**2. System model**

#### **2.1 Signal model**

In Fig. 1 and 2, the baseband models of an OFDM transmitter and receiver are depicted. In OFDM, information data are transmitted blockwise. A sequence of bits is split into blocks, fed to different subcarriers and modulated. For the *k*-th block, an inverse discrete Fourier transform (IDFT) of length *N* on the symbols of all carriers is carried out. Subsequently, in order to combat interblock interference, a cyclic prefix of sufficient length *N*g is preceded before transmission via the frequency-selective radio channel.

At the receiver side, the cyclic prefix is removed. In order to decode in OFDM, a discrete Fourier transform (DFT) is carried out. In a perfectly synchronized OFDM system, the received symbol *dn*,*<sup>k</sup>* on the *n*-th subcarrier (1 ≤ *n* ≤ *N*) of the *k*-th OFDM block (1 ≤ *k* ≤ *K*) can be modeled by

2 Will-be-set-by-IN-TECH

S/P IDFT P/S Add CP

d1,k

CE

d2,k

Rem. CP P/S Bit sink

time-division duplex (TDD) systems in which the channel can be regarded as reciprocal. In contrast to other research work, a lot of new constraints are taken into account. Namely, many parameters are known by the receiver that can be utilized to enhance the classification

In Fig. 1 and 2, the baseband models of an OFDM transmitter and receiver are depicted. In OFDM, information data are transmitted blockwise. A sequence of bits is split into blocks, fed to different subcarriers and modulated. For the *k*-th block, an inverse discrete Fourier transform (IDFT) of length *N* on the symbols of all carriers is carried out. Subsequently, in order to combat interblock interference, a cyclic prefix of sufficient length *N*g is preceded

At the receiver side, the cyclic prefix is removed. In order to decode in OFDM, a discrete Fourier transform (DFT) is carried out. In a perfectly synchronized OFDM system, the received symbol *dn*,*<sup>k</sup>* on the *n*-th subcarrier (1 ≤ *n* ≤ *N*) of the *k*-th OFDM block (1 ≤ *k* ≤ *K*)

dN,k

Demod

EQ

Demod

Demod

s2,k

s1,k

Mod

Mod

Mod

S/P DFT

sN,k

Bit source

Fig. 1. Block diagram of an OFDM transmitter

Fig. 2. Block diagram of an OFDM receiver

**2. System model 2.1 Signal model**

reliability (Häring et al., 2010a; Häring et al., 2010b; 2011).

before transmission via the frequency-selective radio channel.

$$d\_{n,k} = H\_n \cdot s\_{n,k} + v\_{n,k} \, . \tag{1}$$

where *sn*,*<sup>k</sup>* and *Hn* denote the transmitted data symbol and the transfer function value on the *n*-th subcarrier of the *k*-th OFDM block, respectively. We consider a propagation scenario with slowly time-variant channels, typical for indoor communications. Thus the channel transfer function does not change significantly during one transmission frame, i. e. it holds: *Hn*,*<sup>k</sup>* = *Hn*. The additive white noise exhibits a complex Gaussian distribution: *vn*,*<sup>k</sup>* ∼ CN (0, *<sup>σ</sup>*<sup>2</sup> *<sup>v</sup>* ). Due to the multicarrier principle, low-data rate signals are transmitted via flat-fading subchannels. This enables a simple frequency domain channel estimation (CE) and equalization (EQ) shown in Fig. 2.

In OFDM systems using adaptive modulation, symbols on different subcarriers can emanate from different symbol alphabets. Without loss of generality, we restrict ourselves to the digital modulation schemes with maximum bandwidth efficiencies 6 bit/symbol according to Table 1. In Fig. 3, the respective signal constellations are depicted.

Fig. 3. QAM signal constellations: no modulation, BPSK, 4QAM, 8QAM, 16QAM, 32QAM, 64QAM


Table 1. Considered digital modulation types

#### **2.2 Adaptive modulation**

Due to the frequency-selective nature of the radio propagation channel, some subcarriers exhibit good channel conditions whereas others suffer from a low signal-to-noise power ratio (SNR). The overall system performance in terms of the raw bit-error ratio is dominated by the poor subcarriers.

The idea of adaptive modulation is to distribute the total amount of data bits among all subcarriers in an optimal way. If the subcarrier SNR is high, more bits than the average are loaded and higher-order modulation schemes are used. If the subcarrier SNR is low, less or even no bits are loaded such that the bit-error ratios on different subcarriers are evened out.

Using this principle, either the average bit-error ratio can be decreased at the same data rate or the data rate can be increased at the same target bit-error ratio. Since the knowledge about the data rate turns out to be an important feature of the AMC, the first approach with a fixed data rate is investigated here.

A huge amount of research on adaptive modulation algorithms has been carried out during the last twenty years (Campello, 1998; Chow et al., 1995; Czylwik, 1996; Fischer & Huber, 1996; Hughes-Hartogs, 1987). In the following, we focus on algorithms that utilize the bit metric:

$$b\_{\rm nl} = \log\_2\left(1 + \frac{\gamma\_{\rm n}}{k \cdot \gamma}\right) \quad \text{s.t.} \quad \sum\_{n=1}^{N} b\_{\rm nl} = N\_{\rm b} \,\,\,\tag{2}$$

where *γ* and *γ<sup>n</sup>* denote the average signal-to-noise power ratio and the SNR of the *n*-th subcarrier. This bit metric *bn* is motivated by the channel capacity formula which takes the SNR gap (Starr et al., 1999) into account. As an example of adaptive modulation, the magnitude of the channel transfer function |*Hn*| in a typical indoor propagation scenario (dashed line) and the corresponding bandwidth efficiencies (solid line) are shown in Fig. 4. There are two challenges involved in the application of AM in practical systems:

Fig. 4. Example of adaptive modulation

• *Channel knowledge at transmitter side*

In order to be able to apply AM, the transmitter must know about the subcarrier SNRs. There are two ways to obtain this knowledge: 1) via feedback from the receiver or 2) using reciprocity in time-division duplex systems. Here, the focus is on TDD systems.

In our analysis, the channel transfer factors *Hn* are therefore obtained by a preamble-based channel estimation in the receive mode.

• *BAT knowledge at receiver side*

In order to be able to decode the transmitted information, the receiver must know about the bit allocation table which includes the assignment of modulation schemes to subcarriers. Either this information is transmitted via a signaling channel or it is automatically classified.
