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:
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:
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:
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
The CDF of the
-order statistic
is generalized to
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
they prove the following relation:
where
, and
with
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:
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
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
where
and
Therefore, the CDF of the received CIR in band
can be expressed as
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:
Considering overall bandwidth, therefore, the average throughput of band-AMC system is provided by
.