Efficient Pseudonoise Code Design for Spread
Spectrum Wireless Communication Systems
Mau-Lin Wu, Kuei-Ann Wen, and Chao-Wang Huang
Abstract—Power and bandwidth efficient communication
schemes are of major concerns in wireless communication sys-tems. One kind of efficient pseudonoise code is proposed in this paper that provides combined power-bandwidth efficiency. A novel algorithm for verifying the power and bandwidth efficient properties of a pseudonoise code is proposed with systematic anal-ysis on code parameters. Applications of the derived codes had been implemented on 802.11 DS/SS system, which performs 36% bandwidth reduction and 14% power consumption reduction. Several new pseudonoise codes with different code lengths are also proposed.
Index Terms—Bandwidth reduction, CMOS implementations,
low power design, pseudonoise code, spread-spectrum communi-cation, wireless LAN.
I. INTRODUCTION
I
N RECENT years, low-power design has become a very important issue in the modern very large scale integration (VLSI) design. A lot of design methodologies of minimizing power consumption in CMOS VLSI circuits were proposed in [1]–[4], where approaches of technology, circuit style and topology, architecture, and algorithm are included.As is known, the power dissipation in CMOS VLSI systems contributed mostly from the dynamic power dissipation of the system. Therefore, there was much research that focused on reducing the dynamic power dissipation of CMOS circuits. The dynamic power dissipation of CMOS circuits relates to the transition activity , capacitance load , power-supply voltage , and switching frequency , as seen in [5].
(1) The dynamic power dissipation of CMOS circuits could be reduced by reducing switching frequency [6]–[9], power-supply voltage [10], [11] and capacitance load [12]–[14]. According to the methodology newly proposed in this paper, the authors de-signed the low-power system by reducing the transition activity. We proposed one kind of efficient pseudonoise (PN) code that possesses both power and bandwidth efficiency. At first, the properties and definition of the power-saving pseudonoise Manuscript received November 5, 1999; revised August 31, 2000. This work was supported in part by the Ministry of Education and the National Science Council, R.O.C., under Contract 89-E-FA06-2-4. This paper was recommended by Associate Editor M. Ismail.
M.-L. Wu is with the Logic Research and Development Department I, In-tegrated Circuit Solution Incorporation, Hsin-Chu, Taiwan, R.O.C. He is also with the Institute of Electronics Engineering, National Chiao Tung University, Hsin-Chu, Taiwan, R.O.C.
K.-A. Wen and C.-W. Huang are with the Institute of Electronics Engineering, National Chiao Tung University, Hsin-Chu, Taiwan, R.O.C.
Publisher Item Identifier S 1057-7130(01)06238-3.
(PSPN) code are shown. The correlation between the PSPN code and the performance of the spread spectrum communi-cation system is then explored. By exploring the correlation, we proposed an efficient algorithm for search of PSPN code. Several examples of PSPN codes are derived. The properties of these codes are analyzed. Application of the proposed code had been done on spread spectrum communication system.
II. PSPN A. Conventional Definition of PN Code
The spreading code is the code sequence which is used to be multiplied with the data sequence and thus to spread the band-width of the data sequence. In general conditions, the PN codes are usually the good candidates for spreading codes. However, it is not easy to define PN code. In the past, a lot of PN codes were proposed and the randomness properties of these codes were demonstrated. For example, maximal length sequence (m-se-quence) is the well-known and widely applied PN code. The randomness characteristics of m-sequence were demonstrated in [15]. The definition of PN code in [16] is that the binary se-quence has the following “randomness criteria:”
1) The out-of-phase periodic autocorrelation function (ACF) should be a small constant, that is
(2)
where , which is in bipolar
binary code format and , which is in binary code format.
2) In every period, the number of 1s is nearly equal to the number of 0s.
3) In every period, half the runs have length one; one-quarter have length two; one-eighth have length three, etc., as long as the number of runs of a given length exceeds 1. However, there are a lot of PN codes, which are useful for spread spectrum communication but don’t meet the above three randomness criteria. In the following, we will extend the defini-tion of PN code to find the codes, which are applicable to wire-less, spread spectrum communication system. We define the PN code according to the system performance of the spread spec-trum communication system, to which the code is applied.
B. System Performance versus PN Code
For the system performance of the spread spectrum commu-nication, the processing gain of the spreading code is one of major concern. The processing gain depends on the code length 1057–7130/01$10.00 © 2001 IEEE
of the spreading code. On the other hand, one of the most im-portant system performances of the spread spectrum commu-nication system is the average acquisition time of the code ac-quisition structure in the receiver. The average acac-quisition time depends on the probability of detection and the probability of false alarm [17]. After further manipulations, we can cor-relate and to processing gain and periodic ACF of the spreading code [18]. The larger the processing gain is, the better the system performance is. The smaller the value of (2) is, the better the system performance is. Therefore, the spreading code with good system performance can be derived by checking its out-of-phase value of the ACF of the spreading code. We de-rived an index of the spreading code to indicate the system per-formance.
Definition 1: The “corrpower” of a spreading code is the
sum of squares of the periodic autocorrelation coefficients of the spreading code. We denote the corrpower of a spreading code
by
(3)
where is the periodic autocorrelation function of the spreading code .
Definition 2: The orthogonal degree of a spreading code
is defined as
(4) From the definition above, if the out-of-phase values of were small, the system performance is better, would be close to 1. Therefore, the spreading code with larger orthog-onal degree is the code with better system performance. One of the advantages of this definition of the spreading code is to skip the “randomness criteria,” which are very difficult to meet. Another advantage of this definition is to directly consider the system performance of the spread spectrum system with the spreading code.
C. Power and Bandwidth versus PN Code
Definition 3: The toggle rate of the spreading code is defined as
sign
(5) where means the absolute value of , and
sign
.
For example, consider the code . The
time diagram of the code is plotted in Fig. 1. It is very easy to verify that there are six toggles in one period of the code. Therefore, the toggle rate is .
In the spread spectrum system, the data pattern of the output spreading data is decided by the data pattern of the spreading code. As we know, the CMOS VLSI system only consumes
Fig. 1. Time diagram of codefa g, which is used to demonstrate the toggle rate of the code.
power during the period when the output signal is toggled. The relationship had been shown in (1). In the spreading output of the spread spectrum system, the transition activity depends on the transition activity of the spreading code. The larger toggle rate means much more transition activity of a spreading code. Therefore, the larger the toggle rate is, the more transition ac-tivity and the power consumption the spread spectrum VLSI system has. For low-power CMOS spread spectrum commu-nication system design, a spreading code with low toggle rate is highly expected. Moreover, the time pattern of the output-spreading signal is decided by the output-spreading code. If the toggle rate is low, the changing of the output-spreading signal is slow. The slow changing in the time domain means the low frequency in the frequency domain. Therefore, it means narrow bandwidth occupation as well. The toggle rate of the spreading code could be used as a merit of figure for power consumption and band-width occupation of the spread spectrum system.
D. PSPN Code
From the previous discussions, we know that a PN code should have a great orthogonal degree, and a low-power spreading code requires low toggle rate. Therefore, a PSPN should be a spreading code with great orthogonal degree and low toggle rate. In the following, we proposed the definition of the PSPN code.
Definition 4: A PSPN code of length with factor ( , ), PSPN , is the spreading code with the orthogonal degree
and the toggle rate .
The main idea of this approach is to search a spreading code with good power, bandwidth, and system performance proper-ties by calculating parameters of the code, instead of simulating the whole system. The computational complexity of the latter is much more than the previous one.
III. DERIVATION OFPSPN CODES
In considerations of high performance, low-power, and band-width efficiency, a spreading code with large orthogonal de-gree and low toggle rate is the best choice. However, there is a tradeoff between the orthogonal degree and the toggle rate of
TABLE I
THEORTHOGONALDEGREES ANDTOGGLERATES OFSOMEUSEFULPSPN CODES
Fig. 2. Autocorrelation function of PSPN code.
the spreading code. In general, a spreading code with great or-thogonal degree usually has high toggle rate, and a spreading code with low toggle rate usually has low orthogonal degree. In regard to orthogonal degree and toggle rate, lower and upper bound should be carefully specified. By system performance and power consumption simulation, we found that the PSPN codes with and would be efficient for the spread spectrum communication application. Therefore, by an efficient searching algorithm, all the PSPN codes with
and had been explored for .
The efficient searching algorithm is described in details in the Appendix.
In Table I, part of PSPN codes had been listed for illustration of the properties of the PSPN codes. The code length is used to subscript the code name for distinguishing, which is shown in the last column of Table I. The orthogonal degrees of these PSPN codes are larger than 0.80 and the toggle rates are all less than 0.45. PSPN is taken as an example to illustrate the computational complexity of orthogonal de-gree and the toggle rate of the PSPN code. If we express the PSPN code in the bipolar binary code format, then PSPN
. By simple calculation, we find that the periodic autocorrelation function of PSPN
code ,
which is plotted in Fig. 2. The out-of-phase values of the ACF
are small except the two values of 3 at indexes of 1 and 10. The corrpower and orthogonal degree of PSPN code could be calculated from the autocorrelation function by (3) and (4). Therefore, PSPN (6) PSPN PSPN (7) It is easy to check that the toggle number of PSPN code is 4. The toggle rate of this code can be easily calculated by
. From the procedures of the calculations of the orthogonal degree and toggle rate of PSPN code, the reader may realize that it is a very simple and efficient method for searching the low-power and bandwidth efficient PSPN codes by calculating the orthogonal degree and toggle rate. The complemented and the shifted version of these PSPN codes are also PSPN codes and they have the same values of orthogonal degree and toggle rate. The shifted version of these PSPN codes could form a PSPN code set for multiuser application such as CDMA wire-less communication system.
IV. ANALYSIS ANDSIMULATION
Comparison between the proposed PSPN codes and conven-tional PN codes in bandwidth occupation, system performance, and power consumption can be observed with Tables I and II. Each PN code is subscripted with its code length. The PN code is exactly the Barker code, which is the specified PN code ap-plied in the wireless local area network (WLAN) standard, IEEE 802.11 [19]. The PN code is the so-called maximal length se-quence with degree 4 [15]. It is also called m-sese-quence. Other codes are codes with large orthogonal degree and the proposed efficient searching algorithm obtains them. The orthogonal de-grees of the conventional PN codes are usually larger than those of PSPN codes, while they have larger toggle rates.
In the following, the bandwidth, system performance, and the power consumption of the proposed PSPN codes are analyzed.
TABLE II
THECONVENTIONALPN CODES ANDTHEIRORTHOGONALDEGREES ANDTOGGLERATES
Fig. 3. Power spectral density of PSPN code and PN code.
A. Bandwidth Analysis
For bandwidth analysis, we plotted the power spectral density of the proposed PSPN codes and the conventional PN codes. In Fig. 3, the power spectral density functions of PSPN and PN are plotted for comparison. The power of the PSPN code is observed to be more concentrated at low frequency. Define the 90% bandwidth and 95% bandwidth, BW and BW , as
(8)
(9)
where is the power spectral density of the code and the unit of the BW and BW is Hertz.
By (8) and (9), we calculate these values of PSPN code and PN code. BW of PSPN code and PN code are
and , respectively, where is the chip rate of the spread spectrum system. is equal to the data rate multiplied by the code length. It is shown that the bandwidth of PSPN code is only about 74% of that of PN code. That is to say, the per-centage of reduction of bandwidth of PSPN code is about 36% compared to PN code. There is the similar result for BW . For other codes with different code lengths, the proposed PSPN codes perform 10% to 36% reduction of bandwidth. These re-sults are included in Table III. We plot the bandwidth versus toggle rate plot in Fig. 4 and it prevails that the spreading code with a lower toggle rate has a narrower bandwidth. The positive
correlation between bandwidth and toggle rate could be con-firmed from this plot.
B. Performance Analysis
In the system performance analysis, we take PSPN and PN codes as the examples to do the simulation. In the following, the probability of detection of the spread spectrum systems are simulated in different SNR values, which is in the range from 10 dB to 10 dB. The proposed algorithm in [18] is applied in this simulation to design the spread spectrum systems with constant probability of false alarm and maximal probability of detection. In the simulation, the constant prob-ability of false alarm is set to 0.01. Because the bandwidth of PSPN code is only 74% of that of PN code, the effective SNR value of PSPN code should be compensated by 1.94 dB ( ). Based on these assumptions, the simulation results of the probabilities of detection are shown in Fig. 5. Because the probabilities of false alarm of these two systems are both equal to 0.01, the system with larger probability of detection performs better in this simulation. Therefore, it is shown that the system with PSPN code performs better probability of detection than the system with PN code. The difference of the system performance is about 1 dB.
For the spread spectrum communication system, the band-width of the transmitted signal is usually several times of the bandwidth of the source data. If some interference signal appears within the bandwidth of the transmitted signal, it will be rejected by the despreading procedure in the receiver of the spread spectrum system. This is the interference-rejection characteristics of the spread spectrum system. Therefore, the bandwidth-efficient spread spectrum system we proposed in this paper will perform better in the viewpoint of interference. The probability that an interference signal occurs within the bandwidth of the transmitted signal is lower due to the narrower bandwidth of the transmitted signal. At the same time, the effective SNR of the derived system is higher than that of the conventional one. All the above effects conclude better system performance of the proposed spread spectrum system.
C. Power Consumption Simulation and Analysis
For the simulation of the power consumption, we imple-mented a spread spectrum system of CMOS VLSI circuits. This VLSI circuits are implemented by a 0.25– m CMOS logic process. The function blocks of this spreading system are shown in Fig. 6. The VLSI circuit is designed by using the standard library of TSMC 0.25– m CMOS logic process. Spreader is used to multiply the source data with the PN code.
TABLE III
BANDWIDTHCOMPARISONRESULTSBETWEENPSPN CODES ANDPN CODES
Fig. 4. Plot of bandwidth versus toggle rate of the spreading codes.
The block of “frequency divider” generates the clock with data rate. PN code generator generates the PN code. Despreader is used for despreading procedure and the decision circuit detects the signal. The transistor netlist of the blocks in Fig. 6 is implemented. The circuit level simulator Hspice simulates the power consumption of the transistor netlist. All the blocks shown in Fig. 6 are included in this power consumption simulation. The circuit schematics described in Fig. 6 could be operated by different spreading codes with different code lengths. That is to say, this is a soft-coded spread spectrum system. The simulation results of the power consumption are listed in Table IV. From Table IV, we find the percentages of reduction for power consumption range from 8% to 14% with PSPN codes compared to PN codes. The concept of low toggle rate means low-power consumption has been verified by the simulation results.
D. Power-Bandwidth-Product Performance Index
Because power consumption and bandwidth are both impor-tant system performances for a spread spectrum communica-tion system, we define a power-bandwidth combined perfor-mance index to evaluate the power-bandwidth efficiency of the proposed PSPN codes. Because the effect of bandwidth to the system performance is more important than that of the power consumption, the weight of bandwidth is twice of that of power
Fig. 5. System performance comparison between PSPN code and PN code.
Fig. 6. Function blocks of the spreading system are plotted.
consumption. For the same reason, the weight of BW is two times of that of BW . The PBPI (power-bandwidth
perfor-mance index) of the spread spectrum system is given by
PBPI (10)
The PBPIs of the PN codes and PSPN codes in the case of 1–MHz chip rate are listed in Table V. The percentage of per-formance improvement for the proposed PSPN codes is listed in the last column of Table V. The percentages are between 16%
TABLE IV
COMPARISON OFPOWERCONSUMPTIONBETWEENPSPN CODES ANDPN CODES
TABLE V
COMPARISON OFPOWER-BANDWIDTHPERFORMANCEINDEXBETWEENPSPN CODES ANDPN CODES
and 36% for different PSPN codes. This result is consistent with the results in Tables III and IV.
V. CONCLUSION
The low-power, bandwidth-efficient, and randomness proper-ties of the spreading code could be verified by the toggle rate and the orthogonal degree of the spreading code. Because the calcu-lation of the toggle rate and the orthogonal degree is very simple, we proposed an efficient algorithm to search a low-power and bandwidth-efficient PN code. The bandwidth efficient property of the proposed code is confirmed by calculating the power spectral density function of the code and the 90% and 95% power bandwidths of the code. The system performance of the proposed code is also simulated to verify that the proposed code is suitable for the spread spectrum applications. The power con-sumption property is confirmed by the circuit simulation. Sev-eral PSPN codes are proposed and analyzed in this paper, which are found by the proposed efficient algorithm. These proposed PSPN codes have better bandwidth and power consumption per-formance than the conventional system. These proposed PSPN codes are the good choice for the power-efficient and band-width-efficient spread spectrum communication systems.
APPENDIX
THEEFFICIENTSEARCHINGALGORITHM
The efficient searching algorithm of proposed PSPN code is described in this appendix. Let us assume that the code length is and the minimal orthogonal degree and the maximal toggle rate of the PSPN code are and , respectively. The purpose of this proposed algorithm is to search all the PSPN code
with and . The following are the
procedures of the proposed algorithm:
Step 1: Set and .
is the flag for the status of the th code . means the code is not checked yet. means the code is checked and it is
a PSPN code. means the code is
checked and it is not a PSPN code.
Step 2: . The code is
denoted by
(A.1) If , then go to Step 6.
Step 3: Calculate . If , then set
and go to Step 5.
Step 4: Checking by
(A.2) where is the coefficients of
. IF (A.2) holds, then set
, otherwise .
Step 5: Set the shifted and complemented version codes of the same status as .
5.1) Set , , and . 5.2) . 5.3) If , then . 5.4) Set and . 5.5) . 5.6) If , then go to 5.2).
Step 6: If , then go to Step 2.
Step 7: The PSPN codes are those with . The above algorithm is a simplified exhaustive search method. Because the orthogonal degrees and toggle rates of the complemented and shifted version codes of are the same as those of , only one of the codes is required to be calculated for verifying that they are PSPN codes or not. This is done by Step 5. Therefore, the total candidate codes for searching in this algorithm is , instead of for the exhaustive search. Because the computational complexity of toggle rate is much simpler than that of orthogonal degree, toggle rate is calculated first and the codes with
are impossible to be a PSPN code and the computational of the orthogonal degrees of these codes are omitted. This is done by Step 2. This reduces the computational complexity of this algorithm. For the calculation of orthogonal degree, a modified approach is also proposed to reduce computational complexity. The condition of can be reformed to
(A.3)
where the ACF of is .
After some manipulation, (A.3) is reformed to (A.2). In the right-hand side (RHS) of (A.2), is a constant and can be calculated in advance. In the left-hand side (LHS) of (A.2), we can find that (A.2) doesn’t hold by only calculating several terms of for some cases. For example, if there exists a number
, such that
(A.4) then we can be sure that (A.2) doesn’t hold and is not a PSPN code. This is because and
(A.5) The detailed calculation procedures of (A.2) are described in the following:
Step 1: Set , , and .
Step 2: , calculate .
Step 3: . If , then go to
Step 5.
Step 4: If , then holds and go to
Step 6. Otherwise, go to Step 2.
Step 5: . is not a PSPN code. The pro-cedure is finished.
Step 6: is a PSPN code.
Not all the coefficients of are required to be calculated in the above approach, the computational complexity of is multiplication and addition. However, the computational complexity of the above approach is reduced to multiplication and addition, where depends on . For general conditions, is below for the non-PSPN codes. From the above descriptions, the computational com-plexity of this searching algorithm is nearly less than
times of that for an exhaustive search.
REFERENCES
[1] A. P. Chandrakasan, S. Sheng, and R. W. Brodersen, “Low-power CMOS digital design,” IEEE J. Solid-State Circuits, vol. 27, pp. 473–484, Apr. 1992.
[2] G. M. Blair, “Designing low-power digital CMOS,” Electron. Commun. Eng. J., vol. 6, pp. 229–236, Oct. 1994.
[3] A. P. Chandrakasan and R. W. Brodersen, “Minimizing power consump-tion in digital CMOS circuits,” Proc. IEEE, vol. 83, pp. 498–523, Apr. 1995.
[4] J. M. C. Stork, “Technology leverage for ultra-low power information systems,” Proc. IEEE, vol. 83, pp. 607–618, Apr. 1995.
[5] N. H. E. Weste and K. Eshraghian, Principles of CMOS VLSI Design–a System Perspective, 2nd ed. Reading, MA: Addison-Wesley, 1994. [6] M. Alidina, J. Monteiro, S. Devadas, A. Ghosh, and M. Papaefthymiou,
“Precomputation-based sequential logic optimization for low power,” IEEE Trans. VLSI Syst., vol. 2, pp. 426–436, Dec. 1994.
[7] C. Y. Wang and K. Roy, “An activity-driven encoding scheme for power optimization in microprogrammed control unit,” IEEE Trans. VLSI Syst., vol. 7, pp. 130–134, Mar. 1999.
[8] T. Xanthopoulos and A. P. Chandrakasan, “A low-power IDCT macro-cell for MPEG-2 MP@ML exploiting data distribution properties for minimal activity,” IEEE J. Solid-State Circuits, vol. 34, pp. 693–703, May 1999.
[9] S. Ramprasad, N. R. Shanbhag, and I. N. Hajj, “A coding framework for low-power address and data bused,” IEEE Trans. VLSI Syst., vol. 7, pp. 212–221, June 1999.
[10] T. Kuroda, K. Suzuki, S. Mita, T. Fujita, F. Yamane, F. Sano, A. Chiba, Y. Watanabe, K. Matsuda, T. Maeda, T. Sakurai, and T. Furuyama, “Vari-able supply-voltage scheme for low-power high-speed CMOS digital de-sign,” IEEE J. Solid-State Circuits, vol. 33, pp. 454–462, Mar. 1998. [11] M. R. Stan and W. P. Burleson, “Low-power encodings for global
communication in CMOS VLSI,” IEEE Trans. VLSI Syst., vol. 5, pp. 444–455, Dec. 1997.
[12] J. T. Ludwig, S. H. Nawab, and A. P. Chandrakasan, “Low-power digital filtering using approximate processing,” IEEE J. Solid-State Circuits, vol. 31, pp. 395–400, Mar. 1996.
[13] A. T. Erdogan and T. Arslan, “Low-power coefficient segmentation algorithm for FIR filter implementation,” Electron. Lett., vol. 34, pp. 1817–1819, Sept. 1998.
[14] S. H. Cho, T. Xanthopoulos, and A. P. Chandrakasan, “A low power variable length decoder for MPEG-2 based on nonuniform fine-grain table partitioning,” IEEE Trans. VLSI Syst., vol. 7, pp. 249–257, June 1999.
[15] E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and wideband CDMA cellular networks,” IEEE Commun. Mag., pp. 48–54, Sept. 1998.
[16] P. Fan and M. Darnell, Sequence Design for Communications Applica-tions. New York: Wiley, 1996.
[17] A. Polydoros and C. L. Weber, “A unified approach to serial search spread-spectrum code acquisition—Part I: General theory,” IEEE Trans. Commun., vol. COM-32, no. 5, pp. 542–549, May 1984.
[18] M.-L. Wu, K.-A. Wen, and C.-S. Chen, “The optimized threshold deci-sion of pseudo noise code acquisition in spread spectrum communica-tion,” IEICE Trans. Fundament. Electron., Commun. Comput. Sci., vol. E83-A, no. 11, pp. 2152–2159, Nov. 2000.
[19] Wireless Medium Access Control and Physical Layer WG, IEEE Draft Std. P802.11, Wireless LAN: IEEE Standards Dept., D3, Jan. 1996.
Mau-Lin Wu received the B.E.E. and M.E.E.
degrees from the Department of Electrical Engi-neering, and the Institute of Electrical EngiEngi-neering, National Taiwan University, Taipei, Taiwan, R.O.C., in 1994 and 1996, respectively. Since 1998 he has been pursuing the Ph.D. degree at the National Chiao Tung University.
From 1996 to 2000, he was a VLSI Circuit De-signer with Taiwan Semiconductor Manufacturing Company, Hsin-Chu, Taiwan, R.O.C. Since 2000, he has been an IC Designer with Integrated Circuit Solution Incorporation, Hsin-Chu, where he is focused on the design of wireless communication systems.
Kuei-Ann Wen received the B.E.E., M.E.E., and
Ph.D. degrees from the Department of Electrical Engineering and the Institute of Electrical and Computer Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., in 1983, 1985, and 1988, respectively.
Ms. Wen is currently a Professor with the Depart-ment of Electrical Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.
Chao-Wang Huang received the B.S. and M.S.
de-grees from the Department of Electrical Engineering and the Institute of Electronics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1996 and 1998, respectively, and is currently pursuing the Ph.D. degree with the same institute.
