1

A Chirp Scheme for Robust Power Line Communication Stephen Robson and Manu Haddad, Member, IEEE

Abstract—This paper proposes the use of a LoRa like chirp This paper proposes a PLC modulation scheme based on spread spectrum physical layer as the basis for a new Power Line the Chirp Spread Spectrum (CSS) scheme of the recently stan- Communication modulation scheme suited for low-bandwidth dardised LoRa physical layer [4]. The modification is designed communication. It is shown that robust communication can be established even in channels exhibiting both extreme multipath to combat the two major problems of extreme multipath and interference and low SNR (-40dB), with synchronisation require- low SNR. The former is resolved by subdividing the LoRa ments significantly reduced compared to conventional LoRa. symbol into a reduced set, thereby containing the multipath ATP-EMTP simulations using frequency dependent line and energy into a single symbol. The latter is resolved through the transformer models, and simulations using artificial Rayleigh use of statistical averaging of the modified signal over consec- channels demonstrate the effectiveness of the new scheme in providing load data from LV feeders back to the MV primary utive symbols. This trading off of data rate for performance substation. We further present experimental results based on a makes possible a communication scheme in which many LV Field Programmable Gate Array hardware implementation of feeder monitoring devices can communicate back to a primary the proposed scheme. substation at timescales of several seconds or minutes. Index Terms—PLC, LoRa, LV Monitoring. II.BACKGROUND A. Requirements for Robust Communication on the LV-MV I.INTRODUCTION channel The communication channel linking the LV and MV parts ISTRIBUTION Network Operators (DNOs) already de- of a distribution network is characterised by extreme mul- ploy a wide range of communication technologies to D tipath conditions (σrms = 10’s to 100’s of µs). The main support the move towards smart grids. Advances in the stan- contributing factor to this is not the attenuation of the power dardisation of narrowband Power Line Communication (PLC) line itself, rather it is a result of delayed versions of the solutions such as Prime and G3-PLC, and growing options signal reaching the receiver from many different paths. On in long range wireless communication (i.e. LoRa) have only the MV network, the typical lengths of the line become much added to the options in the last decade. But there remains an larger than the wavelength of the narrowband PLC signal, and unmet requirement for low-cost and robust communication of, lines are terminated by open circuits or transformers with for example, load data from secondary substations. The prob- large reflection coefficients. Therefore, much of the signal lem is amplified by the sheer number of required monitoring energy remains in the power line until it dissipates. Empirical points (typically tens of thousands in a large regional distribu- measurements of the RMS delay spread on MV distribution tion network) and the fact that secondary substations are often networks is in the tens of µs [5]. In contrast, the RMS delay located in rural areas with limited access to conventional wired spread on LV networks is less than 10 µs [6]. Therefore, a or wireless communication infrastructure. robust communication scheme suited to this environment must Previous attempts at providing widescale communication accommodate extremely high RMS delay spreads, far beyond across large distribution networks have tended to focus on what is typical in LV and conventional wireless systems. arXiv:2106.13965v1 [eess.SP] 26 Jun 2021 the use of conventional wired media (i.e. ethernet), wireless When considering cross-network (LV-MV) transmission, for solutions (LoRa, GSM) or PLC. example in a system which relays load information from a Narrowband PLC solutions such as Prime [1] and G3-PLC secondary to a primary substation, a second major problem [2] are now firmly established on Low-Voltage (LV) networks, emerges. Though it has been demonstrated that PLC signals and are often deployed in automatic meter reading (AMR) in the narrowband range (15-500 kHz) can indeed propagate applications and increasingly in support of other smart grid through transformers, the attenuation is large. Empirical mea- services. Over longer distances and across voltage levels, these surements show an average 35 dB attenuation with a high technologies struggle to cope with the increased attenuation degree of frequency selectivity [7]. The SNR penalty imposed and extreme multipath conditions associated with transmission by this scale of attenuation renders existing narrowband PLC through transformers and Medium Voltage (MV) networks [3]. technologies unusable. The situation is further exacerbated by New technologies are required in this space. regulatory limits on transmit power on power lines. Therefore, reliable inter-transformer communication is only possible with S. Robson and A. Haddad are with the Advanced High Voltage Engi- communication schemes that can work at low SNRs. neering Research Centre (AHIVE) , Cardiff University, UK. e-mail: rob- [email protected] The dual problem of extreme multipath and high attenu- Manuscript received June 19, 2021; revised:. ation makes the design of a communication system for this 2

channel extremely challenging. Recently, the emerging LoRa Channel Impulse Response standard was proposed for PLC communication [8], and then for time disemmination [9][10]. LoRa has several favourable Impulse response appears as “reversed” properties, including excellent receiver sensitivity and low in the LoRa correlator output power. However, in its raw form, it performs poorly in severe multipath. Here, we exploit the unique properties of LoRa, with a few key modifications, for robust performance in the low SNR and high multipath regime. LoRa Correlator Output, y k-5 k-4 k-3 k-2 k-1 k k+1 2SF

B. The LoRa physical layer Fig. 1. The correlator output resulting from transmission in a multipath channel. The mathematical basis underpinning the LoRa physical layer has been studied extensively in several recent works [11][12][13]. LoRa transmits symbols as frequency shifted delay spreads of several tens of µs have been recorded. In 1 this case, the multipath energy will smear across samples and chirps. With a bandwidth of B = T , the transmitted symbol, wk is defined as: will be more appropriately modelled as frequency selecting fading. A basic model of the situation can be constructed r Es j2π·(k+n) mod 2SF · n in which delayed versions of the transmitted symbol arrive w (nT ) = e 2SF (1) k 2SF at the receiver. Due to the unique way LoRa is modulated - The above equation describes a series of n = effectively as time-shifted versions of a base chirp - a delayed 0, 1, 2 ... 2SF −1 consecutive samples forming a LoRa symbol. version of a transmitted symbol will be demodulated as if it SF ∈ {7, 8 ..., 12} is the so called Spreading Factor, which belonged to an adjacent symbol, as shown in Eqn. 4, where i = k − 1 . . . k − x α . . . α determines the number of transmitted samples per LoRa index are proportionate to 2 x, α symbol. k ∈ 0, 1, 2 ... 2SF −1 is the transmitted symbol and where is the impulse response of the channel. This is shown graphically in Fig. 1. Es is the symbol energy. It has been shown in [11] that SF the 2 basis functions are orthogonal allowing a sufficiently √ r  α E + φ i = k synchronised receiver to demodulate using correlation. If k  1 s i √ is the received symbol corrupted by Additive White Gaussian SF −1  α2Es + φi i = k − 1 ∗ 2  Noise (AWGN), φi, and w is the complex conjugate of X . . i r (nT ) · w∗(nT ) = . . (4) k k i . . symbol (i.e. that corresponding to the transmitted symbol), √ y k n=0  α E + φ i = k − x the correlator output will exhibit a peak at index .  x s i  φi elsewhere 2SF −1 (√ X ∗ Es + φi i = k Therefore, the channel impulse response can be mapped out rk(nT ) · wi (nT ) = (2) φi i 6= k from the correlator output. In standard LoRa modulation, the n=0 presence of strong multipath interference in which the signal p yk = arg max(|δk,i Es + φi|) (3) arrives by one or more indirect paths presents a problem for the LoRa demodulator because strong correlation peaks caused by It is demonstrated in [11] how the more computationally these paths will compete against the true transmitted symbol, efficient method removes the need to perform the full cor- raising the SER. relation over all 2SF basis functions. Indeed, the method used by LoRa requires only the multiplication of rk with the III.DESCRIPTIONOFTHE PROPOSED METHOD complex conjugate of the base down chirp (a process known as A. Enhancement for Robustness in Extreme Multipath dechirping). The dechirped signal comprises a pure frequency tone which is proportionate to k, so an FFT and find max It is interesting to note that the correlator output of the LoRa routine completes the process. demodulator mimics the channel impulse response. This was Equation 2 shows that correct demodulation will take place noted in [14], which exploits the regularity of the channel √ impulse response across subsequent LoRa symbols through when Es + φk exceeds the maximum value of φ across all correlations. Although there may be significant distance the use of cross-correlation. This method would be particularly √ interesting in PLC applications because the channel is fixed. between the PDFs of φ and Es + φk, it is actually the PDF of the maximum of φ per symbol that is of interest in Symbol However, the performance is similar to that of conventional Error Rate (SER) calculations. LoRa systems in the AWGN channel, which is still not good enough to perform reliably on the particularly hostile LV-MV channel. We also remark that the synchronisation requirements C. Performance of LoRa in Multipath Channels match that of conventional LoRa, which is difficult to achieve In most conventional LoRa applications, the RMS delay on the power line channel. spread is in the ns or low µs range. This contains the majority In the proposed method, which is shown graphically in of the multipath energy within a single sample and can be con- Fig. 2, the convenient grouping of multipath energy into a sidered as frequency flat fading. However, in PLC applications, predictable place in the correlator output is exploited in a 3

Each bar represents the sum of samples in consecutive W-sample bins

Sum samples in each bin LoRa-Mod LoRa-Mod-Enhanced ADC S Find Max Find Max

W=64

Synchronisation 1 Σ Moving Sum 0 64 128 192 256 320 384 448 512 FFT Bin (R) 2 Σ Moving Sum

Dechirping FFT | | Split Into G Bins 2 3 Σ Moving Sum

Conventional LoRa Find Max G Σ Moving Sum

Fig. 2. Schematic diagram showing the proposed receiver architecture. The deviation from conventional LoRa starts at the “Split into G Bins” block. This SF M subdivides the 2 bins into a reduced set of G = P ‘superbins’. different way. If the correlator output is termed y(k), where LoRa transmission in the AWGN channel) and a dispersed each term in y represents the absolute value of one of 2SF share of the symbol energy when k − x ≥ i ≤ k in the case output bins of the FFT operation, we can group the bins into of transmission on the multipath channel with a delay spread a reduced set of g ‘superbins’. of x samples. Every term in y is also made up of a complex Assuming that the length of the channel impulse response zero-mean Gaussian noise process, φ. is significantly smaller than the symbol time, Ts, the set of M The find max routine must now choose from a reduced set M possible symbols can be reduced to a smaller set of G = P of terms. The energy in each term is now made up of the sum Z possible symbols, each encoding SF −log2 P bits, where P 2 of P noise terms and, in the case of the correct symbol, the is the number of samples in each superbin. The modulator dispersed symbol energy. If the condition that PTe > σrms, now encodes into a reduced set of g ∈ 0 ...G − 1 possible the majority of the symbol energy will fall within a single positions. If PTe is longer than the channel impulse response, term. Therefore, the find max routine can still demodulate the the spread of energy resulting from multipath interference will symbol even in multipath channels, albeit at the expense of a be contained to a single superbin. To implement this scheme reduced data rate. at the transmitter, data should be encoded into one of a set Each superbin comprises the sum of P squared noise term of possible symbols described by mg ∈ P, 2P, . . . GP . The samples, |φ|2, from the correlator output of Eqn. 4. Since |φ| is restricted set of symbols are separated by P samples, which, if a Rayleigh distributed random variable, its square is distributed longer than the manifestation of the channel impulse response exponentially, and the sum of P of these samples follows a within Rm, will contain the multipath energy to within the Gamma distribution. We have approximated this as a Gaussian symbol being transmitted. distribution with µ equal to the expected value of the sum of At the receiver, the process is identical to standard LoRa the noise terms and σ equal to the sum of the noise variance, 2 demodulation except that a reduced set of G symbols are Sφ ∼ N (P µ, P σ ). derived from the sum of the previous P bins: The superbin which corresponds to the correct symbol, E, follows a Rician distribution with shape parameter kβ = gP E /2σ2 = E /N N X 2 s s 0, where 0 is the single-sided noise power S(g) = |y(n)| (5) spectral density. n=(g−1)P The demodulation process performs a find max routine Equation 5 shows a set of S output terms, with each term which can be simplified as the comparison between E and representing the sum of P correlator output terms from the the maximum of all other g − 1 symbols. The distribution FFT output, y. The summation combines the multipath energy describing the maximum of g −1 normally distributed random within the symbol into a single number. The receiver can variables is denoted Mφ. The expected value of Mφ can be p commence to finding the maximum index within S in the same approximated as 2 log(g − 1) standard deviations greater way as the conventional LoRa demodulation process finds the than the expected value of Sφ. A correct demodulation is achieved if E > M . maximum y. Equation 4 shows√ that y is made up of the square φ root of the symbol energy ( Es) when i = k (in the case of Fig. 3 shows Sφ, Mφ and E resulting from 30,000 Monte 4

1 . 0 1 . 0 8 0 0 - 1 5 d B - 2 0 d B 4 0 0 1 7 0 0 0 . 8 0 . 8 e e

t 4 t

6 0 0 a a

3 0 0 R 8 R

r 0 . 6 r 0 . 6 t t

5 0 0 o o

r 1 6 r n n r r u u

E E

o o 4 0 0 2 0 0 l 0 . 4 3 2 l 0 . 4 o o C C 3 0 0 b 6 4 b m m y 0 . 2 1 2 8 y 0 . 2 2 0 0 S S 1 0 0 2 5 6 1 0 0 0 . 0 0 . 0 0 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 0 . 5 0 0 . 7 5 1 . 0 0 1 . 2 5 1 . 5 0 1 . 7 5 2 . 0 0 2 . 2 5 2 . 5 0 - 2 5 - 2 0 - 1 5 - 1 0 - 5 0 - 2 5 - 2 0 - 1 5 - 1 0 - 5 0 N o r m a l i s e d S y m b o l E n e r g y N o r m a l i s e d S y m b o l E n e r g y S N R ( d B ) S N R ( d B ) (a) SNR = -15 dB (b) SNR = -20 dB (a) 10 sample channel SF=12 (b) 10 sample channel SF=14

3 5 0 - 3 0 d B 3 0 0 - 3 5 d B 1 . 0 1 . 0 3 0 0

2 5 0 e 0 . 8 e 0 . 8 t t

2 5 0 a a R R

2 0 0 r r t t 0 . 6 0 . 6 2 0 0 o o n n r r r r u

u

E E o o 1 5 0 l l

1 5 0 C C

o 0 . 4 o 0 . 4 b b

1 0 0 m m

1 0 0 y y 0 . 2 0 . 2 S S 5 0 5 0 0 . 0 0 . 0 0 0 0 . 5 0 0 . 7 5 1 . 0 0 1 . 2 5 1 . 5 0 1 . 7 5 2 . 0 0 2 . 2 5 2 . 5 0 0 . 5 0 0 . 7 5 1 . 0 0 1 . 2 5 1 . 5 0 1 . 7 5 2 . 0 0 2 . 2 5 2 . 5 0 - 2 5 - 2 0 - 1 5 - 1 0 - 5 0 - 2 5 - 2 0 - 1 5 - 1 0 - 5 0 N o r m a l i s e d S y m b o l E n e r g y N o r m a l i s e d S y m b o l E n e r g y S N R ( d B ) S N R ( d B ) (c) SNR = -30 dB (d) SNR = -35 dB (c) 20 sample channel SF=12 (d) 20 sample channel SF=14

Fig. 3. Histograms Superbin size = 64, Quarter channel (worst case) 1 . 0 1 . 0

e 0 . 8 e 0 . 8 t t a a R R

r 0 . 6 r 0 . 6 o o r r r r E E

Carlo simulations for a spreading factor of 12 and a superbin l l

o 0 . 4 o 0 . 4 b b m m size of 64. A Rayleigh channel model with RMS delay spread y 0 . 2 y 0 . 2 S S

τ = 100 µs is used, representing an equivalent bin size of 10 0 . 0 0 . 0 samples at an arbitrarily chosen 100 kHz LoRa sampling rate. - 2 5 - 2 0 - 1 5 - 1 0 - 5 0 - 2 5 - 2 0 - 1 5 - 1 0 - 5 0 This guarantees that most of the multipath energy will fall S N R ( d B ) S N R ( d B ) within a single superbin. The vertical reference lines labelled (e) 40 sample channel SF=12 (f) 40 sample channel SF=14 S¯φ and E¯ represent the means of the noise and transmitted ¯ Fig. 4. Performance of LoRa-Mod: SNR Versus Symbol Error Rate as a symbol, respectively. The X scale is normalised to Sφ, and function of superbin size, SF=12, 14, and various length Rayleigh channels. we retain this convention throughout the rest of the paper. In Fig 3(a) (SNR = -15dB), there is a clear separation between Sφ and E. LoRa-Mod, which relies on a comparison Mod-Enhanced henceforth, uses the principle of statistical between E and Mφ, can operate successfully at this SNR. averaging to estimate the means of E and the noise symbol Fig 3(b) (SNR = -20dB) shows a more pronounced overlap Sφ distributions. As shown in Fig. 2, this comes at the cost between E and Mφ, which leads to an increasing symbol error in hardware of a recursive running sum or running mean for rate for LoRa-Mod. Beyond this point, LoRa-Mod cannot be each superbin. used. However, it is noted that the mean of E is still larger In extremely low SNRs, the difference between the means than the mean of Sφ, even at extremely low SNRs (e.g. in the of E and Sφ is small but non-zero. Should the same transmitted case of -35dB in Fig. 3(d)). symbol be repeatedly sent, the receiver can estimate the mean Fig. 4 shows the performance of LoRa-Mod in three sepa- of the previous Q symbols of E (the transmitted symbol) rate Rayleigh channels (τrms = 10, 20 and 40 LoRa samples) and Sφ (all noise symbols). Unlike LoRa-Mod, which is and for two different spreading factors (SF=12, 14). Firstly, the a comparison between the maximum noise symbol (Mφ, general level of performance improves with increasing spread- shown in orange in Fig. 3), and E, LoRa-Mod-Enhanced is ing factor. Secondly, there is a requirement for the superbin a comparison between the mean of the previous Q E symbols size to be at least as large as τrms. For example, in Fig. 4(a) with the maximum of the means of the previous Q Sφ symbols. and 4(b), which is the 10 sample channel, all superbin sizes Q 1 X perform relatively well. In the 20 sample channel (Fig. 4(b) H(g) = S(g − n) (6) and 4(d)), the 4, 8 and 16 sample binsize schemes exhibit Q n=0 a drop in performance. In the 40 sample channel, the trend H S continues. The variance of is narrowed compared to φ:  P σ2  S¯ = H ∼ N P µ, (7) B. Enhancement for Robustness in Extremely Low SNRs φ φ Q Lora-Mod has the flexibility to perform well in channels Although the symbol error rate is still dependent on the with arbitrarily long RMS delay spreads and poor SNRs, but comparison between the transmitted symbol and the maximum a further trade-off of data rate can improve the performance of the noise symbols, both terms have distributions which are to even lower SNR regimes. This scheme, termed Lora- significantly narrowed by the averaging. 5

Z o o m e d V i e w S y m b o l E r r o r R a t e S N R = - 3 0 d B S N R = - 2 5 d B Q = 1 5 0 0 0 % B i n = 1 2 8 Q = 5

Q = 1 0 0 0 < 0 . 1 % Q = 5 0

Q = 2 0 0 Q = 5 0 0 1 3 %

1 . 0 0 5 1 . 0 1 0 1 . 0 1 5 1 . 0 2 0 1 . 0 2 5 1 . 0 3 0 1 . 0 3 5 B i n = 6 4 Q = 5 Q = 5 0 0

Q = 5 0 Q = 1 0 0 0 Q = 2 0 0 Q = 1 5 0 0

B i n = 3 2 Q = 5

8 0 Q = 5 0

t 6 0 Q = 2 0 0 n u

o 4 0 C 2 0 0 . 5 1 . 0 1 . 5 2 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 0 0 . 5 0 0 . 7 5 1 . 0 0 1 . 2 5 1 . 5 0 1 . 7 5 N o r m a l i s e d S y m b o l E n e r g y N o r m a l i s e d S y m b o l E n e r g y N o r m a l i s e d S y m b o l E n e r g y Fig. 6. Boxplots summarising the distributions of Sφ, E and H (LoRa- Fig. 5. Demonstration of how LoRa-Mod-Enhanced can provide robust Mod-Enhanced) for Q=5, 50 and 500 symbols. Increasing Q narrows the communication in a low SNR environment (-40 dB here) .The bottom distribution of H and creates a wider normalised separation, making error free communication possible. panel shows the distribution of Sφ (red), E (blue) and Mφ (orange). The middle panel shows the boxplot version of these distributions, alongside H for Q=1500, 1000 and 500. The top panel is a zoomed view of H, showing clearly how the symbol and noise distributions separate with increasing Q. reducing the complexity of both transmitter and receiver and These simulations are performed with the Rayleigh 20 sample channel, SF=12 removing the requirement for a preamble.

Since it can be guaranteed that most of the transmitted IV. CASE STUDY symbol energy will fall within E, a high enough Q is able to A. Development of a test network detect the statistical difference between the two means, even at extremely low SNRs. The test network, as shown in Fig. 7, has 5 LV feeders and This approach requires a compromise in terms of the a radial MV network. The LV feeders use underground cable maximum achievable datarate since, in effect, any gains made models (three-phase in an enclosed pipe) and the HV network in robustness due to an increase in Q are matched by a pro- comprises an overhead line based on an 11 kV wood pole portionate reduction in datarate. However, in grid applications model. All models use the frequency dependent JMarti model where load data is only required on the timescale of minutes, generated by the Lines and Cables Constants (LCC) routine this comprimise might be acceptable. of the EMTP. The MV/LV transformers are modelled with Fig. 6, which retains the colour scheme from Fig. 5, shows the high frequency Catallioti model [15] and each LV line is the distributions (represented as horizontal lines) of normalised terminated on the load side by a three-phase 10 Ω resistance. symbol energy for a spreading factor of 12 and for various bin sizes. It also shows the effect of varying the running mean B. Simulation Methodology length, Q. The same LoRa parameters deployed in Fig. 5 are Two LoRa-Mod-Enhanced devices are placed within each used, meaning the majority of the multipath energy falls within of the 5 feeders (labelled A-E in Fig. 7). A single receiver the transmitted symbol superbin, E. It is interesting to note is placed near the primary substation (labelled ‘O’). The that increasing the bin size beyond that which is necessary to modulation code, which is executed in Matlab, automatically contain the multipath energy actually deteriorates performance writes each sample to a text file. This text file is read by a of LoRa-mod-enhanced, as indicated by the narrowing of the ‘foreign model’, which is a custom piece of code executed gap between the purple lines (S¯ and the E¯). φ natively within the EMTP, and provides the source signal for a TACS source. The process can be repeated for any number C. Synchronisation of TACS sources within the simulation, providing scope for a The synchronisation requirements are drastically relaxed in full system-wide simulation incorporating several transmitters. comparison to conventional LoRa because it does not matter if This methodology also resolves the challenge of writing many energy smears across LoRa bins (the energy will remain inside millions of samples into EMTP, and allows the communication the superbin). This opens up the possibility of using zero- signal to be read at the same ∆T as the simulation (1E-7). On crossing detectors to estimate the start point of each symbol, completion, the EMTP simulation results are converted to a 6

Feeder B Primary Substation 30m 30m 60m Underground Cable Catallioti Transformer Model B2 75m Rin = 0.01457m B1 Rin Rins = 0.01826m 73m O 35m Rout = 0.01616m rout =0.0066m 292m rin = 0.0055m 98m 122m 170m 244m 280m 232m Rout Rins Feeder A rout rin 75m = 2.1 1 402m =1.68E-8 A 159m 268m 85m 158m 30m 30m 45m 62m Overhead Line 45m 65m Feeder E A2 61m 244m 60m 30m 30m 1.2m 183m 75m E2 E1 Feeder C 39m 159m 9m C2 Feeder D 30m 30m 60m 61m 61m 75m 439m D2 75m C1 122m 62m 45m 30m 30m 65m 45m D1

Fig. 7. ATP-EMTP Test Network comprising 5 LV feeders and a radial MV network.

TABLE I SIMULATION PARAMETERS

Time on Air (s) 0 . 0 0 0 . 2 5 0 . 5 0 0 . 7 5 1 . 0 0 I m p u l s e R e s p o n s e s Tx SF Q=1 Q=10 Q=100 fc BW - 2 0 E 1 t o O

- 3 0 A1 13 0.33 3.3 33 50 kHz 25 kHz - 4 0 A2 13 0.33 3.3 33 80 kHz 25 kHz - 5 0 B1 13 0.33 3.3 33 110 kHz 25 kHz

B2 13 0.33 3.3 33 140 kHz 25 kHz - 2 0 D 1 t o O C - 3 0

13 0.33 3.3 33 170 kHz 25 kHz

1 C2 13 0.33 3.3 33 210 kHz 25 kHz - 4 0 D1 13 0.33 3.3 33 240 kHz 25 kHz - 5 0 - 6 0 D2 13 0.33 3.3 33 270 kHz 25 kHz

) - 2 0 C 1 t o O E1 13 0.33 3.3 33 300 kHz 25 kHz B

d - 3 0

(

E2 13 0.33 3.3 33 330 kHz 25 kHz e - 4 0 d

u - 5 0 t i - 6 0 n g a .MAT file using the PL42MAT routine and processed by the - 2 0 B 1 t o O M demodulation code within Matlab. - 3 0

Fig. 8 shows the magnitude and impulse responses between - 4 0 a selection of 5 transmitters and the observation point (‘O’). - 5 0 The shape of these responses is representative of the MV power line channel, which is characterised by extreme multi- - 2 0 A 1 t o O path and regions of high attenuation. The RMS delay spread is - 3 0 observed to vary between 100 µs and 500 µs. In the context - 4 0 of a network-wide implementation of the proposed scheme, - 5 0 the magnitude responses show the importance of bandwidth 0 . 0 0 0 . 2 5 0 . 5 0 0 . 7 5 1 . 0 0 0 1 2 3 selection. For example, fluctuations of just a few kHz exhibit F r e q u e n c y ( H z ) T i m e ( m s ) differences of tens of dBs. Fig. 8. Magnitude and Impulse responses for 5 selected channels separating feeders A-E from the observation point, O. C. Simulation Results Fig. 10 shows the symbol error rate as a function of SNR for transmitters A1 to E1. At the chosen spreading factor 7

(SF=13) and the parameters shown in Table I, the results 1 . 0 Q = 1 0 1 . 0 1 . 0 Q = 1 0 0

e Q = 5 0 0 e e t t t show that LoRa-Mod breaks down at an SNR of around -20 a Q = 1 0 0 0 a a R R R

r Q = 2 0 0 0 r r o o o

r L o R a - M o d r r dB. However, LoRa-Mod-Enhanced continues to perform well r 0 . 5 r 0 . 5 r 0 . 5 E E E

l l l o o o b b b up to -25 dB (Q=10), -35 dB (Q=100) and -39 dB (Q=500). m m m y y y S S S

The results are similar across all transmitter points (E2 is not 0 . 0 0 . 0 0 . 0 shown here but shares the same trend). Further simulations - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 S N R ( d B ) S N R ( d B ) S N R ( d B ) confirm that additional improvements can be achieved with (a) A1-O (b) A2-O (c) B1-O higher spreading factors (at the cost of a decreased data rate). Longer Q’s reduce the effective data rate, but the ability 1 . 0 1 . 0 1 . 0 e e e t t t a a a R R R to adjust this provides flexibility. For example, more hostile r r r o o o r r r r 0 . 5 r 0 . 5 r 0 . 5 E E E channels can increase Q, effectively trading off data rate l l l o o o b b b m m m y y y for improved robustness. We have simulated 10 transmitters S S S operating simultaneously on a mixed LV-MV network, how- 0 . 0 0 . 0 0 . 0 - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 ever, much like LoRa, many more transmitters can operate S N R ( d B ) S N R ( d B ) S N R ( d B ) simultaneously, sharing both time and frequency resources due (d) B2-O (e) C1-O (f) C2-O to the orthogonality of the chirps at various combinations 1 . 0 1 . 0 1 . 0

of SF and bandwidth. This is an important feature of the e e e t t t a a a R R R

r r r proposed scheme given the vast and sprawling nature of o o o r r r r 0 . 5 r 0 . 5 r 0 . 5 E E E

l l l o o o

MV/LV networks, and the necessity for LV feeder load data b b b m m m y y y (voltage and current) from all parts of the network. S S S 0 . 0 0 . 0 0 . 0

- 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 V. HARDWARE IMPLEMENTATION AND EXPERIMENTAL S N R ( d B ) S N R ( d B ) S N R ( d B ) RESULTS (g) D1-O (h) D2-O (i) E1-O Lora-Mod-Enhanced is implemented in Field Programmable Fig. 10. SNR Versus Symbol Error Rate for SF=13, with 7,000 runs per Gate Array (FPGA) hardware using the high level architecture simulation point. shown in Fig. 9. The receiver is connected via UART to a Matlab App for visualisation and logging. The main features gain-bandwidth product of 17 MHz. The LoRa bandwidth is of the transmitter and receiver architectures are described next. 50 kHz.

A. Transmitter The FPGA based transmitter is based on a design first B. Receiver utilised in [16]. The baseband complex chirp (Re and Im) The receiver architecture shown in Fig. 9(b) digitises the is stored in a pair of 32,708 point Read Only Memory (ROM) incoming signal using a 65 MSPS, 14-bit Analog to Digital blocks. This is equivalent to an upscaling factor of 32 for a Converter (ADC), operating at a lower sampling rate of 1.6 SF=10, 1,024 point symbol. Modulation is achieved by the MHz. A Gaussian Noise generator provides the option of ROM address counter, which allows the transmitter to output introducing an arbitrary level of Additive White Gaussian phase shifted versions of the complex chirp. A Numerically Noise (AWGN) to the incoming signal. The core has 16- Controlled Oscillator (NCO) is used to generate a carrier bit resolution with a random distribution of ±9.1σ and a 176 frequency (fc) for quadrature mixing of the complex chirp period of 2 . Following downconversion and decimation by from the baseband to the . A 125 MSPS Digital an FIR decimation filter (which downsamples the 1.6 MHz to Analog Converter (DAC) is used to output the passband input signal by a factor of 32, down to the 50 kHz baseband), signal and amplification is provided by the OPA564 Power the dechirping process is carried out by a complex multiplier Operational Amplifier, which is capable of driving 1.5A at a with a 1024-point ROM-based complex chirp.

5CGXFC5C6F7C7 Intel FPGA 5CGXFC5C6F7C7 Intel FPGA SPI 10-bit address counter Recursive Moving Sum LTC2308 Choose Symbol Delay by Q 15-bit address counter Address Counter ADC Shift Address Shift Register - Delay by 1 Address Counter 1,024 Points Chirp Into Network From Network 32,768 Points Chirp + For Testing only Transducer OPA564 AWGN ROM Part ROM Part Power Amplifier Generator Coupler 1,024 Points Chirp 32,768 Points Chirp Coupler Dechirping Downconversion Generate Carrier ROM Part Embedded UART Split into ROM Part ADC NCO Complex Multiplier FFT Processor G Bins NCO PA AD9248 65 MSPS Downsample FIR Decimation Complex x Filters Multiplier Complex Multiplier Adder DAC AD9767 125 MSPS

(a) Transmitter (b) Receiver

Fig. 9. FPGA based hardware architectures for the transmitter and receiver. 8

1 . 2 5 E x p e r i m e n t a l 1 . 2 5 S i m u l a t e d REFERENCES [1] I. Berganza, A. Sendin, and J. Arriola, “Prime: Powerline intelligent 1 . 2 0 1 . 2 0 metering evolution,” in SmartGrids for Distribution, 2008. IET-CIRED. y

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N 1 . 0 0 1 . 0 0 Transactions on Power Delivery, vol. PP, no. 99, pp. 1–1, 2016. [4] Semtech, LoRa Modulation Basics: Application Note. Semtech, May 0 . 9 5 0 . 9 5 2015. [5] Y. Xiaoxian, Z. Tao, Z. Baohui, N. H. Xu, W. Guojun, and D. Jiandong, 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 “Investigation of transmission properties on 10-kv medium voltage S y m b o l N u m b e r S y m b o l N u m b e r power lines—part i: General properties,” IEEE Transactions on Power Delivery, vol. 22, no. 3, pp. 1446–1454, 2007. Fig. 11. Comparison of Experimental results, obtained with the FPGA [6] H. Gassara, F. Rouissi, and A. Ghazel, “Statistical characterization of prototype, and Simulation results using the same conditions. The AWGN is the indoor low-voltage narrowband power line communication channel,” set to -19dB, SF=10. IEEE Transactions on Electromagnetic Compatibility, vol. 56, no. 1, pp. 123–131, 2014. [7] R. Lefort, R. Vauzelle, V. Courtecuisse, N. Idir, and A.-M. Poussard, An embedded processor is used to send the Lora-Mod “Influence of the mv/lv transformer impedance on the propagation of the plc signal in the power grid,” IEEE Transactions on Power Delivery, output, S and the Lora-mod-enhanced output, H via UART vol. 32, no. 3, pp. 1339–1349, 2017. (baud = 115,200bps) to a Matlab app for visualisation and [8] S. Robson and A. M. Haddad, “On the use of LoRa for Power logging of the demodulated data. Line Communication,” in 2019 54th International Universities Power Engineering Conference (UPEC), 2019, pp. 1–6. To emulate a frequency selective channel, we have im- [9] S. Rinaldi, M. Pasetti, F. Bonafini, P. Ferrari, A. Flammini, E. Sisinni, plemented a shift register and multiplier before the AWGN G. Artale, A. Cataliotti, V. Cosentino, D. Di Cara, N. Panzavecchia, and is added. This arrangements realises a simple 4-tap channel G. Tine,` “Design of a Time Dissemination System using Chirp Modula- tion for Medium Voltage Smart Grid Applications,” IEEE Transactions response with a separation of 4 LoRa samples between taps. on Instrumentation and Measurement, pp. 1–1, 2020. [10] S. Robson and A. M. Haddad, “Development of an fpga based time C. Experimental Results of arrival estimator for plc applications,” in 2020 55th International Universities Power Engineering Conference (UPEC), 2020, pp. 1–6. Fig. 11 shows a comparison between experimental results [11] L. Vangelista, “Frequency shift chirp modulation: The lora modulation,” and simulation using the same parameters. Here, an SNR of IEEE Signal Processing Letters, vol. 24, no. 12, pp. 1818–1821, 2017. -19 dB is chosen, which, for SF=10, is below the threshold [12] U. Raza, P. Kulkarni, and M. Sooriyabandara, “Low Power Wide Area Networks: An Overview,” IEEE Communications Surveys Tutorials, in which LoRa-Mod can operator. The plots show E and the vol. 19, no. 2, pp. 855–873, 2017. noise symbols Sφ with a Q of 64. In this case, LoRa-Mod [13] T. Elshabrawy and J. Robert, “Closed-form approximation of lora enhanced can achieve error-free communication with a time modulation ber performance,” IEEE Communications Letters, vol. 22, SF 1 no. 9, pp. 1778–1781, 2018. on air of 64·(2 )·( 50,000 ) ≈ 1.3 s per running average. Good [14] Y. Guo and Z. Liu, “Time-delay-estimation-liked detection algorithm for agreement between experimental and simulation is observed. lora signals over multipath channels,” IEEE Wireless Communications Letters, vol. 9, no. 7, pp. 1093–1096, 2020. VI.CONCLUSION [15] A. Cataliotti, V. Cosentino, D. Di Cara, and G. Tine, “Oil-filled mv/lv power-transformer behavior in narrow-band power-line communication • A new PLC modulation scheme, based on a modification systems,” IEEE Transactions on Instrumentation and Measurement, of the LoRa physical layer, has been proposed. This vol. 61, no. 10, pp. 2642–2652, 2012. [16] S. Robson and A. M. Haddad, “Development of an fpga based time scheme has two versions i) LoRa-Mod, which subdivides of arrival estimator for plc applications,” in 2020 55th International the demodulated LoRa signal into a reduced set of ‘su- Universities Power Engineering Conference (UPEC), 2020, pp. 1–6. perbins’, and ii) LoRa-Mod-Enhanced, which performs statistical averaging on each superbin. • The proposed scheme performs exceptionally well in the notoriously hostile LV-MV channel, coping with both low SNRs and extreme multipath. The condition of setting the superbin size to at least as great as the RMS delay spread is emphasised. • A new simulation methodology in the ATP-EMTP was developed, allowing millions of samples and numerous transmitters to be simulated simultaneously on a mixed (LV/MV) test network. The results demonstrate robust performance in extreme multipath and SNRs as low as -40 dB, with even better performance possible at higher spreading factors and longer moving averages. • The proposed scheme is implemented in FPGA hardware and experimental results match simulation.