**3. Practical challenges of interference alignment**

Interference alignment can be realized in different domains such as space (across multiple antennas [3], [4]), time (exploiting propagation delays [6], [7] or coding across time-varying channels [4], [8]), frequency (coding across different carriers in frequency-selective channels [9]), and code (aligning interference in signal levels [10]). Combinations of domains can also be used e.g. space and frequency, [11]. In the following, we briefly introduce *Degrees of Freedom*

Consider the *K*-user interference network in Fig. 1. Source S*k* (*k* ∈ {1, 2,..., *K*}) intends to send an independent message w*<sup>k</sup>* ∈ W*k* to its destination, where W*<sup>k</sup>* denotes the corresponding

*RK*) is said to be achievable if a sequence of codebooks exists, such that the probability that each destination decodes its message in error can be arbitrarily small, by choosing long enough codewords. The capacity region of the network is the closure of the set of all achievable rates. In Gaussian interference networks where the noise is additive white Gaussian, the capacity region depends on the transmission powers of sources, the noise powers and channel gains. Since the exact capacity region is difficult to find, as a starting point one can use the DoF region to characterize/approximate the capacity/achievable rate region in the high-SNR region (where interference is the dominant phenomenon that degrades system performance). The DoF region

1 1 ( ,..., ) | ( ,..., ) ( ), lim ,1 , log

"Book˙Chapter˙MFZNS" — 2014/10/14 — 15:09 — page 5 — #5

where *C(P)* denotes the capacity region, and P is the transmission power of each source. The DoF can be seen as the pre-log factor of the achievable rate and the DoF region describes how

Source Encoder Power Control Beamformer Channel Filter Decoder Destination

Feedback Channel f

Fig. 2: Transmitter and Receiver Structure.

III. PRACTICAL CHALLENGES OF INTERFERENCE ALIGNMENT

signal for transmission over the channel according to the interference alignment concept.

receiver and the transmitter. In the following, we will explain these parts in more detail.

October 14, 2014 DRAFT

At the receiver side, *channel estimation* module computes the estimation of incoming channel gains. These channel estimations can be used for recovering the transmitted message and computing the channel state information feedback signal. The *filter* module exploits estimated channel gains to recover the desired signal from interference signals according to the interference alignment concept. The *decoder* module decodes the message using an estimate of the incoming channel gain. The feedback encoder module denoted by 'f' in Fig. 2 computes the feedback signal according to the estimated channel gains. Also, there is a *synchronizer* module at the receiver to synchronize the

The structure of a canonical transmitter and receiver for the implementation of interference alignment is shown in Fig. 2. At the transmitter side, there is an *encoder* which encodes the messages to the corresponding codewords suitable for transmission over the channel. The transmission can be enhanced by the adaptation of the transmitted signal according to the received channel state infomation feedback. Specifically, in a class of communication systems that transmission powers are fixed and a maximum throughput is desired, the encoder may adapt transmission rate according to the estimate of the mutual information of the channel (computed by the *rate adaptation* module). On the other hand, in another class of systems which desire fixed-rate transmission, *power control* module should adjust transmitted power according to the channel state feedback to maintain mutual information of the channel larger than a certain level. Each transmitter has a *beamformer* which compute the proper

*<sup>R</sup> d d R R Pd k K*

ì ü = Î\$ Î í ý £ £

*K Kk <sup>P</sup>*



*k*

®¥

=

D C ¡ (1)

*P*

Channel Estimation

þ

wk


5

*(DoF)* which is a performance measure for wireless networks at high-SNR regime.

**2.1. Degrees of freedom region**

54 Contemporary Issues in Wireless Communications

wk

where |

wk

+

the capacity region expands as transmission power increases.

message set. The message |

Rk<sup>=</sup> log <sup>|</sup> wk | n

is defined as follows

î

Rate Adaptation

region expands as transmission power increases.

**Figure 2.** Transmitter and Receiver Structure.

code rate is

The structure of a canonical transmitter and receiver for the implementation of interference alignment is shown in Fig. 2. At the transmitter side, there is an *encoder* which encodes the messages to the corresponding codewords suitable for transmission over the channel. The transmission can be enhanced by the adaptation of the transmitted signal according to the received channel state infomation feedback. Specifically, in a class of communication systems that transmission powers are fixed and a maximum throughput is desired, the encoder may adapt transmission rate according to the estimate of the mutual information of the channel (computed by the *rate adaptation* module). On the other hand, in another class of systems which desire fixed-rate transmission, *power control* module should adjust transmitted power accord‐ ing to the channel state feedback to maintain mutual information of the channel larger than a certain level. Each transmitter has a *beamformer* which compute the proper signal for trans‐ mission over the channel according to the interference alignment concept.

At the receiver side, *channel estimation* module computes the estimation of incoming channel gains. These channel estimations can be used for recovering the transmitted message and computing the channel state information feedback signal. The *filter* module exploits estimated channel gains to recover the desired signal from interference signals according to the interfer‐ ence alignment concept. The *decoder* module decodes the message using an estimate of the incoming channel gain. The feedback encoder module denoted by '*f* ' in Fig. 2 computes the feedback signal according to the estimated channel gains. Also, there is a *synchronizer* module at the receiver to synchronize the receiver and the transmitter. In the following, we will explain these parts in more detail.
