- Research Article
- Open Access

# Group-Orthogonal Code-Division Multiplex: A Physical-Layer Enhancement for IEEE 802.11n Networks

- Felip Riera-Palou
^{1}Email author and - Guillem Femenias
^{1}

**2010**:483758

https://doi.org/10.1155/2010/483758

© F. Riera-Palou and G. Femenias. 2010

**Received:**8 August 2009**Accepted:**21 March 2010**Published:**3 May 2010

## Abstract

The new standard for wireless local area networks (WLANs), named IEEE 802.11n, has been recently released. This new norm builds upon and remains compatible with the previous WLANs standards IEEE 802.11a/g while it is able to achieve transmission rates of up to 600 Mbps. These increased data rates are mainly a consequence of two important new features: (1) multiple antenna technology at transmission and reception, and (2) optional doubling of the system bandwidth thanks to the availability of an additional 20 MHz band. This paper proposes the use of Group-Orthogonal Code Division Multiplex (GO-CDM) as a means to improve the performance of the 802.11n standard by further exploiting the inherent frequency diversity. It is explained why GO-CDM synergistically matches with the two aforementioned new features and the performance gains it can offer under different configurations is illustrated. Furthermore, the effects that group-orthogonal has on key implementation issues such as channel estimation, carrier frequency offset, and peak-to-average power ratio (PAPR) are also considered.

## Keywords

- Orthogonal Frequency Division Multiplex
- Orthogonal Frequency Division Multiplex Symbol
- Channel Estimation Error
- Soft Information
- Complementary Cumulative Distribution Function

## 1. Introduction

The last decade has seen an explosive growth in the deployment of wireless local area networks (WLANs) making the concept of nomadic computing a reality. Nowadays, most of these networks are based on one of the flavours of the IEEE 802.11 family of standards. The original standard, usually referred to as 802.11 *legacy*, was introduced with limited success in 1997. Operating at 2.4 GHz, it was based on direct sequence spread spectrum modulation (DSSS) and supported a maximum data rate of 2 Mbps. Wide WLAN deployment was achieved by the enhanced versions, IEEE 802.11a and IEEE 802.11b, released in 1999. The 11b version uses a refined form of DSSS, based on complementary code keying (CCK), allowing data rates up to 11 Mbps to be realised. In contrast, the 11a version operates at 5 GHz and it is based on orthogonal frequency division multiplexing (OFDM) leading to data rates up to 54 Mbps. More recently, in 2003, another OFDM-based version operating at 2.4 GHz, namely, IEEE 802.11g, has been introduced supporting the same data rates as 11a. The newer OFDM-based versions remain backward compatible with DSSS-based systems by switching to CCK when connecting to 802.11b equipment. A comprehensive treatment of WLANs standards can be found in [1].

Very recently, the standardization of what should be the next generation of WiFi systems, named IEEE 802.11n, has been completed by the IEEE 802.11 High Throughput Task Group committee [2]. The new standard supports much higher transmission rates thanks to the use of multiple antenna technology and other enhancements such as the possibility of operating on a 40 MHz bandwidth (employing more subcarriers), transmission modes using a reduced guard interval and frame aggregation to minimize the overhead introduced by packet preambles. In its fastest mode, 802.11n is expected to reach a transmission rate of 600 Mbps. Despite all the introduced enhancements, it is mandatory for the new standard to remain compatible with multicarrier legacy systems (802.11a/b/g) and therefore, 802.11n-compliant devices should have means to fall back to older 802.11 specifications when necessary. The standard incorporates three mechanisms to exploit the available spatial diversity in different MIMO configurations, namely, space-time block coding (STBC) [3], spatial division multiplexing (SDM) [4], and cyclic delay diversity (CDD) [5]. By appropriately combining these three techniques, different operating points in the bit rate versus reliability plane can be attained making 802.11n-compliant systems extremely flexible and adaptable to the environment and quality of service (QoS) requirements.

The new 802.11n standard, like its predecessors 802.11a and 802.11g, deals with the severe frequency selectivity of the indoor radio channel using OFDM. This is a block transmission scheme where the incoming user symbols are grouped, serial-to-parallel (S/P) converted, and modulated onto different subcarriers. Choosing the subcarriers to be orthogonal, and assuming perfect synchronisation, allows the block of symbols to be transmitted in parallel with minimal bandwidth usage and without interference. The S/P conversion allows the transmission rate to be reduced to a fraction of the original user rate combating in this way the frequency selectivity of the channel.

A significant improvement over conventional OFDM was the introduction of multicarrier code division multiplex (MC-CDM) by Kaiser in [6]. In MC-CDM, rather than transmitting a single symbol on each subcarrier as in conventional OFDM, symbols are code-division multiplexed by means of orthogonal spreading codes and simultaneously transmitted onto the available subcarriers. Since each symbol travels on more than one subcarrier, thus providing frequency diversity, MC-CDM offers improved resilience against subcarrier fading. This technique resembles very much the principle behind multicarrier code-division multiple access (MC-CDMA) [7] where each user is assigned a specific spreading code to share a group of subcarriers with other users. It should be noted that MC-CDMA and MC-CDM differ in the use made of the subcarriers: while in MC-CDMA subcarriers are employed to multiplex different users, in MC-CDM subcarriers are used to multiplex symbols from a given user. In MC-CDM, user multiplexing is typically implemented by means of time division multiple access (TDMA) or orthogonal frequency division multiple access (OFDMA). Group-orthogonal MC-CDMA (GO-MC-CDMA) [8] has recently been introduced as a particular flavour of MC-CDMA whereby users are split in groups and each group exclusively uses a (small) subset of all the available subcarriers. The subcarriers forming a group are chosen to be as separate as possible in the available bandwidth in order to maximise the frequency diversity gain [8]. A GO-MC-CDMA setup can be seen as many independent MC-CDMA systems of lower dimension operating in parallel. This reduced dimension allows the use of optimum receivers for each group based on maximum likelihood detection at a reasonable computational cost. Group-orthogonality has also been proposed for the (uncoded) MC-CDM systems in [9] where results are given for group dimensioning and spreading code selection. The idea is to split suitably interleaved symbols from a given user into orthogonal groups, and then, apply a spreading matrix on each group with the objective of further exploiting the channel frequency diversity. By keeping the group size relatively small, optimum detection can be implemented to fully use the available diversity.

The goal of this paper is to present an overview on the application of a particular flavour of MC-CDM, namely, group-orthogonal CDM (GO-CDM), within the context of IEEE 802.11n. This technique has been shown to be useful in those cases where the transmitter does not have a priori information about the state of the channel, hence this paper focuses on this scenario. It is shown how GO-CDM is able to exploit the extra diversity offered by the additional transmit antennas and larger bandwidth to improve the error performance while keeping the transmission and reception architectures computationally feasible. The rest of the paper is structured as follows. In Section 2, a concise description of the basic architecture of IEEE 802.11n physical layer is presented, particular attention is paid to the different multiple transmit antenna configurations the standard allows. Section 3 explains in detail the concept of GO-CDM and why it is a desirable extension to IEEE 802.11n. A receiver architecture for the enhanced system is proposed in Section 5. Numerical results are presented in Section 6 showing the gains achieved through GO-CDM while demonstrating its robustness against key implementation issues such as channel/offset estimation errors and peak-to-average power ratio (PAPR) performance. Finally, Section 7 concludes the paper by summarizing the main results.

This introduction ends with a notational remark. Vectors and matrices are denoted by lower- and uppercase bold letters, respectively. The -dimensional identity matrix and the zero matrix (or vector) are represented by and , respectively. The symbol serves to denote a diagonal matrix with at its main diagonal and the operator defines the Kronecker product of two matrices. Finally, superscript is used to denote the transpose of a vector (or matrix).

## 2. IEEE 802.11n General Transmitter

## 3. GO-CDM Enhancement

The dashed boxes in Figure 1 detail the steps required to implement the GO-CDM extension. These processing stages take place on a per-stream basis just after the modulation mapping stage and comprise the following steps for an arbitrary spatial stream (with ).

- (1)
Segmentation of the incoming symbol stream (including pilot symbols) into blocks of length , and serial to parallel conversion (S/P) resulting in , with denoting the OFDM-symbol index and representing the number of OFDM-symbols per stream in a packet.

- (2)
- (3)
Group spreading by linear combining, , where is a orthonormal matrix, typically chosen to be a rotated and scaled Walsh-Hadamard matrix [9].

- (4)
Frequency interleaver , operating across the different OFDM-symbols composing the packet, designed to ensure that modulated symbols from different OFDM-symbols in each group have experienced uncorrelated noise samples upon deinterleaving at the receiver end.

Notice that the frequency interleaver implicitly performs the group subcarrier allocation taking care that subcarriers forming a group are frequentially well separated in order to maximise the frequency diversity gain. It is easy to show that, generally, this is achieved by choosing group subcarriers to be equispaced across the available bandwidth [8]. An special case to be taken into account is when CDD is employed, in which case a certain number of adjacent subcarriers are totally uncorrelated and therefore groups might be formed by combining both adjacent and well-separated subcarriers.

Despite the proven benefits of CDM in uncoded scenarios [6], the benefits of CDM-OFDM are rather limited when measuring the coded performance in typical operating scenarios conforming to IEEE 802.11a specifications. This is due to the large subcarrier correlation found in many wireless environments, which severely limits the achievable frequency diversity gain [11]. However, GO-CDM becomes attractive in IEEE 802.11n when multiple transmit and receive antennae are employed and/or the expanded bandwidth (e.g., 40 MHz) is operational. Under these circumstances, the subcarrier correlation within a group can be greatly reduced by picking up the subcarriers forming a group taking into account the spatial dimension and/or the available wider bandwidth. Numerical results presented in Section 6 show that, when using an adequate receiver, GO-CDM becomes again an attractive add-on, leading to significant performance gains.

## 4. Channel Model

which, when evaluated over the operating subcarrier frequencies, yields the vector where . Given the group-based operation of the whole system, it is also useful to define the channel frequency response for the th group as . Provided that group subcarriers are chosen equispaced across the available bandwidth in order to maximise frequency diversity [8, 9], all groups will have statistically identical behaviour. Without loss of generality, and since groups are orthogonal to each other, subsequent modeling and analysis can solely focus on a single group. Moreover, assuming the channel to be static over the duration of a packet encompassing several OFDM symbols, the time index can be dropped from this point onwards.

## 5. Receiver for GO-CDM-Enhanced IEEE 802.11n

### 5.1. Reception Equation

The reception equation for the baseband samples of an arbitrary group depends on the spatial processing technique in use, therefore, each case is treated separately.

#### 5.1.1. SDM

is the vector of transmitted symbols with representing the symbol vector transmitted on the th antenna, and denotes the receiver noise.

#### 5.1.2. STBC

with , where represents the Alamouti combining step [12]. The transmitted symbol vector in this case is given by . Finally, is the AWGN component. Note in (6) that the index is used to represent individual STBC blocks, each related to two consecutive OFDM sampling instants (e.g., ). It is easy to check that the matrix affecting symbol group in (6), that is, , has a 2-block diagonal structure thanks to the Alamouti code orthogonality. This implies that the symbols transmitted over the two time instants ( and ) can be independently detected without any performance degradation.

#### 5.1.3. CDD

and represents the additive noise component. Notice that, due to the CDD component, this is equivalent to transmit the information stream over a channel derived from a delay profile with increased frequency selectivity.

It is important to mention that the data symbols to be transmitted , are suitably scaled to have power , allowing the operating signal to noise ratio to be written as .

### 5.2. Iterative Detection and Decoding

A naive implementation of the ML detector would be computationally very demanding as its complexity grows exponentially with , and , therefore, alternatives should be sought. The list sphere detector (LSD) [14, 15] is an efficient method to conduct an exhaustive search among a set of candidates (i.e., ML detection) producing not only the most likely estimate but also a list with the closest candidates, which can then be used to form likelihood ratios (LLRs) for each bit (i.e., soft information). Moreover, this detector not only produces soft information but it can also incorporate any available a priori information (also in the form of LLRs) into the detection process. This feature, in combination with a soft-input soft-output channel decoder, allows the implementation of iterative reception schemes. Three factors play a role in limiting the computational complexity of this detector: first, a subset of candidates (the most likely ones), rather than an exhaustive list, is used when computing the LLRs [14], second, the detection is conducted on a per-group basis whose size, as shown in [9], can be kept relatively small ( ) and last, group independence facilitates the parallelisation of the detection process.

where the symbols and represent the sets of bit vectors whose th position is a "+1'' or " '', respectively. The vector contains the a priori LLR for each bit in except for the th bit. All a priori LLRs are assumed to be zero for the first iteration. Moderate values of and/or make the sets and extremely large, making the search in (14) computationally unfeasible. To address this issue, LSD limits the search to the sets and where is the set containing the bit vectors corresponding to the group candidates closer, in an Euclidean sense, to the received group vector, that is, where with being the group candidates for which is smallest.

Notice in Figure 2 that each group detector, apart from the received samples , gets as input the a priori LLRs for the bits in the group ( ), which will obviously be zero for the first iteration. In posterior iterations, the a priori LLRs can be incorporated into the information provided by the LSD to yield the a posteriori LLRs for each group ( ). The LLR De-grouping block takes care of gathering the LLRs produced by the detector for the different OFDM symbols composing the packet and structure them in the form of spatial streams . As typically done in iterative schemes, only new (e.g., extrinsic) information is interchanged among the different subsystems. To this end, by subtracting the interleaved extrinsic information generated by the maximum a posteriori (MAP) decoder properly structured in streams , the extrinsic information of the detection process is formed . Deinterleaving and spatial deparsing of results in the a priori information for the MAP decoder, labeled in Figure 2 as . The receiver deinterleaving ( )/interleaving( ) processes include both the IEEE 802.11n (de)interleaver and the one proposed in the GO-CDM extension. The MAP decoder returns the LLRs of the information bits to be sliced in order to form the final bit estimates and also produces LLRs for the coded bits , which can then be fed back for the next iteration.

Obviously, the overall complexity of the reception process depends on the number of iterations conducted. A simplified noniterative receiver can be obtained by discarding the soft information (e.g., list of candidates) and relying only on the ML estimates provided by the LSD. After symbol slicing and proper restructuring, these can be supplied to a conventional hard decision Viterbi decoder.

## 6. Numerical Results

Simulation results are now presented for three different IEEE 802.11n configurations all making use of MIMO processing. Without loss of generality antenna elements at Tx/Rx are assumed to be sufficiently spaced apart so as to make the spatial correlation negligible. Channel Model E-NLOS [16] has been used in all simulations. This channel profile corresponds to a large office environment and it is made of 38 independent paths distributed among 4 clusters, characterized by an delay spread of 100 ns. Quasi-static fading has been assumed, that is, each packet sees an independent channel realisation that remains fixed for the whole packet. Initially, perfect channel estimation and no carrier frequency offset are assumed while later the effects of these implementation inaccuracies are taken into account.

Results are presented for three different detection strategies, namely, Viterbi with hard decisions, noniterative MAP (i.e., soft Viterbi), and MAP with two additional iterations. The LSD detector was upper-limited to candidates when generating the soft information (notice that for some of the studied configurations this bound was sufficient to take into account all candidates in the search space). For the sake of clarity, when GO-CDM is active, the number of subcarriers per group has been fixed to , which provides a good compromise between performance enhancement and detection complexity [9].

In any multicarrier system, there are implementation issues that should be taken into account when evaluating their performance. Three important effects that must be considered are channel estimation imperfections, channel frequency offset (CFO) due to synchronisation mismatch between transmitter and receiver, and peak to average power ratio (PAPR).

It is fair to recognize that GO-CDM is not effective in all situations. When there are many (uncorrelated) antennas at the receiver, the large amount of spatial diversity available renders the extra frequency diversity provided by GO-CDM marginal. Also, when the channel is markedly frequency nonselective, GO-CDM does not provide significant gains, in very much the same way that MIMO gains are greatly diminished when the antenna elements exhibit large correlations. The point to be noted with this work is that GO-CDM is an attractive option in many configurations, specially on those where the number of receive antennas is roughly the same as the number of transmitted spatial streams. Moreover, GO-CDM, by properly adjusting the spreading factor , can act as a performance/complexity knob.

## 7. Conclusions

In this paper, the use of GO-CDM in IEEE 802.11n networks as a means to improve performance has been proposed. It has been shown that this technique can exploit the availability of multiple transmit antennas (and its various MIMO processing mechanisms) and larger spectrum bandwidth, not available in previous WLANs standards. A soft iterative receiver, based on the LSD algorithm, has been proposed. This detector has been shown to be able to exploit the additional frequency diversity provided by GO-CDM yet remaining computationally feasible. Numerical results for different configurations, with parameters derived from the new standard, show that GO-CDM is able to offer significant performance gains over the conventional IEEE 802.11n specification. Implementation issues like channel estimation errors, carrier frequency offset and peak to average power ratio have been shown to further reinforce the potential of GO-CDM.

Finally, it is important to stress that the techniques presented in this paper could also be applied to other multicarrier-based systems such as 3GPP-LTE, WiMax, or the proposal developed within the European project WINNER. In this latter system, where bandwidths in the order of 100 MHz are being considered, GO-CDM would allow large frequency diversity gains to be realised boosting in this way its performance.

## Declarations

### Acknowledgments

This paper has been supported in part by MEC and FEDER under Project COSMOS (TEC2008-02422), Govern de les Illes Balears under Grant PCTIB-2005GC1-09, and a Ramon y Cajal fellowship (partially funded by the European Social Fund), Spain.

## Authors’ Affiliations

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