Implementation of a Bandwidth-Efficient M-FSK Demodulator for Powerline Communications Gerasimos Maniatis, Kostas Efstathiou, Georgios Papadopoulos Applied Electronics Laboratory, Department of Electrical and Computer Engineering, University of Patras, GR-265 00 Rio – Patras, Greece
[email protected]
Abstract In this paper, an implementation of a bandwidth – efficient M-ary frequency-shift keying (M-FSK) demodulator for powerline communication is presented. Signal demodulation is performed in a direct mode, by undersampling and analyzing consecutive triplets of signal samples. The method, which will be analyzed, is characterized by low complexity and can be realized in a solid-state circuit or embedded in a programmable device. A DSP based implementation will be presented, consisting of a bandpass filter, an A/D converter and a low cost DSP. The demodulator is targeted to powerline communications and operates at a bit rate of 19.2kbps, achieving a bandwidth usage of 3 bits/Hz and a satisfactory noise performance, optimizing the cost-andperformance to bitrate ratio.
1. Introduction During the last years the interest for Powerline Communications (PLC) in the domestic environment has been increased due to the advantage of using the existing power network for data transfer. The majority of powerline products lies either as high-speed and relatively costly powerline modems offering an alternative to wired LAN, such as [1] or as low speed products targeted to home automation, such as the US standard X10 or the European standard EHS [2], [3]. An attempt to bridge the two categories has lead to the investigation of a powerline transmission solution that could offer adequate bitrate for the transmission of data signals while considering the bandwith limitations of powerline medium and European CENELEC regulations. The consideration of the factors has resulted in the adoption of the M-ary Frequency-Shift Keying (M-FSK) modulation as the trade-off between performance, bandwidth usage and implementation complexity. The key factor in any M-FSK system is the demodulator. Up to the present time, a variety of methods have been developed. Non-coherent demodulation with the use of correlator or matched filter provides excellent noise performance but limits the
bandwidth usage up to 2 bits/Hz [4]. Analog-based demodulation using a discriminator [4], [5] or a PLL [6], [7] removes the above limitation without considerable noise performance sacrifice. Finally, fully digital demodulators, implying FFT methods, such as [8] have been presented. However, the research for a uncomplicated but efficient demodulator has lead to a method that will be analyzed in the following section. The method is direct, using triplets of signal samples to calculate the signal frequency and incorporates undersampling to reduce the operating frequency and energy consumption. Moreover, its excellent discrimination characteristics make it suitable for bandwdith-efficiency critical applications. The demodulator can be realized either as a circuit or as a programmable device. In this paper, a DSP implementation of a M-FSK receiver will be presented, suitable for powerline communications. The demodulator can achieve operation at 19.2kbps, using an M-FSK-16 modulation over a bandwidth of only 6500Hz.
2. The M-FSK demodulation method Let us suppose a sinusoidal modulated signal of the general form : s(t)=A cos(ωt+φ) (1) Where A, ω=2πfin and φ are considered constant but unknown during the transmission of a single symbol. The signal is being sampled with a constant sampling frequency of fs. Suppose that we take three samples, s1, s2 and s3, at sampling intervals ∆ts=1/fs. If s2 is sampled at time t=t0, then s1 is sampled at time t=t0-∆ts and s3 is sampled at time t= t0+∆ts (see Fig.1). Hence, the equation (1) can be written for the three sampling points: s1=A cos[ω(t0-∆ts)+φ] s2=A cos(ωt0+φ) s3=A cos[ω(t0+∆ts)+ φ]
(2)
(2) is a system of three equations with three unknown quantities: Α, ω, φ. By applying mathematical operations and trigonometric rules to (2), we get:
a (Demod. output)
s2
s1 s3 ∆ ts t 0 -∆ Τ s
0.5 0 -0.5 -1 0
∆ ts t0
0.5
t 0 +∆ Τ s
1
1.5 fin / fs
2
2.5
Fig. 2. The characteristic curve of the demodulator
Fig. 1. Sampling of a sinusoidal signal
s1+ s3 = Acos(ωt0+φ) cos(ω∆ts) + A sin(ωt0+φ) sin(ω∆ts) + A cos(ωt0+φ) cos(ω∆ts) – A sin(ωt0+φ) sin(ω∆ts) = 2Acos(ωt0+φ) cos(ω∆ts) = s2 cos(ω∆ts) (3) s1 + s 3 (4) ⇒ cos(ω∆t ) = 2s 2 f s + s3 ⇒ cos(2π in ) = 1 2s 2 fs
1
(5)
s + s3 fs cos −1 1 (6) 2π 2s 2 Therefore, the equation (6) can be used for the determination of the frequency of a given sinusoidal signal, given only the three sampling points s1, s2, s3 and the sampling frequency fs. The cos-1 operation is strongly non-linear and difficult to be implemented in either analog or digital form, thus only the term s + s3 a= 1 (7) 2s 2 is required to be determinded and the actual frequency can be found by the use of a look-up table (LUT), considering that the a term is bound to the space [-1,1]. For the remaining of the text, a will be assumed as the output of the demodulator, and (7) will be considered as the demodulator equation. Because f f f + nf s cos(2π in ) = cos(2π in + 2πn) = cos(2π in ) (8) fs fs fs where n is an integer, from (5) it can be understood that the demodulator output for a random frequency f = fin + nfs will be the equal to the output for frequency fin. Thus, all frequencies are aliased to the [0, fs] space. Moreover, because f f f − f in cos(2π in ) = cos(2π − 2π in ) = cos(2π s (9) ) fs fs fs frequencies of the [fs/2, fs] are mirrored to the [0, fs/2] space, limiting the demodulator frequency range to fs/2. Fig. 2 shows the transfer characteristic a=f(fin) of the demodulator. a gets the highest value (+1) when n +1 (10) f in = fs 2 and the minimum value (-1) when n f in = f s (11) 2 Equation (9) illustrates that the demodulator operates not only for fin
