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Dual Carrier Modulation Demapping Methods and Performances for Wireless USB Runfeng Yang and R. Simon Sherratt Email: {r.yang, r.s.sherratt} @reading.ac.uk Signal Processing Laboratory The University of Reading, UK Abstract — Dual Carrier Modulation (DCM) was chosen as the higher data rate modulation scheme for MB-OFDM (Multiband Orthogonal Frequency Division Multiplexing) in the UWB (UltraWide Band) radio platform ECMA-368. ECMA-368 has been chosen as the physical implementation for high data rate Wireless USB (W-USB) and Bluetooth 3.0. In this paper, different demapping methods for the DCM demapper are presented, being Soft Bit, Maximum Likely (ML) Soft Bit and Log Likelihood Ratio (LLR). Frequency diversity and Channel State Information (CSI) are further techniques to enhance demapping methods. The system performance for those DCM demapping methods simulated in realistic multi-path environments are provided and compared 1 . Index Terms — DCM, Soft-Bit, ML Soft-Bit, LLR.
I. INTRODUCTION UWB (Ultra-Wideband), historically, was employed in military radar systems. Recently UWB systems were proposed to standardize wide bandwidth wireless communication systems. The fundamental issue of UWB is that the transmitted signal can be spread over an extremely large bandwidth with very low power spectral density (PSD). In 2002, the USA Federal Communications Commission (FCC) agreed to allocate 7500 MHz spectrum in 3.1-10.6 GHz band for unlicensed use for the UWB devices [1] and limit the UWB Effective Isotropic Radiated Power (EIRP) to -41.3dBm/MHz [2]. In 2005 the WiMedia Alliance [3] working with ECMA (the European Computer Manufacturers Association) announced the establishment of the WiMedia MB-OFDM (Multiband Orthogonal Frequency Division Multiplexing) UWB radio platform as their global UWB standard, ECMA-368. Recently ECMA-368 has been published a second updated version [4]. ECMA-368 was also chosen as physical layer of high data rate wireless specifications for high-speed Wireless USB (W-USB) [5] and Bluetooth 3.0. ECMA-368 specifies a MB-OFDM system occupying 14 bands. Each band with a bandwidth of 528 MHz can support up to 480 Mbit/sec. The OFDM symbol is the basic quanta of MB-OFDM based UWB radio. Each OFDM symbol is constructed from the Inverse Fast Fourier Transform (IFFT) of a set of 128 complex valued carriers made from 100 data
carriers, 12 pilot carriers, 6 NULL valued carriers and 10 guard carriers. The 10 guard carriers used for mitigating Inter Symbol Interference (ISI) are located on either edge of the OFDM symbol and they are the same value as the 5 outermost data carries. In addition, the guard carriers can be used as another form of time and frequency diversity resulting in improved performance for the receiver [6]. Each OFDM symbol is appended with zero-padded suffix to aid multipath interference mitigation and settling times of the transmitter and receiver. To transmit a Packet Service Data Unit (PSDU) that contains information bits, ECMA-368 has eight transmission modes by applying various levels of coding and diversity, which offers 53.3, 80, 106.7, 160, 200, 320, 400 or 480 Mbit/sec to the MAC layer. After the bit interleaver, the coded and interleaved binary data sequence is mapped onto a complex constellation. A Quadrature Phase Shift Keying (QPSK) constellation is used for data rates 200 Mbit/sec and lower. Dual Carrier Modulation (DCM) is used as a fourdimensional constellation for data rates 320 Mbit/sec and higher. DCM was introduced to the MB-OFDM proposal by Batra and Balakrishnan [7] as one of the enhancement changes to create the current WiMedia Alliance standard. Fig. 1 and 2 depict the encoding and decoding process for the coded PSDU respectively. This paper discusses different demapping methods and techniques for the DCM demapper, and system performance resulted by the proposed DCM demappers. Chapter II introduces DCM mapping. Chapter III discusses the different DCM demapping methods and techniques. Chapter IV discusses the performance measurements while Chapter V presents future work and chapter VI presents conclusions. Scrambled PSDU
ISBN: 978-1-902560-19-9 © 2008 PGNet
Bit Interleaver
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Fig. 1. Encoding process for the scrambled PSDU at Transmitter
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Scrambled PSDU 1 This work was supported in part by The University of Reading Overseas Research Postgraduate Studentships.
Convolutional Encoder / Puncturer
Viterbi Decoder
Bit Deinterleaver
QPSK or DCM Demapper
Channel Equalizer
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Fig. 2. Decoding process for the scrambled PSDU at Receiver
YR(k )
II. DCM MAPPING A. Frequency diversity Coded information on a single tone is unreliable if a channel has deep fade. However, the probability of experiencing a channel deep fade is extremely small if two tones with the same information are separated by a large bandwidth. Frequency diversity is used in the DCM by mapping the same coded information but different forms onto two different tones at different channel frequencies with a large bandwidth separation. B. DCM constellation mapping After bit interleaving, the 1200 interleaved and coded bits are divided into groups of 200 bits, and further grouped into 50 groups of 4 reordering bits. Each group of 4 bits is represented as (bg(k), bg(k)+1, bg(k)+50, bg(k)+51), where k ∈ [0…49] and k ∈ [ 0 K 24] ⎧ 2k g (k ) = ⎨ 2 k + 50 k ∈ [ 25 K 49] ⎩
(1)
These four bits are mapped to two QPSK symbols (xg(k)+jxg(k)+50), (xg(k)+1+jxg(k)+51) as illustrated in (2). ⎡ x g ( k ) + jxg ( k )+50 ⎤ ⎡ (2bg ( k ) − 1) + j(2bg (k )+50 − 1) ⎤ ⎢x ⎥=⎢ ⎥ ⎣ g ( k )+1 + jxg ( k )+51 ⎦ ⎣(2bg (k )+1 − 1) + j(2bg ( k )+51 − 1)⎦
(2)
Then the DCM mapper uses a DCM matrix H as in (3) to execute mapping of the two QPSK symbols into two DCM symbols (yT(k), yT(k+50)) as illustrated in (4). The resulting DCM symbols are formed into two 16-QAM like constellations [4]. ⎡2 1 ⎤ H =⎢ ⎥ ⎣1 − 2⎦
(3)
⎡ yT ( k ) ⎤ 1 ⎡2 1 ⎤ ⎡ x g ( k ) + jx g ( k )+50 ⎤ ⎥ ⎥= ⎢y ⎥⎢ ⎢ 10 ⎣1 − 2⎦ ⎣ x g ( k )+1 + jx g ( k ) +51 ⎦ ⎣ T ( k +50) ⎦
(4)
where 1/ 10 is a normalization factor for normalizing the average symbol power to be a constant unit. The two resulting DCM symbols (yT(k), yT(k+50)) are allocated into two individual OFDM data sub-carriers with 50 subcarriers separation to achieve frequency diversity. In total 100 DCM symbols (complex numbers) are given to the 128pt IFFT block for building an OFDM symbol. Each OFDM sub-carriers occupies a bandwidth of about 4 MHz. Therefore the bandwidth between the two individual OFDM data sub-carriers related to the two complex numbers (IT(k), QT(k)) and (IT(k+50), QT(k+50)) is at least 200 MHz, which offers good frequency diversity gain against channel deep fading. Fig. 3 depicts the DCM mapping process.
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Fig. 3. DCM mapping process
III. PROPOSED DCM DEMAPPING A. Soft bit Demapping The proposed DCM soft demapping employs the DCM mixing matrix to combine the two equalized complex numbers previously transmitted on different sub-carriers into a subgroup of 4 soft bits as in (5), and then outputs groups of 200 soft bits. ⎡ I R ( k ) + jQR (k ) ⎤ ⎡ hk ⎤ ⎧⎪ 10 ⎡ xg ( k ) + jxg ( k ) +50 ⎤⎫⎪ ⎡ nk ⎤ (5) H⎢ ⎢I ⎥=⎢ ⎥⎬ + ⎢ ⎥ ⎥ •⎨ ⎣ xg ( k ) +1 + jxg ( k ) +51 ⎦⎪⎭ ⎣nk +50 ⎦ ⎣ R( k +50) + jQR ( k +50) ⎦ ⎣hk +50 ⎦ ⎪⎩ 5
where [hk hk+50]T are channel coefficients and [nk nk+50]T is noise. Suppose the symbols are received through the channel with no noise and multi-path, then [hk hk+50]T=[1 1]T and [nk nk+50]T=[0 0]T. In addition, demapping performance can remain without using the factor 10 /5. Hence the group of 4 soft bits can be obtained in (6), (7), (8) and (9). Soft (b g ( k ) ) = 2 I R ( k ) + I R ( k + 50)
(6)
Soft (bg ( k )+1 ) = I R ( k ) − 2 I R ( k +50)
(7)
Soft (bg ( k )+50 ) = 2QR ( k ) + QR ( k +50 )
(8)
Soft (bg ( k )+51 ) = QR ( k ) − 2QR ( k +50)
(9)
B. Enhancement by exploiting Channel State Information In OFDM modulation, the OFDM sub-carriers suffer from different noise powers, for example, echoes, deep fades, etc. Each OFDM sub-carrier position has a dynamic estimation for the data reliability. This dynamic estimation in frequencydomain is defined as Channel State Information (CSI), which is used to enhance the channel decoder’s error correction performance [8]. Each data carrier has a potentially different CSI based on the power of the channel estimate at the corresponding frequency. The more reliable CSI is applied to the associated data sub-carrier, the better decoding performance can be. The proposed CSI aided scheme coupled with the band hopping information maximizes the soft demapping performance [9]. As a result, each soft bit with incorporated CSI is derived as in (10), (11), (12) and (13).
Soft (b g ( k ) ) = (2 I R ( k ) + I R ( k + 50 ) )∗ min {CSI k , CSI k + 50 }
Soft (bg ( k )+1 ) = (I R ( k ) − 2 I R ( k +50) )∗ min{CSI k , CSI k +50 }
Soft (bg ( k )+50 ) = (2QR ( k ) + QR ( k +50) )∗ min{CSI k , CSI k +50 } Soft (bg ( k )+51 ) = (QR ( k ) − 2QR ( k +50) )∗ min{CSI k , CSI k +50 }
(10) (11) (12) (13)
min{A,B} refers to minimum of A and B. C. Maximum Likely Soft bit demapping The more reliable soft bit values are given to Viterbi decoder, the more accurate binary bit can be decoded. Maximum Likelihood (ML) offers finding parameters to obtain the most probable emitted symbols [10], as in (14). In our case, the large probable soft bit value with incorporated CSI can be expressed in (15), (16), (17) and (18). f ( x ) = arg max l(θ )
(14) (15)
Soft (bg ( k ) +1 ) = (I R ( k ) − 2 I R ( k +50 )θ )∗ CSI
(16)
Soft (b g ( k ) ) = (2 I R ( k )θ + I R ( k + 50 ) )∗ CSI
Soft (bg ( k ) +50 ) = (2QR ( k )θ + QR ( k +50 ) )∗ CSI
Soft (bg ( k ) + 51 ) = (QR ( k ) − 2QR ( k + 50 )θ )∗ CSI
(17) (18)
To find the appropriate parameter θ, two conditions need to be satisfied. a. Applying θ to equations (15)-(18) to make soft magnitude large possible; b. The two resulting symbols are always transmitted in different symbol pairs. Suppose the symbol with small magnitude is received as inverted while the other symbol with large magnitude remaining the same; apply that with searching maximum θ in equations (15)-(18) until making the sign of soft bit value inverted. With these two conditions, the appropriate θ is approximately 1.5, which gives the maximum likely soft bit as in (19), (20), (21) and (22). Soft (b g ( k ) ) = (3I R ( k ) + I R ( k + 50 ) ) ∗ CSI
Soft (bg ( k )+1 ) = (I R ( k ) − 3I R ( k +50 ) )∗ CSI
Soft (bg ( k ) +50 ) = (3QR ( k ) + QR ( k +50 ) )∗ CSI
Soft (bg ( k ) +51 ) = (QR ( k ) − 3QR ( k + 50 ) )∗ CSI
(19) (20) (21) (22)
D. Log likelihood ratio demapping As well as improving reliability for an input of Viterbi decoder, Log Likelihood Ratio (LLR) is another alternative demapping approach. The generic format of LLR equation can be expressed in (23). LLR = log(exp( A) + exp( B ) ) − log(exp( X ) + exp(Y ) )
(23)
In our case, a LLR is calculated from the received DCM symbols yR(k) and yR(k+50). In addition, the LLR functions
related to the two 16-QAM like constellations are independent. Hence the LLR for a group of 4 bits (bg(k), bg(k)+1, bg(k)+50, bg(k)+51) is formed from combining the two independent LLR, as in (24), (25), (26) and (27). σ2 is noise variance associated with the channel. 2 ⎧⎪ ⎡ (I ⎡ (I )2 ⎤ ⎫⎪ −I ) ⎤ −I LLR(bg ( k ) ) = log ⎨ ∑ exp ⎢ T ( k ) 2R ( k ) ⎥ + ∑ exp ⎢ T ( k +50 ) 2 R ( k +50 ) ⎥ ⎬ −σk − σ k +50 ⎪⎩bg ( k ) =1 ⎣⎢ ⎦⎥ bg ( k ) =1 ⎣⎢ ⎦⎥ ⎪⎭ ⎧⎪ ⎡ (I T ( k ) − I R ( k ) )2 ⎤ ⎡ (I T ( k +50) − I R ( k +50 ) )2 ⎤ ⎫⎪ − log ⎨ ∑ exp ⎢ ⎥ + ∑ exp ⎢ ⎥⎬ − σ k2 − σ k2+50 ⎪⎩bg ( k ) =0 ⎣⎢ ⎦⎥ bg ( k ) =0 ⎣⎢ ⎦⎥ ⎪⎭
2 ⎧⎪ ⎡ (I ⎡ (I )2 ⎤ ⎫⎪ −I ) ⎤ −I LLR (bg ( k )+1 ) = log ⎨ ∑ exp ⎢ T ( k ) 2R ( k ) ⎥ + ∑ exp ⎢ T ( k +50 ) 2 R ( k +50 ) ⎥ ⎬ −σk − σ k +50 ⎪⎩bg ( k )+1 =1 ⎢⎣ ⎥⎦ bg ( k )+1 =1 ⎢⎣ ⎥⎦ ⎪⎭
2 ⎧⎪ ⎡ (I ⎡ (I )2 ⎤ ⎫⎪ −I ) ⎤ −I − log ⎨ ∑ exp ⎢ T ( k ) 2R ( k ) ⎥ + ∑ exp ⎢ T ( k +50 ) 2 R ( k +50 ) ⎥ ⎬ −σk − σ k +50 ⎪⎩bg ( k )+1 =0 ⎣⎢ ⎦⎥ bg ( k )+1 =0 ⎣⎢ ⎦⎥ ⎪⎭ ⎧⎪ ⎡ (QT ( k ) − QR ( k ) )2 ⎤ ⎡ (QT ( k +50) − QR ( k +50) )2 ⎤ ⎫⎪ LLR(bg ( k )+50 ) = log⎨ ∑ exp⎢ ⎥ + ∑ exp⎢ ⎥⎬ − σ k2 − σ k2+50 ⎪⎩bg ( k )+50 =1 ⎣⎢ ⎦⎥ bg ( k )+50 =1 ⎣⎢ ⎦⎥ ⎪⎭
⎧⎪ ⎡ (Q − Q )2 ⎤ ⎡ (Q )2 ⎤⎫⎪ −Q − log⎨ ∑ exp⎢ T ( k ) 2 R ( k ) ⎥ + ∑ exp⎢ T ( k +50) 2 R ( k +50) ⎥ ⎬ −σk − σ k +50 ⎪⎩bg ( k )+50 =0 ⎢⎣ ⎢⎣ ⎥⎦ bg ( k )+50 =0 ⎥⎦ ⎪⎭ ⎧⎪ ⎡ (QT ( k ) − QR ( k ) )2 ⎤ ⎡ (QT ( k +50) − QR ( k +50) )2 ⎤ ⎫⎪ LLR(bg ( k )+51 ) = log⎨ ∑ exp⎢ ⎥ + ∑ exp⎢ ⎥⎬ − σ k2 − σ k2+50 ⎪⎩bg ( k )+51=1 ⎣⎢ ⎦⎥ bg ( k )+51 =1 ⎣⎢ ⎦⎥ ⎪⎭
(24)
(25)
(26)
(27)
⎧⎪ ⎡ (QT ( k ) − QR ( k ) )2 ⎤ ⎡ (QT ( k +50) − QR ( k +50) )2 ⎤ ⎫⎪ − log⎨ ∑ exp⎢ ⎥ + ∑ exp⎢ ⎥⎬ 2 −σk − σ k2+50 ⎪⎩bg ( k )+51 =0 ⎣⎢ ⎦⎥ bg ( k ) +51=0 ⎣⎢ ⎦⎥ ⎪⎭
For a Gaussian channel, the LLR can be approximated as two piecewise-linear functions which depend on the amplitude of I/Q signals [11], [12]. Furthermore, the maximum LLR value can be approximated to be soft magnitude with the associated bit completely depending on the amplitude of the I/Q signals. In our case, there are two bits associated with each of the two 16-QAM like constellations completely relying on their soft magnitude of the I/Q. Hence the LLR functions related to these two bits from each constellation are considered to be partially linear. Therefore some terms of these LLR functions are approximated by the proposed soft magnitude, as in (28), (29), (30) and (31). ⎧⎪ ⎡ (I )2 ⎤ ⎫⎪ −I LLR (bg ( k ) ) = 3I R ( k ) + log ⎨ ∑ exp ⎢ T ( k +50 ) 2 R ( k +50 ) ⎥ ⎬ σ − ⎪⎩bg ( k ) =1 k +50 ⎣⎢ ⎦⎥ ⎪⎭ ⎧⎪ ⎡ (I T ( k +50 ) − I R ( k +50 ) )2 ⎤ ⎫⎪ − log ⎨ ∑ exp ⎢ ⎥⎬ − σ k2+50 ⎪⎩bg ( k ) =0 ⎣⎢ ⎦⎥ ⎪⎭ ⎡ (I T ( k ) − I R ( k ) )2 ⎤ ⎪⎫ ⎪⎧ LLR (bg ( k )+1 ) = log ⎨ ∑ exp ⎢ ⎥⎬ − σ k2 ⎪⎩bg ( k )+1 =1 ⎥⎦ ⎪⎭ ⎢⎣ ⎡ (I T ( k ) − I R ( k ) )2 ⎤ ⎪⎫ ⎪⎧ − log ⎨ ∑ exp ⎢ ⎥ ⎬ − 3I R ( k +50 ) − σ k2 ⎪⎩bg ( k )+1 =0 ⎦⎥ ⎪⎭ ⎣⎢ ⎧⎪ ⎡ (QT ( k +50) − QR ( k +50) )2 ⎤ ⎫⎪ LLR(bg ( k )+50 ) = 3QR ( k ) + log ⎨ ∑ exp ⎢ ⎥⎬ − σ k2+50 ⎪⎩bg ( k )+50 =1 ⎣⎢ ⎦⎥ ⎪⎭
⎧⎪ ⎡ (Q )2 ⎤ ⎫⎪ −Q − log⎨ ∑ exp ⎢ T ( k +50) 2 R ( k +50) ⎥ ⎬ − σ k +50 ⎪⎩bg ( k )+50 =0 ⎣⎢ ⎦⎥ ⎪⎭ 2 ⎧⎪ ⎡ (QT ( k ) − QR ( k ) ) ⎤ ⎫⎪ LLR (bg ( k )+51 ) = log ⎨ ∑ exp ⎢ ⎥⎬ − σ k2 ⎪⎩bg ( k ) +51 =1 ⎥⎦ ⎪⎭ ⎢⎣ ⎡ (QT ( k ) − QR ( k ) )2 ⎤ ⎪⎫ ⎪⎧ − log ⎨ ∑ exp ⎢ ⎥ ⎬ − 3QR ( k +50) − σ k2 ⎪⎩bg ( k )+ 51 =0 ⎥⎦ ⎪⎭ ⎢⎣
(28)
(29)
(30)
(31)
IV. SYSTEM PERFORMANCE MEASURMANCE A. Simulation Configuration The system is simulated in a realistic multi-path channel environment of 100 channel realizations in Foerster’s Channel Model 1 (CM1) [13]. All simulations results are averaged over 2000 packets with 1024 octets per PSDU and 90th-percentile channel realization (the worst 10% channels are discarded). The link success probability is defined as system can be achieved with a Packet Error Rate (PER) less than 8% [14]. We maintain strict adherence to timing and use a hopping characteristic of Time Frequency Code (TFC) =1, and incorporate 2.5 dB implementation loss [4] in the floating point system model, while fixed point model raises more practical loss due to quantization error [15].
V. FUTURE WORK CSI can offer enhancing the channel decoder’s error correction performance. However CSI does not always offer the improvement gain to each OFDM data sub-carrier due to the perfect CSI or imperfect CSI. Selecting good and reliable CSI for each OFDM data sub-carrier need further investigation to maximize the CSI enhancement.
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B. Performance gains for the DCM demapping methods Fig. 4 presents system performance running at 480 Mbit/sec (CM1, 90%ile) exploiting soft bit, ML soft bit, and LLR demapping methods with frequency diversity and CSI techniques for enhancement. As shown in Fig. 4, LLR with CSI is the best demapping method that can achieves 3.9 meters. ML soft bit demapping method can also achieve similar performance as LLR at 8% PER, but with slightly worse performance in shorter distances. Soft bit demapping with CSI can only achieve 3.4 meters at 8% PER level.
However soft bit or ML soft bit demapping method has lower computation complexity and extremely reduces hardware implementation cost [16]. CSI is incorporated to enhance the demapping performance. Fig. 5 depicts good improvement for ML soft bit demapping with CSI. However the performance gains achieved by LLR demapping with CSI are minimal, shown in Fig. 6. Frequency diversity can enhance DCM performance by mapping the same coded information but different forms onto two different OFDM sub-carriers with 200 MHz bandwidth separation. Without this large bandwidth separation, the information mapped in adjacent data sub-carriers in each OFDM symbol has no robustness against channel fading and no signal compensation from the associated CSI. Thereby the system performance drops 0.9 meter with only achieving 3 meters, which is shown in Fig. 7.
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Fig. 4. PER performances for proposed DCM demapping methods
Fig. 6. Proposed CSI enhancement for LLR demapping method
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Fig. 5. Proposed CSI enhancement for ML soft bit demapping method
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VI. CONCLUSION The transport mechanism of MB-OFDM in UWB radio platform (ECMA-368) has been standardized for high speed Wireless-USB physical layer specifications. This paper proposes high performance demapping methods for DCM that is adopted as a modulation scheme when the data rate is over 320 Mbit/sec. This paper has presented different proposed DCM demapping methods and techniques. The system performances for all the demapping methods and techniques have been compared. By using ML soft bit or LLR DCM demapping methods, system performance is approximately 3.9 meters at 480 Mbit/sec, while ML soft bit demapping offers costeffective computing solution.
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