This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE CCNC 2006 proceedings.
Advanced Coding Schemes for a Multiband OFDM Ultrawideband System towards 1 Gbps Timo Lunttila and Sassan Iraji Nokia Research Center P.O. Box 407, FIN-00045 Helsinki, Finland
[email protected] [email protected]
Heikki Berg Nokia Research Center P.O. Box 100, FIN-33720 Tampere, Finland
[email protected]
Abstract
MHz width each [1, 2, 3]. Devices with MB-OFDM UWB technology provide data payload rates up to 480 Mbps. The forward error correcting code (FEC) used for this system is convolutional codes (CC) [1]. Although the commercial version of the MB-OFDM UWB chip still is in its way to come in the near future, there are some demands to increase the data rate of MBOFDM UWB further beyond 480 Mbps, up to 1 Gbps and even higher. This is due to the fact that in future, wireless personal area network (PAN) devices should support transferring huge amount of data, e.g., multimedia, among themselves with very high speed. One way to increase the data rate of the current MB-OFDM UWB is to use higher order modulation. Theoretically it is easy to see that MBOFDM UWB provides uncoded bit rate of 1280 Mbps using 16-QAM modulation [1, 2, 3]. On the other hand advanced FEC not only can improve the performance of the current MB-OFDM UWB in terms of PER but also must be used in the future high-rate MB-OFDM UWB in order to gain good performance. In this paper, we propose structured LDPC and PCZZ codes for an MB-OFDM UWB system aiming for the high-rate up to 1 Gbps. We demonstrate the performance of the system using these advanced coding schemes with 16-QAM modulation and compare it to that of convolutional codes. The range of such systems considering the available link budget are addressed too. We have done the complexity analysis for a transmitter and receiver using these schemes, which is subject of some other publications. It is noteworthy to mention that the advanced coding scheme can be even implemented in the current MBOFDM UWB system using QPSK modulation to further improve their performance. The price to pay is somewhat increased transmitter and receiver complexities. The rest of the paper is organized as follows. Section II covers a brief description of an MB-OFDM UWB system. Section III gives an overview of the zigzag and proposed structured LDPC codes. In Section IV, we provide the simulation, link budget and range results . Section V contains
Advanced coding schemes such as parallel concatenated zigzag (PCZZ) and LDPC codes are shown to provide performance close to turbo codes. In this paper we propose PCZZ and structured LDPC coding for an MB-OFDM UWB system with 16-QAM modulation aiming at increasing the data rate of the current system up to 1 Gbps. We evaluate the performance of the PCZZ and LDPC coding schemes in such a system. In particular, it is shown that the PCZZ and LDPC codes provide 3-4 dB gain in packet error rate compared to convolutional codes. We also address the link budget and achievable ranges for such a system with different coding rates. The proposed PCZZ and structured LDPC codes may be considered as a potential channel coding scheme for the future Multiband OFDM UWB systems providing data rates up to 1 Gbps or higher.
1. Introduction The Federal Communications Commission (FCC) has defined the ultrawideband as any radio technology with a spectrum that occupies greater than 20 percent of the center frequency or a minimum of 500 MHz. In 2002 the FCC allocated unlicensed radio spectrum from 3.1 GHz to 10.6 GHz for these purposes. The FCC defined a specific minimum bandwidth of 500 MHz at a -10 dBm level rather than requiring an UWB radio to use the entire 7.5 GHz band to transmit information. The new definition for UWB given by the FCC, has been a driver to shift away the UWB system design based on a traditional impulse radio technique to a multiband design. Among different proposals for UWB systems, one of the most interesting designs is based on Multiband OFDM (MB-OFDM) approach [1, 2, 3]. In this method, the available frequency spectrum is divided into several bands of 528
1-4244-0086-4/06/$20.00 ©2006 IEEE.
553
conclusions. Scrambler
CC
Puncturer
3-Stage Interleaver
QPSK Mapper
IFFT
DAC
Time Frequency Kernel
2. Brief system overview of an MB-OFDM UWB
Figure 2. Transmitter block diagram for a MBOFDM UWB system.
As it was mentioned, in the current MB-OFDM UWB system, the available frequency spectrum is divided into several bands of 528 MHz width each [1, 2, 3]. This system employs a multiband orthogonal frequency division modulation scheme for transmitting information from one device to another. The forward error correcting code (FEC) used for this system is a rate 1/3 convolutional code (CC) with additional punctured rates of 1/2, 5/8 and 3/4. The encoded data is spread using a time-frequency code (TFC) and then interleaved [1].
3. Advanced coding schemes 3.1. Zigzag code One of the simplest codes is single parity check (SPC) code. Zigzag codes was first introduced in [5] and it is based on SPC code. In the same paper it is claimed that the performance of the concatenated zigzag codes are close to the standard turbo codes (with only about 0.3 dB difference). The greater advantage of the concatenated zigzag codes is the low complexity of its decoder [5].
Let us consider for simplicity an MB-OFDM UWB system with only three bands. Figure 1 shows an example of the transmission method in this system. In MB-OFDM UWB system, zero-padded (ZP) prefix is added to an OFDM symbol. The advantage of using ZP prefix instead of common cyclic prefix (CP) is that the power back off at the transmitter can be avoided [2]. Both ZP prefix and CP provide robustness against multipath channels in an OFDM system [4].
A zigzag code can be described graphically as it is shown in Figure 3. The information bits are denoted by {d (i, j)} , i = 1, 2, · · · , I & j = 1, 2, · · · , J. The parity bits are represented by {p (i)} , i = 1, 2, · · · , I. A segment is defined as [p (i − 1) , d (i, 1) , d (i, 2) , · · · , d (i, J) , p (i)].
Freq (MHz) Zero-Padded Prefix
4752
4224
3696
3168 OFDM Symbol
Time
Figure 1. An example of the transmission method using 3 bands.
Figure 2 shows the transmitter block diagram for an MBOFDM UWB system. The information data are convolutionally encoded, interleaved (in 3 stages) and mapped onto QPSK symbols. Then symbols are arranged into groups of 100 symbols each. Necessary pilot tones and null tones are added to each group to extend their lengths to 128. Each group of 128 tones is subjected to an IFFT block with the length of 128 tones. After that, zero-padded prefix is added to each OFDM symbol. More details can be found in [1].
Figure 3. Zigzag Code with J = 3.
The parity bits are chosen such that each segment contains even numbers of ones (even party). The code is systematic and it is easily seen that the rate is J/(J + 1). Mathematically, the parity bits are calculated as follows
554
p (1) = p (i) =
J j=1 J j=1
d(1, j) mod 2 (1) d(i, j) + p (i − 1) mod 2, i = 2, 3, . . . , I
For the decoding of zigzag codes, Max-Log-APP (MLA) decoding algorithm can be used as it is explained in [5]. A concatenated zigzag code is described by a triplet (I, J, M ). M is the number of constituent encoders used in concatenation. The information data block, matrix of dimension I × J, is first passed through a random interleaver. Then, using the equations for calculating the parity bits, the vector of parity bits, P1 , of this block of intereaved data are calculated. One more time the original information data block is passed through a second random interleaver and the parity bit vector, P2 , is computed for this block of data. The operation of random interleaving and computing of parity bits for M -times will go on. Therefore, at the end, M vectors of parity bits (each with length of I) are in hand and they are transmitted along with the original information data block. As we can see, the number of total transmitted bits is I · (J + M ) (I · J is the number of the information bits and I · M is the number of the parity bits). The code rate now is J/(J + M ). Figure 4 shows the encoding process for the concatenated zigzag codes. This construction will be referred as parallel concatenated zigzag codes (PCZZ).
Figure 4. A) encoding process, B) overall codeword
matrix H specifies it, the code x is simply the null space of H, thus and n-tuple x over GF(2) is a codeword only if HxT = 0 [6]. An LDPC code defined in null space of a parity-check matrix H has following structural properties: (1) each row consists of r 1’s; (2) each column consists of g 1’s; (3) the number of 1’s in common between any two columns is no greater than 1; (4) both r and g are small compared with the length of the code and number of rows in H [6]. Since both r and g are small compared to the code length and to the number of rows in matrix, H has small density of 1’s. Therefore, the code is called low-density parity-check code. Properties (1) and (2) state that parity check matrix has constant row and column weights. This definition applies to regular LDPC codes. If all the columns or all the rows of the parity check matrix do not have the same weight, an LDPC code is said to be irregular. Early LDPC constructions were pseudorandom codes, and especially the long codes were found by computer generation. Structured LDPC constructions that rely on a general algorithmic approach to constructing LDPC matrices and require much less non-volatile memory than random constructions. Thus, the problem is to design irregular structured LDPC codes that have good overall error performance (both BER and BLER) for a wide range of code rates and block sizes with attractive storage requirements. The result of such LDPC codes is a better performing communication system with lower cost terminals. LDPC construction used here is presented in [7]. These codes have seed matrices for code rates 1/2, 3/4 and 5/6 of dimensions (24×48), (12×48) and (5×30). The given seed matrices are almost upper triangular, and as a result all expanded LDPC matrices using these seeds also have a nearly upper triangular construction that lend themselves well for encoding purposes. LDPC codes are decoded using belief-propagation algorithm, or modified versions of it. Here layered belief propagation combined with min-sum algorithm is used [8]. The decoding complexity and the architecture of the decoder is tightly coupled to the LDPC code design. Structured irregular LDPC codes, where the parity-check matrix is partitioned in smaller sub-matrices and each sub-matrix is essentially a circularly shifted identity matrix possess properties that make them well suited for hardware implementation.
4. Link budget and simulation results In this section, we provide simulation results for the PCZZ and LDPC codes with some comparisons to convolutional codes (CC). The convolutional encoder according to [1], uses the rate R=1/3 and constraint length=7 code with generator polynomials g0 = 1338 , g1 = 1658 , and
3.2. LDPC code LDPC codes are linear block codes. Linear block code C of length n is uniquely specified by generator matrix G or by corresponding parity check matrix H. If the parity-check
555
MB−OFDM UWB, 16−QAM, CC vs. ZZ vs. LDPC, 640 Mbps
0
MB−OFDM UWB, 16−QAM, CC vs. ZZ vs. LDPC, 960 Mbps
0
10
10
−1
−1
10
PER
PER
10
−2
−2
10
10
CC ZZ LDPC −3
10
−3
5
10
15
20
25
10
30
10
CC ZZ LDPC 12
14
16
18
Es/No
20
22
24
26
28
30
Es/No
Figure 6. PCZZ vs. LDPC vs. CC, 16-QAM, rate=3/4 (960 Mbps).
Figure 5. PCZZ vs. LDPC vs. CC, 16-QAM, rate=1/2 (640 Mbps).
MB−OFDM UWB, 16−QAM, CC vs. ZZ vs. LDPC, 1067 Mbps
0
10
g2 = 1718 . Additional coding rates are derived from this CC by employing puncturing. We use the IEEE standard multipath channel, CM1 [9]. CM1 channel is a line-of-sight (LOS) multipath fading channel with transmitter-receiver distance of less than 4 meters. The symbol detection scheme is based on MMSE algorithm and the channel estimate is based on simple pilot-based estimation algorithm. In the concatenated ZZ, M = 3 (number of random interleavers). The information block size (packet length) is 9600 bits and the codeword length is 2400 bits. The number of decoding iterations used for PCZZ and LDPC codes is 20. Figure 5 presents the results for CC, PCZZ and LDPC codes with 16-QAM modulation and rate 1/2 (640 Mbps). As can be seen from the figure, in case of rate 1/2 PCZZ codes there is about a good improvement in packet error rate (PER) compared to the CC (up to 3 dB at 10% PER).
−1
PER
10
−2
10
CC ZZ LDPC −3
10
10
15
25
20
30
35
Es/No
Figure 7. PCZZ vs. LDPC vs. CC, 16-QAM, rate=5/6 (1067 Mbps).
5. Conclusions
Figure 6 and Figure 7 show the results of simulations for CC, PCZZ and LDPC for the MB-OFDM UWB system using 16-QAM and rates 3/4 (960 Mbps) and 5/6 (1067 Mbps). It is seen for PCZZ and LDPC codes about 3 dB gain in performance is achievable at 10% PER compared to that of CC. The difference in performance between PCZZ and LDPC is negligible.
We have presented advanced coding schemes with 16QAM for the current MB-OFDM UWB system aiming at increasing the data rate up to 1 Gbps. The proposed coding schemes include PCZZ and structured LDPC codes. we have evaluated the performance of PCZZ, LDPC and convolutional codes in an MB-OFDM UWB system with 16QAM modulation. It has been shown that the PCZZ and the proposed structured LDPC codes provide several dB gain compared to convolutional codes while the performance difference between PCZZ and LDPC are negligible. We have also addressed the link budget and range issues for the high rate UWB system. For the PER of 10%, the achievable range is 3.0, 1.5 and 1.1 meters at 640, 960 and 1067 Mbps, respectively. Taking into account low encoding and rather
The link budget used in the calculation of ranges is shown in Table 1 [1, 3]. The antennas are assumed to be omnidirectional and the transmit and receive antenna gains are considered zero (i.e., GT = GR = 0). Figure 8 demonstrate the range versus bit rate curves for 640, 960 and 1067 Mbps modes. For the PER of 10%, the achievable range is 3.0, 1.5 and 1.1 meters at 640, 960 and 1067 Mbps, respectively.
556
Information data rate Signal bandwidth (B) Total average transmitted power (PT ) Thermal noise floor (N = −174 + 10log10 (B)) Rx Noise Figure referred to the antenna Terminal (NF ) Noise power (PN = N + NF ) Minimum required signal-to-noise ratio (Es /N0min ) Rx sensitivity level (S = PN + Es /N0min ) Downlink link budget (LB = PT + GT + GR − S) Implementation losses (I) Link margin (M ) Available pathloss for range calculation (PT =√LB − I − M ) fc = fmin fmax : geometric center frequency of waveform (fmin and fmax are -10 dB edges of the waveform spectrum) Free space path loss at 1 meter (L1 = 20 log10 (4πfc /c)) c = 3 × 108 m/s Free space path loss at d meters (L2 = P L − L1 = 20 log10 (d)) ACHIEVABLE RANGE (10L2 /20 )
640 Mbps 528 MHz -9.2 dBm -86.8 dBm 6.6 dB -80.2 dBm 15.0 dB -65.2 dBm 56.0 dB 3.0 dB 0 dB 53.0 dB
960 Mbps 528 MHz -9.2 dBm -86.8 dBm 6.6 dB -80.2 dBm 21.0 dB -59.2 dBm 50.0 dB 3.0 dB 0 dB 47.0 dB
1067 Mbps 528 MHz -9.2 dBm -86.8 dBm 6.6 dB -80.2 dBm 23.0 dB -57.2 dBm 48.0 dB 3.0 dB 0 dB 45.0 dB
3882 MHz
3882 MHz
3882 MHz
44.2 dB
44.2 dB
44.2 dB
8.8 dB
2.8 dB
0.8 dB
2.8 m
1.4 m
1.1 m
Table 1. Link Budget for the high-rate MB-OFDM UWB in CM1 channel, LDPC/ZZ codes, codeword length 2400 bits
References
MB−OFDM UWB, 16QAM, LDPC, PER vs Range
0
10
[1] Multiband OFDM Alliance, http://www.multibandofdm.org/. [2] A. Batra, J. Balakrishnan, G. R. Aiello, J.R. Foerster, and A. Dabak, ”Design of a multiband OFDM system for realistic UWB channel environments”, IEEE Transactions on Microwave Theory and Techniques, pp. 2123–2138, Sept 2004. [3] G. R. Aiello and G. D. Rogerson, ”Ultra–Wideband,” IEEE Microwave Magazine, pp. 36–47, June 2003. [4] B. Muquet, Z. Wang, G. B. Giannakis, M. de Courville, and P. Duhamel, ”Cyclic prefixing or zero padding for wireless multicarrier transmissions?,” IEEE Trans. Communications, vol. 50, Issue 12, pp. 2136–2148, Dec 2002. [5] L. Ping, X. Huang, and N. Phamdo, ”Zigzag codes and concatenated zigzag codes,” IEEE Trans. Inform. Theory, vol. 47, No. 2, pp. 800–807, Feb 2001. [6] S. Lin and D.J. Costello Jr., Error Control Coding, 2nd ed., Pearson Education Inc., New Jersey, 2004 [7] V. Stolpman, N. van Waes, T. Bhatt, C. Zhang, and A. Dixit. ”Irregular Structured LDPC Codes and Structured Puncturing”, IEEE 802.11-04/948. [8] M. Mansour and N. Shanbhag, ”High Throughput LDPC Decoders”, IEEE Transactions on VLSI System, vol. 11, pp. 976-996, Dec 2003. [9] A. F. Molisch, J. R. Foerster, and M. Pendergrass, ”Channel models for ultrawideband personal area networks,” IEEE Wireless Communications Magazine, vol. 10, issue 6, pp. 14– 21, Dec 2003.
Packet Error Rate (PER)
−1
10
−2
10
640 Mbit/s 960 Mbit/s 1067 Mbit/s
−3
10
0
1
2
3
4 Distance [m]
5
6
7
8
Figure 8. Range. low decoding complexities and attractive performance, the proposed PCZZ and LDPC may be seen as a potential channel coding scheme for future development of MB-OFDM UWB systems.
6. Acknowledgement The authors wish to acknowledge Nikolai Nefedov, Victor Stolpman, Jae Son, and Tejas Bhatt for their contributions in this work.
557
