decode this DL-MAP in order to obtain information about the data burst allocated to it. It is to be noted that all bursts are rectangular in the DL.
The Uplink (UL) frame consists of the transmissions from the MS to the BS. The MS which wants to establish a contact with the BS will send a Ranging burst in the uplink. These are special control bursts and are always rectangular. The data bursts sent by the MS in the UL sub-frame can be non-rectangular.
The TTG denotes Transmit Time Gap which is the time gap between the present DL and UL sub-frames. The Receive Time Gap (RTG) denotes the time gap between two consecutive frames.
Transmitted Signal is
The transmission chain is as below:
Figure 4: Block Diagram of Transmitter Chain
Figure 5: Block Diagram of Randomizer Chain
The randomization is done per FEC block for all data (except for FCH). The seed for Randomization is fixed and is a binary vector given by: [LSB] 011011100010101 [MSB].
The purpose of randomization is to maintain better data integrity. Also the output of the randomizer has equal number of 0’s and 1’s for given binary FEC block input.
The mandatory type of FEC is Tail biting Convolution Coding i.e. the CC register is initialized to the last k-bits of the data at the FEC’s input. Here k denotes the constraint length.
Convolution Coding Block:
G1: 171(octal) for X, G2: 133(octal) for Y
The generator sequences G1 and G2 can be derived as below:
Paths which are chosen for binary summation are designated by ‘1’ and those which are not chosen are designated by ‘0’. Moving from right to left, for X output, the generator sequence will be 1001111. Appending 2 ‘0’ to the right, we get, 100111100. Reading this from right to left, G1 = 171(octal). Similarly, we can derive G2 = 133(octal).
The default rate of Convolution Encoding is ½, since for a given input; we get 2 outputs, X and Y.
Figure 6: Convolution Encoder 
The procedure used to implement puncturing in CC is shown below:
For example: For Rate ¾ CC, the bits X2 and Y3 are omitted from transmission, there by changing the rate to ¾. In this table, ‘1’ denotes the transmitted bit, and ‘0’ denotes the omitted bit.
Table 1: Illustration of Puncturing 
The optional FEC schemes available are Zero Tailed Convolution Coding (ZTCC), Block Turbo Coding (BTC) and Convolution Turbo Coding (CTC), Low Density Parity Check Codes(LDPC). The convolution decoding uses the standard Viterbi algorithm.
This is a block-interleaver with block size equal to the encoded block size in bits (Ncbps). For example, a 6 byte data after randomization and ½ rate CC would be of size 12 bytes i.e. 96 bits. So the interleaver size in such a case will be 96 bits. The interleaving is a 2 step permutation process. The first step ensures that adjacent coded bits are mapped onto non-adjacent subcarriers. The second step ensures that adjacent coded bits are mapped onto LSB or LSB of the constellation map alternatively to avoid long runs of low reliable bits.
The first permutation is given by the equation:
The second permutation is given by the equation:
s = Ncpc/2, Ncpc denotes the number of coded bits per sub-carrier (2, 4 and 6 for QPSK , 16-QAM and 64-QAM respectively.)
De-interleaving at the receiver:
Here, the first de-permutation is the reverse of the second permutation.
The second de-permutation is the reverse of the first permutation.
The different modulation schemes available are BPSK, QPSK, 16-QAM and 64-QAM. BPSK is used only for the preamble and pilot modulation only. BPSK scheme is not used for data.
Figure 7: BPSK Constellation
Normalization Constant here is c = 1.
Figure 8: QPSK Constellation 
Figure 9: 16-QAM Constellation 
64 – QAM:
Figure 10: 64-QAM Constellation ]
The frequencies allocated are divided into sub-carriers. Each sub-carrier denotes one frequency bin. A set of 48 data sub-carriers are defined to be a slot. The mandatory frequency processing scheme in 802.16e is Partial Usage of sub-channels (PUSC).
In downlink, 1 PUSC slot is 1 sub-channel X 2 symbols, where each sub-channel consists of 24 data sub-carriers. The basic unit of permutation in DL PUSC is a cluster. A cluster consists of 14 sub-carriers (12 data + 2 pilots). The cluster structure for an even and odd symbol is as shown below:
Figure 11: Cluster structure in DL PUSC 
Considering, 2048 point FFT, there are 184 Left Guard Frequencies and 183 Right Guard Frequencies. Also, there is a DC sub-carrier. Therefore, the number of data and pilot carriers will be 2048-184-183-1 = 1680. Hence, for a 2048 point FFT there will be 1680/14 = 120 clusters.
The carrier allocation to subchannels is performed using the following procedure:
1) Divide the subcarriers into the number of clusters (Nclusters) physical clusters containing 14 adjacent subcarriers each (starting from carrier 0). The number of clusters, Nclusters, varies with FFT sizes. These details for different FFT sizes can be found in the standard.
2) Renumbering the physical clusters into logical clusters using the following formula:
DL_PermBase parameter is provided by the MAC information elements
3) Allocate logical clusters to groups. The allocation algorithm varies with FFT sizes.
For FFT size=2048:
Divide the clusters into six major groups. Group 0 includes clusters 0-23, group 1 includes clusters 24-39, group 2 includes clusters 40-63, group 3 includes clusters 64-79, group 4 includes clusters 80-103 and group 5 includes clusters 104-119. These groups may be allocated to segments, if a segment is being used, then at least one group shall be allocated to it (by default group 0 is allocated to sector 0, group 2 is allocated to sector 1 and group 4 to is allocated to sector 2).
For FFT size=1024:
Divide the clusters into six major groups. Group 0 includes clusters 0-11, group 1 includes clusters 12-19, group 2 includes clusters 20-31, group 3 includes clusters 32-39, group 4 includes clusters 40-51 and group 5 includes clusters 52-59. These groups may be allocated to segments, if a segment is being used, then at least one group shall be allocated to it (by default group 0 is allocated to sector 0, group 2 is allocated to sector 1 and group 4 is allocated to sector 2).
For FFT size=512:
Divide the clusters into six major groups. Group 0 includes clusters 0-9, group 2 includes clusters 10-19 and group 4 includes clusters 20-29. These groups may be allocated to segments, if a segment is being used, then at least one group shall be allocated to it (by default group 0 is allocated to sector 0, group 2 is allocated to sector 1 and group 4 is allocated to sector 2).
For FFT size=128:
Divide the clusters into six major groups. Group 0 includes clusters 0-1, group 2 includes clusters 2-3 and group 4 includes clusters 4-5. These groups may be allocated to segments, if a segment is being used, then at least one group shall be allocated to it (by default group 0 is allocated to sector 0, group 2 is allocated to sector 1, and group 4 is allocated to sector 2).
4) Allocate sub-carriers to sub-channel in each major group is performed separately for each OFDMA symbol by first allocating the pilot carriers within each cluster, and then taking all remaining data carriers within the symbol and using the formula below
Nsubchannels is the number of subchannels (for PUSC use number of sub-channels in the currently partitioned Major group),
ps is the series obtained by rotating basic permutation sequence cyclically to the left s times,
Nsubcarriers number of data subcarriers allocated to a subchannel in each OFDMA symbol
- These can be obtained from the standard according to the FFT size.
DL_PermBase is an integer ranging from 0 to 31, which identifies the particular BS segment and is specified by MAC layer.
In uplink, 1 PUSC slot is 1 sub-channel X 3 symbols, where each sub-channel consists of 16 data sub-carriers. The basic unit of permutation in UL PUSC is a tile. A tile consists of 12 sub-carriers (8 data +4 pilots). The tile structure as shown below:
Figure 12: Tile Structure in UL PUSC 
The usable subcarriers in the allocated frequency band shall be divided into Ntiles physical tiles as defined in the standard. The allocation of physical tiles to logical tiles in subchannels is performed in the following manner:
Logical tiles are mapped to physical tiles in the FFT
Tiles(s,n) is the physical tile index in the FFT with tiles being ordered consecutively from the most negative to the most positive used subcarrier (0 is the starting tile index)
n is the tile index 0…5 in a subchannel
Pt is the tile permutation
s is the subchannel number in the range 0…Nsubchannels-1
UL_PermBase is an integer value in the range 0…69, which is assigned by a management entity
Nsubchannels is the number of subchannels for the FFT
After mapping the physical tiles in the FFT to logical tiles for each subchannel, the data subcarriers per slot
are enumerated by the following process:
1) After allocating the pilot carriers within each tile, indexing of the data subcarriers within each slot is performed starting from the first symbol at the lowest indexed subcarrier of the lowest indexed tile and continuing in an ascending manner through the subcarriers in the same symbol, then going to the next symbol at the lowest indexed data subcarrier, and so on. Data subcarriers shall be indexed from 0 to 47.
2) The mapping of data onto the subcarriers will follow the equation below. This equation calculates the subcarrier index (as assigned in item 1) to which the data constellation point is to be mapped.
Subcarrier(n,s) is the permutated subcarrier index corresponding to data subcarrier n is subchannel s,
n is a running index 0…47, indicating the data constellation point,
s is the subchannel number,
Nsubcarriers is the number of subcarriers per slot.
For example, for subchannel 1 (s = 1), the first data constellation point (n = 0) is mapped onto subcarrier (0,1) = 13, where 13 is the subcarrier with index 13. Considering the PUSC tile structure, it can be seen that this is the second indexed subcarrier on the second symbol within the slot. Similarly, for subchannel 3, the ninth data constellation point (n = 8) is mapped onto subcarrier (8, 3) = 47. This is the last indexed subcarrier of the third symbol within the slot.
Subcarrier enumeration shall not be applied to the slots in the UL-MAP indicated by either UIUC = 0 or UIUC = 12.
The time processing consists of IFFT and CP insertion. IFFT converts the sub-carriers in frequency domain to time domain. CP insertion provides the guard time in time domain. The symbol structure in time domain is as below:
Figure 13: Symbol Structure
The useful time in a symbol is referred to as “Tb”. This is the time length obtained after taking the Inverse Fourier Transform (IFFT) of the frequency domain OFDM/OFDMA carriers. Each symbol also has a guard time “Tg”, a copy of the last Tg samples of Tb pre-fixed to it. This guard time is also called the “cyclic prefix” (CP). The CP length is chosen based on the channel delay spread so that all the multi-paths die out within this time.
The frequency response of the pulse shaping filter is as shown below:
Here “α” denotes the roll-off factor which is taken as 0.25 as default value.
The diversity in WiMAX is achieved through Space Time Coding (STC) and Multi-Input Multi-Output (MIMO) schemes. Also, there is Adaptive Antenna System(AAS) which is combined with Space Division Multiple Access (SDMA) to provide diversity.
Following are some of the key challenges hindering the implementation of WiMAX.
The documents  and  provide an optimal receiver structure for OFDM systems and discuss a method for time and frequency synchronization. The synchronization is achieved in a 2 step process, a pre-FFT timing synchronization followed by post-FFT frequency synchronization. Detailed explanation on this process is discussed in  and .
Various solutions are proposed to this problem by various individual papers. One of the papers providing a suitable approach is . This paper explains the reduction of PAPR in OFDM systems using Combined Symbol Reduction and Inversion method.
The document  proposed by IEEE 802.16 Broadband Wireless Access Working Group gives a standard proposal for downlink preamble structure in WiMAX 802.16e. It claims that the currently used preamble structure has to be modified when used under a frequency reuse factor of “1”. This document gives a revised downlink preamble structure for 2048 point FFT in 802.16e. This eliminates the use of a big look-up table consisting of all possible preambles that has been defined in . The revised preamble structure is generated using a PN sequence generator and Walsh codes. According to the simulations and results provided in , such a structure enhances the capability of frame boundary detection in 802.16e. Hence the proposed solution seems to be a plausible one. For more details refer .
 IEEE Standard for Local and metropolitan area networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems
 IEEE Standard for Local and metropolitan area networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems
 Michael Speth, Stefan A. Fechtel, Gunnar Fock, and Heinrich Meyr, Optimum Receiver Design for Wireless Broad-Band Systems Using OFDM—Part I, IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 11, NOVEMBER 1999
 Michael Speth, Stefan Fechtel, Gunnar Fock, and Heinrich Meyr, Optimum Receiver Design for OFDM-Based Broadband Transmission—Part II: A Case Study, IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 4, APRIL 2001