WiMAX systems use adaptive modulation and coding in order to take advantage of fluctuations in the channel. The basic idea is quite simple: Transmit as high a data rate as possible when the channel is good, and transmit at a lower rate when the channel is poor, in order to avoid exces- sive dropped packets. Lower data rates are achieved by using a small constellation, such as QPSK, and low-rate error-correcting codes, such as rate convolutional or turbo codes. The higher data rates are achieved with large constellations, such as 64 QAM, and less robust error- correcting codes; for example, rate convolutional, turbo, or LDPC codes. In all, 52 configu- rations of modulation order and coding types and rates are possible, although most implementa- tions of WiMAX offer only a fraction of these. These configurations are referred to as burst profiles and are enumerated in Table 8.4.
A block diagram of an AMC system is given in Figure 6.7. For simplicity, we first consider a single-user system attempting to transmit as quickly as possible through a channel with a vari- able SINR—for example, due to fading. The goal of the transmitter is to transmit data from its queue as rapidly as possible, subject to the data being demodulated and decoded reliably at the receiver. Feedback is critical for adaptive modulation and coding: The transmitter needs to know the “channel SINR” , which is defined as the received SINR divided by the transmit power
, which itself is usually a function of . The received SINR is thus .
Figure 6.8 shows that by using six of the common WiMAX burst profiles, it is possible to achieve a large range of spectral efficiencies. This allows the throughput to increase as the SINR increases following the trend promised by Shannon’s formula . In this case, the lowest offered data rate is QPSK and rate 1/2 turbo codes; the highest data-rate burst profile is with 64 QAM and rate 3/4 turbo codes. The achieved throughput normalized by the bandwidth is defined as
K log logK
logK
1/2 3/4
γ γr
Pt γ γr =Ptγ
C=log2(1+SNR)
Figure 6.5 PDF of , the maximum of the K users’ channel gains
(a) (b)
Figure 6.6 For various numbers of users K, (a) average capacity and (b) QPSK bit error rate
Figure 6.7 Adaptive modulation and coding block diagram
0 1 2 3 4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
hmax
p(h max)
K = 1,2, ... , 10
hmax
0 5 10 15 20 25 30
0 2 4 6 8 10 12
Capacity (bps/Hz)
SNR (dB) K = 1, 2,...,10
0 5 10 15 20 25 30
10−25 10−20 10−15 10−10 10−5 100
Bit Error Rate in QPSK
SNR (dB) K = 1, 2,...,10
ECC Encoder
Symbol Mapper
Power Control
Channel
SINR = Demod Decoder
Channel Estimation Adaptive Modulationand Coding
Controller Feedback Channel:
PER,
Queue Select
Code
Select
Const. Pt( ) Bits
In
Bits Out Transmitter
Receiver
, (6.3) where BLER is the block error rate, is the coding rate, and M is the number of points in the constellation. For example, 64 QAM with rate 3/4 codes achieves a maximum throughput of 4.5bps/
Hz, when ; QPSK with rate 1/2 codes achieves a best-case throughput of 1bps/Hz.
The results shown here are for the idealized case of perfect channel knowledge and do not consider retransmissions—for example, with ARQ. In practice, the feedback will incur some delay and perhaps also be degraded owing to imperfect channel estimation or errors in the feed- back channel. WiMAX systems heavily protect the feedback channel with error correction, so the main source of degradation is usually mobility, which causes channel estimates to rapidly become obsolete. Empirically, with speeds greater than about 30 km/hr on a 2,100MHz carrier, even the faster feedback configurations do not allow timely and accurate channel state informa- tion to be available at the transmitter.
A key challenge in AMC is to efficiently control three quantities at once: transmit power, transmit rate (constellation), and the coding rate. This corresponds to developing an appropriate policy for the AMC controller shown in Figure 6.7. Although reasonable guidelines can be developed from a theoretical study of adaptive modulation, in practice, the system engineer needs to develop and fine-tune the algorithm, based on extensive simulations, since performance depends on many factors. Some of these considerations are
Figure 6.8 Throughput versus SINR, assuming that the best available constellation and coding configuration are chosen for each SINR. Only six configurations are used in this figure, and the turbo decoder is a MAP decoder with eight iterations of message passing.
0 2 4 6 8 10 12 14 16 18 20
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
SINR (dB)
Throughput (bps/Hz)
QPSK R1/2
QPSK R3/4
16 QAM R1/2
16 QAM R3/4
64 QAM R2/3
64 QAM R3/4
Shannon Limit
max log
T = (1−BLER)rlog2(M) bps/Hz r≤1
BLER→0
• BLER and received SINR: In adaptive-modulation theory, the transmitter needs to know only the statistics and instantaneous channel SINR. From the channel SINR, the transmitter can determine the optimum coding/modulation strategy and transmit power [8]. In practice, however, the BLER should be carefully monitored as the final word on whether the data rate should be increased (if the BLER is low) or decreased to a more robust setting.
• Automatic repeat request (ARQ): ARQ allows rapid retransmissions, and hybrid-ARQ generally increases the ideal BLER operating point by about a factor of 10: for example, from 1 percent to 10 percent. For delay-tolerant applications, it may be possible to accept a BLER approaching even 70 percent, if Chase combining is used in conjunction with H- ARQ to make use of unsuccessful packets.
• Power control versus waterfilling: In theory, the best power-control policy from a capacity standpoint is the so-called waterfilling strategy, in which more power is allocated to strong channels and less power allocated to weak channels [11, 12]. In practice, the opposite may be true in some cases. For example, in Figure 6.8, almost nothing is gained with a 13dB SINR versus an 11dB SINR: In both cases, the throughput is 3bps/Hz. Therefore, as the SINR improved from 11dB to 13dB, the transmitter would be well advised to lower the transmit power, in order to save power and generate less interference to neighboring cells [3].
• Adaptive modulation in OFDMA: In an OFDMA system, each user is allocated a block of subcarriers, each having a different set of SINRs. Therefore, care needs to be paid to which constellation/coding set is chosen, based on the varying SINRs across the subcarriers.
6.3 Resource-Allocation Techniques for OFDMA
There are a number of ways to take advantage of multiuser diversity and adaptive modulation in OFDMA systems. Algorithms that take advantage of these gains are not specified by the WiMAX standard, and all WiMAX developer are free to develop their own innovative proce- dures. The idea is to develop algorithms for determining which users to schedule, how to allo- cate subcarriers to them, and how to determine the appropriate power levels for each user on each subcarrier. In this section, we will consider some of the possible approaches to resource allocation. We focus on the class of techniques that attempt to balance the desire for high throughput with fairness among the users in the system. We generally assume that the outgoing queues for each user are full, but in practice, the algorithms discussed here can be modified to adjust for queue length or delay constraints, which in many applications may be as, if not more, important than raw throughput.2
Referring to the downlink OFDMA system shown in Figure 6.3, users estimate and feed- back the channel state information (CSI) to a centralized base station, where subcarrier and power allocation are determined according to users’ CSI and the resource-allocation procedure.
Once the subcarriers for each user have been determined, the base station must inform each user 2. Queueing theory and delay-constrained scheduling is a rich topic in its own right, and doing it jus-
tice here is outside the scope of this chapter.
which subcarriers have been allocated to it. This subcarrier mapping must be broadcast to all users whenever the resource allocation changes: The format of these messages is discussed in Chapter 8. Typically, the resource allocation must be performed on the order of the channel coherence time, although it may be performed more frequently if a lot of users are competing for resources.
The resource allocation is usually formulated as a constrained optimization problem, to either (1) minimize the total transmit power with a constraint on the user data rate [21, 39] or (2) maximize the total data rate with a constraint on total transmit power [18, 24, 25, 43]. The first objective is appropriate for fixed-rate applications, such as voice, whereas the second is more appropriate for bursty applications, such as data and other IP applications. Therefore, in this sec- tion, we focus on the rate-adaptive algorithms (category 2), which are more relevant to WiMAX systems. We also note that considerable related work on resource allocation has been done for multicarrier DSL systems [2, 6, 7, 41]; the coverage and references in this section are by no means comprehensive. Unless otherwise stated, we assume in this section that the base station has obtained perfect instantaneous channe-station information for all users. Table 6.1 summa- rizes the notation that will be used throughout this section.