3.6 Simulation Results
3.6.2 BER Performance
In many PAPR research works, the effect on BER is neglected. In fact, the effect on BER may be great in some cases. In our simulation, we use Nt = 2 and K = 256 subcarriers. The available bandwidth is 1MHz and the subcarrier K = 256. We consider the channel with power delay profiles: COST207[22] typical urban six-ray power delay profile. The oversampling factor is J = 4. All the other parameters are just the same as what we use in Section (3.2).
Fig.(3.13) and Fig.(3.14) show the performance of SS-CARI and TDCS using the space frequency code investigated in Section (3.1). In the simulation, we assume that CSI and side information can be recovered correctly by the receiver. Take 7dB clipping ratio case as example. We can observe that the BER performance of both
- 1 0 1 2 3 1 0- 4
1 0- 3 1 0- 2 1 0- 1
E b / N o ( d B )
BER
S S - C A R I( W = 4 )
C l i p r a t i o = 6 C l i p r a t i o = 7 C l i p r a t i o = 8 C l i p r a t i o = 9 N o C l i p p i n g
Figure 3.13: SS-CARI BER performance for W = 4.
schemes are around 10−4 at Eb/N0 = 3dB.
In Eqs.(3.13), multiplying unitary matrix U to the left side of a space-frequency codeoword will not effect the BER performance. Hence the U can be designed by any unitary matrix.
- 1 - 0 . 5 0 0 . 5 1 1 . 5 2 2 . 5 3 1 0- 4
1 0- 3 1 0- 2 1 0- 1
E b / N o ( d B )
BER
T i m e - d o m a i n s c h e m e ( Q = 1 6 )
C l i p r a t io = 6 C l i p r a t io = 7 C l i p r a t io = 8 C l i p r a t io = 9 N o C li p p i n g
Figure 3.14: TDCS BER performance for Q = 16.
Side Information Embedded
In some situations, the side information is embedded into the system. There are many methods to embed the side information into the system. A major concern is that the side information must be well protected. Otherwise, serious error propaga-tion will occur. Here, we consider a simple method which is obtained by inserting the side information into the zero terms of Eqs.(3.1) and Eqs.(3.2) and each reserved subcarrier contains one side information bit. In fact, we can insert more than one bit to one subcarrier if the system needs a large number of the side information bits.
In order to protect the side information bit, the power of side information signals is transmitted four times of original signals. The performance of SS-CARI scheme remain similar to TDCS scheme, shown in Fig.(3.15) and Fig.(3.16). Take the 7dB
clipping ratio condition as example, we can observe that the BER performance of both schemes are around 10−4 at Eb/N0 = 3dB. That is, the system suffers no BER performance degradation by inserting the side information bits in the simple methods described above.
- 1 - 0 . 5 0 0 . 5 1 1 . 5 2 2 . 5 3 3 . 5
1 0- 4 1 0- 3 1 0- 2 1 0- 1
E b / N o ( d B )
BER
S S - C A R I( W = 4 )
C li p r a t i o = 6 C li p r a t i o = 7 C li p r a t i o = 8 C li p r a t i o = 9 N o C l i p p i n g
Figure 3.15: SS-CARI BER performance for W = 4 with side information embedded.
- 1 0 1 2 3 1 0- 4
1 0- 3 1 0- 2 1 0- 1
E b / N o ( d B )
BER
T i m e - d o m a in s h c e m e ( Q = 1 6 )
C l i p r a t io = 6 C l i p r a t io = 7 C l i p r a t io = 8 C l i p r a t io = 9 N o C li p p in g
Figure 3.16: TDCS BER performance for Q = 16 with side information embedded.
Chapter 4
Extending The Linear RAnge of Power Amplifiers with Precoding
In this chapter, the research work about subproject 3 regarding “ extending the linear range of power amplifiers with precoding ” is briefly reported. In the first year of the project, we investigate the idea of using Dirty Paper Coding (DPC) to extend the linear range of power amplifiers (PAs) for the single input single output (SISO) single carrier case. In addition, we also study the effect of peak to average power ratio (PAPR) constraint on the diversity-multiplexing (DM) tradeoff of multiple input multiple output (MIMO) channel. After this issue is addressed, we develop a method that can reduce the PAPR of MIMO single carrier systems without sacrificing the optimality of DM tradeoff.
4.1 Extending the Linear Range of Power Ampli-fiers with DPC
In this project we propose a novel solution to extend the linear range of a given PA with precoding. The idea behind the proposed method is based on the well known information theoretic result on interference cancellation at the transmitter.
In the monumental work by Costa [4], it was proven that if the interference in the channel is known to the transmitter, cancellation of the interference can be done at the transmitter without increasing the transmission power. As a result, the clean channel capacity can be achieved as if the interference does not exist.
Since this technique stems from a completely different philosophy than that of the PAPR reduction and the PA linearization methods, the proposed method can be combined with any of these conventional remedies to achieve linear range extension and PAPR reduction at the same time. Additionally, the proposed method can be combined with the cancellation of channel interferences as a unified precoder with small overhead. Before Costa’s theoretical result, a practical coding structure had already been applied to the inter-symbol interference channel by Tomlinson [23] and Harashima [24]. A few decades later, Erez et al. improved and generalized the Tomlinson Harashima precoding (THP) for the general interference channel [25].
The coding structure they proposed realizes Costa’s theoretical result on ”writing on dirty paper”. Therefore, this coding structure is called DPC. Compared with the well known THP which can also remove the interference at the transmitter under the
same average power constraint, DPC has several advantages in avoiding the shaping loss, power loss, and modulo loss.
To apply the above DPC interference cancellation to a communication system with a nonideal PA, we can treat the distortion caused by the PA as an additive interference. In general, the PA transfer function is known to the transmitter by, for example, online measurement. Thus the distortion can be determined and removed at the transmitter through DPC. As a result the amplitude of the data-carrying signal is allowed to exceed the linear range of the PA. At the receiver, the signal is received as if there was no PA distortion at all. The end result is an extended PA linear range. Such a precoding technique seemingly implies that one could use an arbitrarily large signal amplitude to achieve high channel capacity while the transmission power at the output of the PA is still bounded. We found that this is not the case due to the reason that in this scenario the interference is directly related to the DPC outcome. Therefore, a special attention has to be paid to the relation between the DPC and the interference. In other words, the precoding scheme has to make sure that the interference used in DPC is exactly the distortion due to PA clipping. Otherwise cancellation of the interference will not be possible.
Summary of Results
In Fig.(4.1) the system model of the proposed precoding scheme is shown. After channel coding, the signal to be transmitted goes through a combined shaping and DPC module. Differing from regular DPC, the ”interference” to be cancelled here
Figure 4.1: The system model for the proposed precoding scheme.
is the PA clipping noise which is dependent of the shaped signal. Thus, there is no guarantee that a valid ”interference” matching the shaping output and the clipping effect exists. Detailed analysis of the existence of a valid interference can be found in the full report.
To validate the proposed idea, we compare through simulation the BER versus SNR performance of the proposed scheme with a system without precoding for different minimum distances. The SNR is defined as the ratio of the energy at the PA output to the noise variance at the receiver. Both systems have channel coding and constellation shaping to acquire coding gain and shaping gain. The constellation size we use is 64-QAM. The code length is 128. A rate 1/2 convolutional code with generator [7, 5]8 is used for the sign bit shaping. It has an inverse syndrome former (HsT)−1 with generator [1, 3]8. A rate 1/5 convolutional code with generator [37, 27, 33, 25, 35]8 is used for the channel coding. The linear range of PA is set as 0.3.
The simulation result is shown in Fig.(4.2). Scale 0.48 represents that the four corner points of the 64-QAM constellation are exactly on the boundary of the linear
Figure 4.2: BER versus SNR for the proposed precoding scheme and systems without precoding with different minimum distances.
range. The minimum distance and the number of points outside the linear range increases with the increasing scale. From the simulation we can find that the pro-posed precoding scheme provides gains about 0.8-dB and 0.6-dB at BER = 10−4 and BER = 10−5 respectively over the system without precoding. The gain be-comes larger with decreasing SNR because the area of the extended linear range increases with decreasing SNR and the proposed scheme can prevent more clipping interference. For systems without precoding, as the scale starts increasing, the gain
from the increased minimum distance of points within the linear range can compen-sate the performance degradation caused by points outside the linear range. Due to shaping, only a small portion of all the constellation points are clipped. The shap-ing operation makes the distribution of the constellation approximately Gaussian, i.e., constellation points with less energy occurring more frequently than those with higher energy. Thus the probability of clipping is reduced. When more points are outside the linear range, for example, when scale=0.82, the errors can no longer be compensated by the gain from the increased minimum distance and the BER in-creases. On the other hand, for the proposed system, because the area of extension decreases with increasing SNR, the effect of precoding becomes less significant. As a result, the performance of the proposed precoding scheme approaches to that of systems without precoding when the scale and the SNR are both high. Thus we can find that at scale=0.82 the BER curves of both cases approach to each other much more with increasing SNR than those of other smaller scales. This condition shows that the gain from increasing the minimum distance is small when SNR is high.