Energy Consumption Improvement of OOK Transmitter Based on Minimum Energy Coding

Energy consumption of Wireless Sensor Networks (WSNs) including OOK transmitter is important for short range transmission and long battery life time requirements. In this paper, the Minimum Energy (ME) coding strategy is adopted to improve the energy e(cid:30)ciency of an OOK transmitter. We (cid:28)rst give the energy consumption model based on a real OOK transmitter, which can completely switch o(cid:27) the transmitter during the transmission of low bit ’0’ and has an energy e(cid:30)ciency of 52 pJ/bit. Based on this energy consumption model, ME-Coding provides an energy e(cid:30)ciency of 30 pJ/bit for coding size k = 3 . Moreover, larger coding size o(cid:27)ers more signi(cid:28)cant improvement, at the sacri(cid:28)ce of spectral e(cid:30)ciency and transmission range. In this paper, we have also determined a closed-form solution for the optimal coding size for a given transmission range constraint.

constrained applications with an unchangeable battery or other limited power supplies by energy harvesting.
An energy ecient modulation scheme in physical layer is signicant for sensors to conserve energy. Many modulation and coding schemes could be employed to operate with low SNR for a given bit error performance, but most of them are often complex and their circuit power consumption is important.
Considering the transmit power and bandwidth eciency, among various modulation techniques, the On/O keying (OOK) modulation scheme is one of the most preferred choices for WSNs, WBANs or WNSNs. Compared with M-FSK and M-PSK, OOK modulation achieves the best energy eciency. FSK has good SNR performance at the cost of complexity in the receiver [1]. And FSK based transmitter in [2,3] has an energy eciency of 1000 and 3 nJ/bit with data rate of 25 and 300 kb/s, respectively. M-PSK sacrices the transmit power to achieve higher bandwidth eciency as the number of symbols increases [4]. While BPSK has better performance in SNR and is robustness to interference, but the transmitter and receiver are much more complex. As OOK employs simple circuits in the transmitter and receiver, OOK based transmitter in [57] has energy eciency of 3.8 nJ/bit, 4.09 nJ/bit and 52 pJ/bit with data rate of 1 kb/s, 330 kb/s and 10 Mb/s, respectively. And it is possible to nd a transmitter which could be switched o during the transmission of bit 0 . [7] describes a realistic low power OOK transmitter, which could be completely switched o for the low power consumption, including both the oscillator and output buer, when transmitting bit 0 . Besides, if a sub-picosecond pulse is transmitted for bit 1 , the power of a sub-picosecondlong pulse is contained within the terahertz frequency band [810], OOK modulation can also be used by nano antenna. So far, most of the researches [1114] on WNSNs are OOK based WNSNs.
Because the OOK transmitter consumes energy only when transmitting high bit (bit 1 ), it is possible to further save the transmission energy by adopting the low-weight coding. The codeword's weight is the number of high bits contained in this codeword. The basic idea [15] of a low-weight coding scheme is mapping source words into codewords with least possible bit 1 , that means transmitting as few high bits as possible to reduce the transmission energy consumption. Prakash et al. [16] propose to map 2 k − 1 bits codewords to k-bit source words. Hence, there is no more than one high bit in the codeword of the corresponding codebook, this low-weight coding scheme is named Minimum Energy Coding (ME-Coding). Other researchers [13,17,18] use the constant weight codewords or variable-length low-weight codes to save energy by minimizing the average weight of codewords. But the complex heuristic algorithm limits its application range.
Recent analyses of WSNs energy eciency have been widely based on a general sensor node power consumption model [19]. In our work, an energy consumption model based on a real physical circuit is adopted, which should be more accurate and practical.
In this paper, we investigate the energy consumption of the ecient OOK transmitter described in [7] by adopting ME-Coding proposed in [16].
The contributions of this paper are as follows, rstly based on the ME-Coding OOK modulation, an energy model is proposed, considering the energy consumption of both the transmission and circuit based on a real transmitter; secondly, ME-Coding is used in the above model to signicantly improve the energy consumption performance; thirdly the coding size k, an important factor is analytically investigated in terms of the transmission range.
The rest of this paper is organized as follows. Section 2 gives the BER analysis of ME-Coding. Section 3 introduces the system model of a realistic OOK transmitter based on ME-Coding OOK modulation. Section 4 presents the numerical results of the energy consumption improvement by ME-Coding. Section 5 describes the coding size optimization problem and gives the optimal coding size in terms of the transmission range. The paper is concluded in Section 6.

BER of Minimum energy coding with soft decision
For low data-rate wireless applications, the simplest form of digital modulation techniques like OOK can be considered thanks to its great energy eciency. ME-Coding can save energy by minimizing the number of ones present in the coded message. The basic idea involves mapping every k bits of a source bitstream into an n-bit (n = 2 k − 1) codeword (standard form, M E[n, k]). In this case, all the source symbols are mapped into codewords with no more than one high bit. It reduces the transmission energy consumption but sacrices the bandwidth eciency. Then by code-by-code detection process (soft decision in [16,21]) we consider the bit with the highest strength and greater than a threshold as bit 1 and the rest is decided as bit 0 .
As examples, the codes for M E [3,2] and M E [7,3] are given in Table 1. The 2 k = n+1 codewords are composed of blocks of n bits. The rst codeword is the all zero codeword and the n other codewords contain only one high bit. In this paper, the elements of the codeword will be denoted as chips. Table 1 Minimum-Energy Code table for k = 2 and 3   Source bits codeword Source bits codeword   00  000  000  0000000  01  001  001  0000001  10  010  010  0000010  11  100  011  0000100  100  0001000  101  0010000  110  0100000  111  1000000 The bit error probability of OOK ME-Coding received through an AWGN (Addition White Gaussian Noise) channel is recalled [21,22] as follows.
Denote P eM and P eS as the error probabilities of a high bit being received as a low bit and a low bit being received as a high bit, respectively, and with the threshold equal to A/2, where A is the amplitude of bit 1 , then for a coherent receiver we have is the energy-to-noise spectral density ratio and erfc(·) is the complementary error function.
As ME-coding with hard-decision decoding does not have any error recovery capability, soft decision decoding (code-by-code detection) is used to improve the performance of ME-coding. There are two situations to be considered.

The original symbol is not all-zeros
Let P m0 the probability of codeword M i being received as M 0 (all zero codeword), we have Let P ij the probability of codeword M i being received as another codeword For the coherent receiver, P ij is given by

The original symbol is all-zeros
The event M 0 being received as M j occurs only when the jth bit changes to bit 1 and all the other n − 1 bits remain zero. Therefore for the coherent receiver, P 0j is given by Assuming transmission over an AWGN channel, the bit error probabilities of dierent ME-Coding schemes can be calculated theoretically by (5), and compared with the simulation results. Figure 1 shows the improvement in bit error probability using soft decision [15]. Compared to the uncoded OOK (k = 1) and for an error probability of 10 −3 , about 3 dB and 5 dB improvements in SNR per bit are respectively obtained with ME [7,3] and ME[63,6] using soft decision. This gain can be used to reduce the transmit power in order to increase the energy eciency. But the total energy budget must also take into account the circuit power consumption. 3 Energy consumption model of a realistic OOK transmitter OOK is a convenient modulation scheme for wireless communication because of its simplicity in implementation both at the transmitter and receiver sides. ME-Coding can be implemented using OOK with the advantage that the circuit power consumption when transmitting bit 0 will be much lower than when transmitting bit 1 . An energy consumption model is proposed in this paper which is specially adapted to ME-Coding using OOK modulation.
The 433-MHz OOK transmitter described in [7] is considered. The circuit completely turns o the transmitter during the transmission of bit 0 , and employs a speed up scheme to obtain high data rates and low wake up time. From the realistic parameters of transmitter [7], the power consumption can be written as where r d is the duty cycle of the message, P h is the average power during the ON state. These parameters can be deduced from the data given in [7]. We have : P dc = 518µW for r d = 1/2. By using (6), we deduce P h = 1.036 mW. For ME coding, the circuit power consumption during a large part of the symbol will be null. Using the circuit consumption model, the energy consumption per source bit for ME-coding can be derived as follows.
When the symbols are equiprobability, the average duty cycle of M E[n, k] is given by when the symbols have the same probability. Assuming a source bit rate R b , the symbol duration is T s = k/R b and the ON duration is T h = 1 Rc = k (2 k −1)R b with R c the chip rate. So, the total energy per bit is We can deduce from this equation that the total energy per bit is a decreasing function of the chip rate R c . For a given modulator, R c is limited (for example 10 MHz in the circuit described in [7]). If we denote this maximum chip rate by R c,max , the maximum bit rate for M E[n, k] is : Assuming that the bandwidth is approximately equal to the chip rate, the spectral eciency can be written as Hence, the spectral eciency is a decreasing function of k. As expected, increasing k reduces the total energy per bit at the price of the spectral eciency (or of the bit rate if the chip rate is limited).
To simplify the design and obtain a low power consumption, the considered transmitter has a nonadjustable transmit power during the ON state, denoted by P out . The average transmitted energy per bit (a part of E b,tot ) can be written as Assuming a free space path loss and thermal noise, the received average bit energy to noise ratio [1] can be expressed as where d is the distance between the transmitter and receiver, λ is the wavelength, k B is the Boltzman constant, T o is the temperature and M g is a safety margin. The values of these parameters are given in Table 2. The safety margin Boltzman's Constant given by a target bit error rate, then the transmission range can be deduced from (12) by replacing R b by its maximal expression (9) We can see from this last expression that the transmission range is a decreasing function of k.

Numerical results
According to the energy consumption model of the ME-Coding based OOK transmitter, we can analyze the energy consumption per bit.
When ME-coding scheme is used for this OOK transmitter, the energy consumption per bit (8) can be plotted in Figure 2, which shows that the energy consumption is a monotonically decreasing function of R b . So increasing the source bit rate can reduce the energy consumption per bit. For uncoded OOK, the energy consumption is near to a small value of 52 pJ/bit when the bite rate is 10 Mbps. More importantly, it is shown that ME-coding can be used to signicantly reduce the energy per bit of this circuit. Furthermore, the improvement of energy consumption performance is more notable as k is larger.
We also analyze the total energy consumption per bit in terms of the coding size k for ME-coding as shown in Figure 3. The total energy consumption decreases when the coding size increases. So the optimal coding size k should be taken as large as possible. For instance, the energy consumptions per source bit are 30 pJ/bit and 17 pJ/bit for coding sizes k = 3 and k = 6 respectively, which is much smaller than the uncoded OOK (k = 1) 52 pJ/bit. However, the improvement is more important for k < 10 than for k > 10.   range. Because the output power of this circuit is xed, increasing the coding size decreases not only the average transmitted energy per bit but also the range of the transmitter, according to (11) and (13). That means k should be as large as possible for more energy eciency but as small as possible for large transmission range. We assume an application where the range of the transmitter must be at least d min and we want to nd k that satises this constraint, and at the same time, minimizes the energy per bit consumed by the transmitter. This problem can be formulated as As the energy consumption and transmission range are both decreasing functions of the coding size k, the constraint is active. According to (12), the solution of the optimization problem is to nd k from the following equation: r 0 is a function of k for a given BER. As shown in [21], the bit error probability of OOK based ME-Coding received through an AWGN channel by a soft decision coherent receiver is given by (5), which is too complex to be used in (14). Therefore, we try to nd a simple function to approximate the bit error probability. Figure 1 shows the true values [22] of signal to noise ratio ( E b No ) for dierent bit error rates. According to the characteristics of these values, we propose to approximate these points by the following simple function: where a and b can be obtained for dierent values of BER, through LS algorithm, their values are given in Table 3.
According to the approximation (16) and (15), (14) can be rewritten as: which can be solved for k: where W L (x) is the Lambert function. Figure 5 shows a comparison between the transmission ranges obtained by the true value of r 0 (mark points) and by the approximation in (16) (solid lines) respectively, for a given k. This gure indicates that the approximation gives good results with the advantage of providing an closed-form solution (18) for the optimization problem (15).  For example in Table 3, assuming two given transmission distances d min of 5 m and 10 m with BER = 10 −3 , the coding sizes calculated by (18) are 5.6 and 2.95 respectively. Therefore the optimal coding sizes k o are 5 (ME[31,5]) and 2 (ME [3,2]) respectively. Besides, Table 3 also presents the energy consumption per bit E ko of the optimal coding size k o and the energy reduction with respect to the uncoded OOK: E R = E ko /E 1 . For small transmission ranges, the coding size can be increased to provide an important energy reduction. As the solution of the optimization problem is to nd k from (13). Figure  6 provides the obtained results for dierent values of the target bit error rate. The optimal k increases when the distance decreases and the bit error rate increases. For each value of P e , a maximum range is obtained when the optimal k reach 1. For example the range is limited to 11m for P e = 10 −4 . Figure 7 shows the total energy per bit consumed by the transmitter for optimal k. This last gure shows that the optimization of the code length allows reducing the total energy per bit to very low values for a given maximum range.

Conclusion
This paper has studied the application of ME-coding to an ecient OOK circuit which completely switches o the transmitter during the transmission of bit 0 . This circuit provides an energy eciency of 52 pJ/bit and high data rate (10 Mbps ) for uncoded OOK. We have proposed OOK matched energy consumption model and described an energy model of the realistic circuit, which show that the energy consumption per bit can be reduced to 30 pJ/bit using coding size k = 3. Moreover, the improvement will be more important as k increases. Due to the xed output power of the circuit, increasing the coding size reduces the transmission distance. A closed-form solution has been found is proposed to determine the optimal coding size for a given maximum range. Even our work is based on a specic transmitter, it can be easily adapted to other OOK based transmitters.