PERFORMANCE OF SPACE-TIME BLOCK CODING OVER THE POWER LINE CHANNEL IN COMPARISON WITH THE WIRELESS CHANNEL A. Papaioannou*, G.D. Papadopoulos*, F.-N. Pavlidou* *Aristotle University of Thessaloniki Dept. of Electrical & Computer Engineering Email:
[email protected] [email protected]
Abstract In this paper, we test the performance of Space-Time Block Coding (STBC) technique applied to the Power Line channel. Two modulation types are implemented; 4PAM and BPSK. We examine the effect of Convolutional coding and the presence/absence of interleaving. The simulation results are focused on the Bit Error Rate (BER) performance of the system. 1. Introduction Communications over power lines have a history of more than a hundred years. The first applications required only very low bit rates, as they included control signaling, metering and load management. The rapid development of communications’ technology recently made it possible to use the power line network for high speed transfer of data. Moreover, as access to Internet is becoming as indispensable as access to electrical power and the need for in-home local area networks is increasing continuously, power line communications (PLC) offer a potentially convenient and inexpensive solution. The unique fact that no new wires are needed, the availability of power outlets in every room and the easiness of installation give PLC the opportunity to compete with other “last mile” technologies, such as digital subscriber line (DSL) [1], wireless local loop, wireless LANs and telephone lines. PLC access networks cover both the public area from the transformer substations to the customer premises (outdoor) and the private area within the customer buildings (indoor). Most of the systems available provide a maximum data rate of more than several Mbps [2].
The study has been partially supported by a bilateral cooperation program of the General Secretariat for Research and Technology (Greece-Yugoslavia).
However, power line grid can be characterized as a rather hostile medium for data transmission, because it was originally designed for the distribution of electrical power in the frequency of 50-60Hz [3]. As a consequence, PLC channel faces some technical problems, such as impedance variations and mismatches, various forms of noise and narrowband interference, multipath propagation phenomena and high attenuation of the medium. Further research should be carried out in the fields of efficient coding, modulation and transmission methodologies, in order to ensure reliable communication over power lines. Space-Time coding is a new codingmodulation technique for multiple antenna wireless systems [3]. Space-time coding combines temporal and spatial diversity in order to provide less attenuated replicas of the transmitted signal to the receiver and thus to mitigate the destructive effects of attenuation. By the implementation of space-time codes in the PLC environment we can take advantage of the intrinsic spatial diversity in the use of a three-phase power line [4]. The outline of this paper is as follows. In the next section the channel model of the simulation is analyzed. The STBC technique applied to PLCs in comparison with the wireless communications is described in section three. In section four we present our system structure. Bit Error Rate (BER) performance and extensive simulation results are depicted in section five. Finally, in section six we present our concluding of this work. 2. Channel Model The communication channel is assumed to be flat fading, quasi-static [5]. The path gains, from one emitting point to one receiving point of the same phase (wire), are modeled as samples of complex Gaussian random variables with variance 0.5 per real dimension. In the simulation’s transmission model we assume that each phase provides a completely isolated path to the transmitted signal [5].
Opposite to many other communication channels, the power line channel does not represent an Additive White Gaussian Noise (AWGN) environment [6]. In the frequency range from some hundred kHz up to 20 MHz it is mostly dominated by narrow-band interference and impulsive noise. One suitable model for this type of noise is the Additive White Class A Noise (AWCN). AWCN is calculated from the combination of AWGN and impulsive noise. The pdf of a Class A noise real variable x is given by [7]:
x2 ∑ am exp(− 2σ 2 ) 2π n =1 σ m m
p ( x) =
where : a m = e
∞
1
−A
1
(1)
Am 2 2 ( m / A) + T , σm =σ , σ2 is m! 1+ T
σ g2 2 , σ g is the 2 σι 2 variance of the AWGN component and σ ι the variance
the variance of Class A noise,
T=
of the impulsive component. The parameter A is called the impulsive index. For small A, for example A=0.1, the noise is highly impulsive whereas for A→ ∞ the Class A noise pdf becomes Gaussian. A Class A noise sample can be expressed as [8]:
n = xG + K m y
(2)
where: xG is white Gaussian background noise sequence with zero mean and variance
σ g2 ,
Km is statistically
independent, Poisson distributed random sequence whose pdf is characterized by A (mean value of Poisson distribution), and y is white Gaussian sequence with zero mean and variance σ ι /Α. 2
3. STBC Space-Time coding has comprehensively been studied in wireless channels with very good performance results. The idea of using multiple transmit and multiple receive antennas was based on linear combining of the transmitted signal at the transmitter, while the inverse process takes place at the receiver [9]. The application of STBC to the PLC channel has some basic differences in comparison with the application to the wireless channel. In wireless communications multiple transmitting and receiving antennas can be used, where in PLC only three emitting and receiving points exist; these are the three
phases of the Power Line channel that are used for the STBC transmission model. Besides, in the wireless communications with multiple transmitting and receiving antennas, the signal at the input of each receiving antenna is calculated through the linear combination of the transmitted signals of all the transmitting antennas; on the other hand, in PLCs, the three phases are assumed to be completely isolated as mentioned above [6]. Thus, the maximum diversity order we can achieve for the PLC case is three, while for M transmitting and N receiving antennas the diversity order is M.N. The general structure of the transmission matrix of the STBC, employing three transmitting antennas and complex constellation, is [10]:
⎛ x1 ⎜ ⎜ − x2 ⎜ − x3 ⎜ ⎜ − x4 ⎜ x1∗ ⎜ ∗ ⎜ − x2 ⎜ −x ∗ ⎜ 3∗ ⎜ −x ⎝ 4
x2 x1 x4 − x3 x2∗ x1∗ x4∗ − x3∗
x3 ⎞ ⎟ − x4 ⎟ x1 ⎟ ⎟ x2 ⎟ x3∗ ⎟ ⎟ − x4∗ ⎟ x1∗ ⎟ ⎟ x2∗ ⎟⎠
(3)
However, in our STBC system the transmission matrix becomes as shown in matrix (4), because of the modulation schemes used; the two modulation types under test are 4-PAM and BPSK, types that generate real symbols to be transmitted. So the STBC scheme is based on a generalized real orthogonal design [10].
⎛ x1 ⎜ ⎜ − x2 ⎜ − x3 ⎜ ⎝ − x4
x2 x1 x4 − x3
x3 ⎞ ⎟ − x4 ⎟ x1 ⎟ ⎟ x2 ⎠
(4)
The transmission matrix above shows that the STBC applied in our system is less complex than in its general form. Finally, we should mention that the transmission rate of the general transmission scheme is 1/2, where in our system structure it becomes 1. 4. System Structure The general layout of the simulated system can be seen below in figure 1. The data to be transmitted is first
coded with Convolutional coding (2,1); the generator polynomial used is [133,171]. The reason why we use Convolutional coding is that it is widely used in wireless channels with very good performance results. Convolutional coding is designed for correcting random errors. In fading channels with high levels of impulsive noise, however, like PLC, the errors have a burst nature. This can be controlled using Burst Error Correcting Techniques. One of them is the Block Interleaving [11]. The signal is block interleaved with interleaving depth 40. The modulation schemes under test are 4-PAM and BPSK. The former modulation type used to be the most common in PLCs some years ago, and it is still applied sometimes when simulating a PLC system. On the other hand, the latter modulation scheme is the most popular in applications using wireless and power line channels today. The STBC scheme has three emitting points and three receiving points, because of the three phases of the PLC channel. The transmission matrix used to produce the encoder and the decoder was described above in (4). Finally, we should mention that perfect channel estimation is assumed at the receiver.
is a coding-modulation technique implemented just before transmitting the signal to the channel, while convolutional coding is a forward error correction code applied straight to the source information bits, with much better performance, as expected.
Figure 2: BER performance of the PLC system (4-PAM modulation)
We obtain similar results to the previous when testing BPSK in the PLC environment, shown in figure 3. To achieve a bit error probability of 4.10-5 we need an SNR of 40dB for the uncoded data and about 18dB and 7dB when applying STBC and convolutional coding respectively. Figure 1: System structure
5. Simulation Results The figures presented below were created running multiple simulations designed in Matlab, in order to minimize the statistical errors and to assure the validity of the results. The system was evaluated by simulating a transmission of about 220 (1048576) data bits to obtain performance results for each of the systems under test. The Bit Error Rate (BER) performance of the aforementioned systems for a wide range of Signal to Noise Ratios (SNR) is given. Figure 2 shows the improvement provided by the convolutional coding and the STBC scheme in the power line channel, using 4-PAM modulation. Although there cannot be a clear comparison between the convolutional coding and the STBC, we observe that the former one offers more to the system, when these two techniques are applied individually. This comparison cannot be transparently done, because of the codes’ nature; STBC
Figure 3: BER performance of the PLC system (BPSK modulation)
In figures 4 and 5 we test the BER performance of our system, simulated through the wireless channel. Here a comparison is made between the behavior of the two
tested channels, using exactly the same parameters described above.
Figure 4: BER performance of the wireless system (4-PAM modulation)
When using PAM modulation, in figure 4, we observe that STBC offers slightly more to the wireless channel, compared to the STBC when applied in the PLC channel, as shown in figure 2. But again the contribution of STBC in the PLC is impressive.
In figures 6 and 7 the efficiency of block interleaving is illustrated, as well as a comparison between 4-PAM and BPSK modulation, using STBC and convolutional coding.
Figure 6: BER performance of the PLC system (4-PAM and BPSK modulation)
In figures 6 and 7 we can see that the capability of block interleaving to face burst of errors is confirmed as expected from theory; in the PLC environment where Class A Noise (AWCN) is present (which includes impulsive noise as mentioned above) with bursts of errors, interleaving clearly offers to the system, even if this offer is not great. In the wireless channel where AWGN exists, interleaving incurs an almost insignificant gain to the BER performance compared to the system without interleaving, until a BER of about 10-3 is achieved; below that BER, interleaving’s improvement becomes clear.
Figure 5: BER performance of the wireless system (BPSK modulation)
In figure 5 BPSK modulation scheme is under test. We perceive similar results to the ones above. The improvement that these coding techniques offer to the uncoded data is greater when using 4-PAM modulation; to transmit uncoded data we need 40 dB to achieve a BER of 5.10-5, while with the contribution of one of these coding techniques individually, we need about 13-14dB.
Figure 7: BER performance of the wireless system (4-PAM and BPSK modulation)
Finally, we should mention that the last two figures indicate that BPSK performs better than 4-PAM; this was expected, because BPSK is supposed to be a completely digital modulation technique. That is the reason why PAM modulation is almost abandoned the last years for communications over the power line channel.
6. Conclusions This paper examines the improvement that SpaceTime Block Coding technique can provide to Power Line Communications, in comparison with the effect that this technique has on wireless communications. The reason why we tested the same system at the wireless environment, too, is that in wireless communications STBC is a very promising coding-modulation technique with unexceptionable results. The conclusion of this comparison is that this technique applied in PLCs is as much promising as it is in wireless communications. Block interleaving is also evaluated as a means to improve this performance. Interleaving seems to perform with better results in PLCs, especially when the required BER is low, because of the nature of the noise in PLCs (AWCN), which includes impulsive noise and can be confronted well with block interleaving. The two chosen modulation types show a quite different behavior. It is clear that coding greatly enhances performance to attain a respectable BER, otherwise this transmission scheme performs poorly. The overall conclusion coming out of this comparison is that Power Line Communications can profit a lot from the application of the presented communication techniques.
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