Throughput Analysis of Band-AMC Scheme in Broadband Wireless OFDMA System

Demands for high bandwidth multimedia information in the mobile environment have spawned the development of various mobile broadband wireless access (BWA) systems for high-speed communication. Particular examples include the mobile WiMAX, which is based on the IEEE 802.16e Mobile Wireless MAN technologies, and 3GPP's new standards for 3G long-term evolution (LTE). The IEEE 802.16e standard aims to unify the underlying solutions [1], specifying two flavors of OFDM systems: one simply identified as Orthogonal Frequency Division Multiplexing (OFDM), the other Orthogonal Frequency Division Multiple Access (OFDMA). OFDMA is considered to be one of the most spectrally efficient multiple access alternatives for mobile BWA systems. It has the ability to dynamically assign a subset of the subcarriers to individual users, attuning the technology to the particular mobility requirement. This scheme fully takes advantage of multiuser diversity, in conjunction with the frequency diversity inherent in the OFDM scheme. In fact, the mobile BWA system must contend with fluctuations across the frequency band, in addition to time variations. In the multiuser scenarios upon a multicarrier system, a subcarrier in deep fading to one user may be of good quality to another user, which lends support to dynamic subcarrier allocation on improving system throughput [2–5]. The different signal quality (e.g., carrier-to-interference ratio or CIR) seen at each subcarrier governs the capacity of each subcarrier. Ideally, a different modulation and coding level should be selected for each subcarrier in order to maximize the capacity. This particular approach is referred to as an adaptive modulation and coding (AMC) scheme.

For the fast selective AMC scheme, Channel Quality Indication (CQI) must be reported immediately for all subcarriers within the entire bandwidth, which allows for selecting the appropriate modulation and coding level for each subcarrier without incurring a channel mismatching problem. It usually involves unrealistic feedback overhead, especially under the fast fading channel. Fortunately, however, recent broadband measurements indicate that per-subcarrier information is typically not necessary [2]. Namely, the feedback coefficient is sufficient for a group of several subcarriers in the fast selective AMC process, while the coherence bandwidth of the channel is larger than that of subband. In general, further enhancement can be realized by providing CQI reports a set of optimum subcarriers. This particular approach is specified as a band-AMC mode in IEEE 802.16 Task Group e standard. Due to the frequency-selective characteristics of a time-varying nature in the broadband channel, it is not straightforward to evaluate the average throughput of the OFDMA system, without resorting to the computer simulation. Furthermore, it becomes more involved as many parameters are configured to optimize system performance. For example, the number of bands selected for reporting CQI information is one important parameter that governs overall average system throughput.

The objective of this paper is to develop an analytical means of evaluating the maximum system throughput of band-AMC mode. In particular, practical features of resource management for the OFDMA system are carefully modeled within the proposed analytical framework. We consider order statistics to model the statistical nature of multiuser/multiband diversity in the OFDMA system. Order statistics have been a unique research area for statisticians for some time, with special application in statistical estimation. Recently, a more general case of order statistics has captured the attention of researchers in the area of signal processing and wireless communication systems [6, 7].

The remainder of this paper is organized as follows. In Section 2, the operational concept of band-AMC mode, is described, formulating the scheduling problem under consideration. In Section 3, the maximum average throughput of the band-AMC system is derived, using the order statistics. Then, Section 4 presents the numerical results to demonstrate the advantage of using the band-AMC mode with the sufficient number of CQI reports for the selection bands. Furthermore, the maximum throughput bounds that depend on the multi-user diversity and multiband effect are provided. Finally, concluding remarks are provided in Section 5.

In this section, the average throughput performance of the band-AMC system is evaluated. It is assumed that a full buffer traffic model is used, that is, infinite traffic waiting for each user. Depending on the channel quality, it is assumed that each user belongs to one of groups. The channel quality of all users in the same group is identically distributed. Let and represent the total bandwidth and coherence bandwidth, respectively. Then, the total number of independent subbands can be given approximately by . Note that the optimal number of subbands may be greater than or equal to . For example, it has been demonstrated in [5] that the optimum contribution to performance improvement is found for , where denotes the bandwidth of subband. Nevertheless, can be still fixed to the minimum number of independent subbands, that is, is just large enough to warrant the independence of channel qualities between the adjacent subbands. Determining a proper is beyond the scope of this paper.

Now let a vector represent the sampled values of a channel quality for user in group . Note that is not always necessarily equal to . Therefore, we consider two different cases: and For the case of there is no correlation between those samples, that is, the channel quality for each subband is independent of each other. Denoting as the expected value of CIR for band in group , then the following probability density function (PDF) for CIR of the corresponding band under the condition that can be obtained:

(4)

For the diversity channel, meanwhile, CIR for each user in group is given by taking average of CIRs for all subbands, that is, . In the case that are identically distributed over a whole bandwidth, turns out to be the normalized random variables.

The design of band-AMC system depends on the bandwidth of each subband, channel characteristics, the number of users served by band-AMC mode, the feedback overhead to report the CQI of subbands, and so on. Consider the situation that the bandwidth of subband, , chosen by band-AMC system is subject to the nonflat fading characteristics. This particular situation can be specified by for , which corresponds to the case of Then, the observed channel quality for each subband cannot be represented by (4). When the bandwidth is divided into several adjacent segments, each with the bandwidth of , it can be now approximated as , . Then, (4) is replaced with the following PDF:

(5)

where denotes the convolution operation: .

3.1. CQI Report for Band-AMC Mode

Suppose that every band-AMC user feedbacks -best CQI reports to the base station in every scheduling interval. To represent the chance that each subband is selected for feedback, define a band selection vector for user as follows:

(6)

where is the probability that user in group has a preference to the band within chances, that is, . In the case that samples in the subband are independent and identically distributed, it is obvious that However, consideration must be taken, that the dependence assumption is retained when the 's are no longer identically distributed, that is, for the inid case.

Let denote the CDF of -order statistics, exclusive of band within the entire band pool, where represents a band set of the system, that is, . Hence, the probability that the user in group selects the band is given by

(7)

The CDF of the -order statistic is generalized to

(8)

where the summation extends over all permutations of for which and [10]. For the distribution of order statistics in the inid case, however, the density of every possible order must be found out separately on a case-by-case basis, which makes (8) involve the complicated and tedious calculation, especially as the number of bands increases. Fortunately, an alternative method for computing has been provided by Cao and West [7]. It is acceptable to have results and recurrence relations valid in the iid case, requiring only simple modification to hold quite generally. For convenience of notation, let denote the . Starting with

(9)

they prove the following relation:

(10)

where , and

(11)

with

(12)

Now from (7) and (9)–(12), the band selection vector can be directly determined. It is obvious that is obtained with , which corresponds to the case of full CQI feedback.

3.2. Maximum System Throughput in Band-AMC Mode

Let denote the total number of users in group . The probability that band is simultaneously selected by users can be written as follows:

(13)

where .

Similarly, a vector is defined to represent the distribution of order statistics in the corresponding band j. By means of the max C/I-scheduling scheme, the received signal quality is then expressed as

(14)

In general, the optimum signal quality in band is expected as the number of users selecting the corresponding band increases. By order statistics, the conditional CDF of the received CIR in band given can be calculated as

(15)

where and

(16)

Therefore, the CDF of the received CIR in band can be expressed as

(17)

When the existing cellular systems are considered, in which multi-path fading is dominant, the rate function of the Shannon type with the log-based linear relationship between rate and CIR may not be valid. In practice, a link-level simulation is performed in order to determine the required CIR for a given data rate, so as to meet the target frame error rate (FER). Let denote a set of MCS levels with the corresponding data rates , with the data rate for MCS level m defined by . To meet the given level of FER, a range of CIR is prescribed for each data rate . More specifically, the CIR required for is prescribed as . For the given target FER, the average system throughout of band is defined as follows:

(18)

Considering overall bandwidth, therefore, the average throughput of band-AMC system is provided by .

Extensive numerical solutions are studied for evaluating a theoretical system throughput in this section. The multi-users diversity effect on system level performance are investigated by varying the number of user groups, for example, 3. For users are divided into 3 groups with a mix of 0.2:0.3:0.5 Furthermore, the number of total active users ranges from 10 to 70, that is, . We consider the OFDMA parameters for the WiBro system, a mobile version of WiMAX, derived from the IEEE 802.16d wireless MAN standard [1]. The corresponding parameters are listed in Table 1. Furthermore, an example of the transmission scheme for AMC under investigation is summarized in Table 2. In Table 2, data rate is for downlink transmission when the ratio of DL:UL is given by 27:15. It also specifies the minimum required CIR to achieve a target FER of 1%.

Parameters	Value
Frequency	2.3 GHz
System bandwidth	8.75 MHz
FFT size	1024
Number of data subcarriers	768
Number of symbols per frame	Downlink: 27 symbols
	Uplink: 15 symbols
Channel coding	Convolutional turbo code
Frame duration	5 ms
Symbol duration	115.2 s
Number of subcarriers per subchannel	48
Number of subcarriers per CQI channel	48

MCS level	Modulation	Coding rate	CIR for 1% FER (dB)	Data rate*   (kbps)
1	QPSK	1/12	2.2	614.4
2	QPSK	1/6	0.1	1,228.8
3	QPSK	1/3	2.9	2,457.6
4	QPSK	1/2	6.0	3,686.4
5	QPSK	2/3	10.2	4,915.2
6	16QAM	1/2	10.9	7,372.8
7	16QAM	2/3	15.2	9,830.4
8	64QAM	2/3	20.2	14,745.6
9	64QAM	5/6	28.6	18,432

Data Rate is for DL transmission when the ratio of DL:UL is given by 27:15.

It is important to note that system throughput is dependent on not only the mean channel quality but also in the user distribution. In the current numerical analysis, we consider the scenarios with the mean channel qualities given by for and respectively. To impartially compare the performance according to various users' distributions, the mean channel quality on the same overall cases needs to be kept. Furthermore, it is assumed that while and 3, respectively.

Figures 3 and 4 present a comparison of average throughout for the band-AMC and diversity schemes by varying the number of users with for and respectively. From these results, a multiuser diversity gain is clearly observed, that is, the system throughput increases with the number of users in the system. Furthermore, it is shown that the band-AMC mode outperforms the diversity mode, when each user provides a sufficient number of band CQI reports. For the results in Figure 3, more than 20% of throughput is improved by the band-AMC mode with a full CQI report, that is, , over the diversity mode. For a partial band CQI report of , however, the band AMC mode performs worse than the diversity mode, suffering from a significant performance loss as compared to that with full band CQI feedback. For , the band-AMC mode outperforms the diversity mode as long as there are a sufficient number of users, implying that its performance is mainly governed by the multi-user diversity gain.

As for it is observed from Figure 4 that not much multiuser gain can be achieved with the diversity mode. We note that band-AMC mode is almost always superior to the diversity mode, even with a very small number of band CQI reports, as long as there are sufficient number of users in the system. It is also found that the maximum multiuser and multiband diversity gain has been achieved by the band-AMC mode, corresponding to an increase in the average throughput of 2.54 Mbps.

Let us now consider a CQI signaling overhead cost associated the band-AMC mode. If the CQI report period is 30 milliseconds, overhead for full band CQI feedback in WiBro can be approximated by (%). For example, feedback overhead in the uplink becomes 10.41% when and . In Figures 3 and 4, note that a diminishing gain is observed as the number of band CQI reports increases. Taking the overhead associated with the CQI report for each band into account, a reasonable number of CQI reports exists to warrant the maximum system throughput, for example, μ = 5 and 6, with a sufficient number of band-AMC users. Adopting the same test parameters as in Figure 4, the mean channel quality of each band for each group is given by Figure 5.

Figure 6 presents the probability that each subband is not chosen by any user, that is, the probability of unfilled band, computed for the cases of iid and inid, respectively. From a practical viewpoint, depending on the amount of band CQI reports for each user and the number of users, some subbands may be not selected such that a part of bandwidth is wasted. This particular point is obviously observed in Figure 6. When and more than 40% of the entire bandwidth is not used. Furthermore, it is found that there is not much difference between the iid case and inid case.

Figure 7 presents a throughput performance as varying the number of bands, that is, and 12, when and As expected, the band-AMC system with 12 bands demonstrates the best throughput performance. Meanwhile, as the number of bands decreases, throughput curves approach that of the diversity scheme. Since the multi-band diversity effect mainly depends on the number of independent subbands, note that no further improvement will be found even if is greater than

In this paper, the maximum possible throughput of the band-AMC mode in the OFDMA system has been numerically evaluated using the order statistics for various system-level parameters, including the number of band CQI reports, the total number of available bands, and mean channel qualities. A conventional system-level simulation involves too much complexity associated with various physical parameters and thus the proposed analytical approach will be useful for dimensioning the system and configuring the optimal set of parameters. Our numerical results confirm the multiuser and multiband diversity gain that can be achieved by the band-AMC mode. It has been shown that the band-AMC mode outperforms the diversity mode only by providing the channel qualities for a subset of good subbands. Depending on the average CINR for each subband and how fast the channel varies for individual subband, for example, measured in terms of standard deviation of CINR for each subband, the band-AMC and diversity modes can be adaptively combined, so as to maximize the overall system throughput. Toward that end, the current analytical framework can be a useful basis for operation of the band-AMC mode under the varying traffic and CQI report constraints.