IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 10, OCTOBER 2009
767
Time Hopped Transmitted Reference with Multiple Autocorrelation Sampling for Ultra Wideband Radio Hen-Geul Yeh, Senior Member, IEEE, and Kareem Shabaik, Student Member, IEEE
Abstract—Transmitted Reference (TR) schemes for Ultra Wideband (UWB) eliminate the need for channel estimation, reducing receiver complexity at the cost of reduced performance. This letter proposes a Transmitted Reference (TR) scheme with multiple autocorrelation sampling detection. The proposed receiver captures the energy in the received signal’s autocorrelation side lobes, outperforming the traditional TR scheme for the operational range of Signal to Noise Ratio (SNR) values. Time hoping, as well as the use of bandwidth efficient signaling with favorable spectral characteristics, facilitate significant improvement in system capacity in comparison to a similar scheme using orthogonal chirp signals in multipath spread channels. Index Terms—Ultra wideband, transmitted reference, multipath channels, multiaccess communication, multiuser channels, correlators.
I
as the chirp based MPMD receiver for multiple user systems. The remainder of this letter is organized as follows: Section II presents the details of the proposed receiver model. Section III discusses the simulation results obtained, and Section IV is the conclusion. II. M ODEL S ETUP In the proposed system, hereafter referred to as Transmitted Reference with Multiple ACF Sampling (TR-MAS), the 𝑛th user’s transmitted signal is expressed as follows: √ +∞ ∑ (𝑛) 𝑠𝑛 (𝑡) = 𝐸𝑇 𝑋 𝑝𝑛 (𝑡 − 𝑗𝑇𝑠 − 𝑐𝑛 (𝑗)𝑇𝑐 ) +
I. I NTRODUCTION
N [1], a Transmitted Reference (TR) scheme using pairs of data and reference pulses, or doublets, was introduced for Ultra-Wideband Impulse Radio (UWB-IR) applications. The TR scheme reduces the receiver’s complexity by eliminating the need for channel estimation, offering a viable alternative to spread spectrum rake receivers [2]. However, it suffers a performance penalty due to its use of a noisy reference signal. Additionally, there is an inherent data rate loss due to the transmission of the un-modulated reference pulse. In [3], [4], bi-orthogonal signaling improves the system data rate, through modulation of both amplitude and phase of the data pulse. However, the proposed receivers only sample the pulse autocorrelation function (ACF) at a single instant, failing to capture the energy available in the ACF side lobes. In [5], the Multi Pulse Multi Delay (MPMD) scheme was proposed wherein the TR receiver samples the received pulse ACF at multiple instants. Users are assigned orthogonal frequency separated chirp signals. In cases of severe channel multipath however, the signals’ orthogonality degrades at the receiver and BER performance is reduced. We propose a modified TR scheme that uses multiple ACF sampling detection. However, unlike the MPMD scheme, our system users are assigned waveforms from a set of orthogonal signal pulses, derived from the numerical solution of the prolate spheriodal functions [6]. The users are also assigned pseudo random (PN) codes to further mitigate Multi User Interference (MUI) at the receiver. Simulations show that the proposed system outperforms traditional TR systems, as well Manuscript received May 21, 2009. The associate editor coordinating the review of this letter and approving it for publication was R. Nabar. This work was supported in part by the University Research Office of California State University, Long Beach. The authors are with the Department of Electrical Engineering, California State University, Long Beach, CA 90840 (e-mail:
[email protected]). Digital Object Identifier 10.1109/LCOMM.2009.091101
𝑗=−∞ 𝑏⌊𝑗/𝑁𝑠 ⌋ 𝑝𝑛 (𝑡 (−1)
− 𝑗𝑇𝑠 − 𝑐𝑛 (𝑗)𝑇𝑐 − 𝐷𝑛 )
(1)
where all parameters with the subscript 𝑛 are user specific and (𝑛) 𝐸𝑇 𝑋 is the transmitted energy per bit for the 𝑛th user. 𝑇𝑠 is the symbol (or frame) time used by the (𝑁𝑠 , 1) repetition coder. 𝑐𝑛 (𝑗) is the 𝑗th element of the 𝑛th user’s unique PN sequence. Note that 𝑐𝑛 is periodic, with periodicity 𝑁𝑝 and cardinality 𝑁ℎ . 𝑇𝑐 is the chip time of the time hopping sequence, and it is set larger than the doublet duration to avoid inter symbol interference, as well as to maintain the orthogonality of the users’ time hopped signals at the receiver. ⌊.⌋ denotes the floor operation, and 𝑏⌊𝑗/𝑁𝑠 ⌋ is the source binary data, where 𝑏⌊𝑗/𝑁𝑠 ⌋ ∈ [0, 1]. Finally, note that the 𝐷𝑛 parameter is fixed per user, and that the entire doublet is time hopped. Each user is assigned a unique pulse shape, derived from the numerical solution of the prolate spheriodal function with spectrum matching the FCC imposed limits on UWB-IR [6]. A significant property of these pulses exploited by the TRMAS receiver is the effect of the pulse time duration, 𝑇𝑚 , on the ACF side lobe amplitudes. The pulse ACFs exhibit greater side lobe amplitudes as 𝑇𝑚 increases. Although this property is advantageous to our TR-MAS design, it must be balanced with the obvious tradeoff in reduced system data rate. In our trials, we found that 𝑇𝑚 equal to 1.0 ns was optimal. To analyze the TR-MAS receiver, we assume the total number of system users is equal to 𝑁𝑢 , and that the first user is the user of interest. The signal at the input of the receiver is then given by: 𝑟1 (𝑡) =
𝑁𝑢 ∑
𝑠𝑛 (𝑡) ∗ ℎ𝑛 (𝑡) + 𝑛1 (𝑡)
(2)
𝑛=1
where ℎ𝑛 (𝑡) represents the channel impulse response experienced by the 𝑛th user and 𝑛1 (𝑡) is AWGN due to the receiver antenna, with double sided power spectral density equal to 𝑁𝑜 /2.
c 2009 IEEE 1089-7798/09$25.00 ⃝
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IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 10, OCTOBER 2009
The TR-MAS receiver auto-correlates the received signal with an appropriately delayed version, which can be written as follows: ∫
10
𝑇𝑗 +𝑇𝑚 /2
𝑇𝑗 −𝑇𝑚 /2
𝑧(𝑡)𝑑𝑡
Here 𝑇𝑗 denotes the integration start time for the 𝑗th frame (1) (1) of 𝑧(𝑡), given by 𝑇𝑗 = 𝛿𝑗 + 𝐷1 , where 𝛿𝑗 represents the frame and chip time offset for the 𝑗th frame of the first user’s transmitted signal, and 𝑧(𝑡) is given by 𝑧(𝑡) = 𝑟1 (𝑡) ⋅ 𝑟1 (𝑡 − 𝐷1 − 𝑑𝑘 )
−1
10
(3) BER
𝑌𝑘 =
0
Conventional TR
−3
10
(4)
where 𝑑𝑘 is the time interval at which the pulse ACF is sampled, and 𝐷1 is the user of interest’s assigned doublet delay time. The output of the TR-MAS receiver is finally given by 𝐾 ∑ 𝑍𝑏𝑖𝑡 = 𝑌𝑘 ∘ 𝐴𝑘 (5)
−2
10
TR−MAS
−4
10
0
2
4
6 8 ERx/No (dB)
10
12
Fig. 1. TR-MAS receiver (𝐾 = 4) compared to TR receiver in an AWGN channel (data rate = 3.2 Mbps).
𝑘=1
where 𝐾 is the total number of samples taken from the received signal’s ACF. The ‘∘’ operator represents the matched filtering operation of the stored ACF sample at time interval 𝑘, denoted by 𝐴𝑘 , to the estimated ACF sample computed by the receiver, 𝑌𝑘 . Expressing (5) in terms of the matched filter impulse response, 𝐻𝑘 , we get 𝐾 ∑
𝑌𝑘 ⋅ 𝐻𝑘 =
𝑘=1
𝐾 ∑
𝑌𝑘 ⋅ 𝐴𝑘 𝛿(𝑛 − 𝑑𝑘 )
(6)
−1
10
BER
𝑍𝑏𝑖𝑡 =
0
10
−2
10
𝑘=1
Therefore, the TR-MAS receiver may be viewed as a mixed signal double correlation receiver, consisting of an analog correlator as given by (3), followed by a digital correlator as given by (6).
MPMD 4 MUI MPMD 1 MUI TR−MAS 4 MUI TR−MAS 1 MUI
−3
10
−4
10
III. S IMULATION R ESULTS The performance of the TR-MAS receiver was compared to a traditional TR receiver, which is equivalent to the TR-MAS receiver with 𝐾 equal to one, in an AWGN channel. The BER performance of both time-hopped receivers for a single user is depicted in Fig. 1. The TR-MAS receiver consistently outperforms the TR one, achieving a 1 dB improvement at BER = 10−2 . We attribute this to the TR-MAS receiver’s ability to capture the energy in the side lobes of the received signal’s ACF, which becomes more pronounced for higher SNR values. Next we compared the BER performance of our TR-MAS receiver to the MPMD receiver, with 𝐾 = 3 for a multi-user system, and plotted the results in Fig. 2. In this case, we removed time hoping from the TR-MAS transmitter, to ensure users of either the TR-MAS or MPMD systems are allocated equal bandwidth. The channel model utilized was the CM1 model proposed by the IEEE 802.15.SG3a UWB study group [7]. The path loss was computed using the parameters reported in [8] for a residential LOS environment. The set of 𝐷𝑛 values for the individual TR-MAS users were computed using the following equation 𝐷𝑛 = 𝐷1 + 5(𝑛 − 1) ns,
for 𝑛 = 1, 2 . . . 𝑁𝑢
(7)
where 𝐷1 = 55 ns. The label ‘X MUI’ indicates that 𝑋 number of foreign users interfere with the main user’s receiver.
0
2
4 6 ERx/No (dB)
8
10
Fig. 2. TR-MAS receiver (without time hopping) compared to MPMD receiver for different numbers of system users in a multipath channel (𝑁ℎ = 1, 𝑁𝑝 = 1, 𝑇𝑐 = 103 𝑛𝑠, 𝑁𝑠 = 10, 𝑇𝑠 = 𝑁ℎ 𝑇𝑐 , data rate = 97 kbits/s).
The plots illustrate that the proposed TR-MAS consistently outperforms the MPMD receiver, which suffers degraded performance with only four interfering users. We attribute this degradation to the reduction in orthogonality of the user chirp pulses, caused by the frequency spreading characteristics of the multipath channel. Furthermore, with time hopping and 𝐾 = 3 in both TR-MAS and MPMD systems, Fig. 3 demonstrates the scalability of the TR-MAS receiver with increasing numbers of users, with curves shown for 12, 24 and 50 interfering users. Note that the multipath channel simulated, and system data rate, are identical to that used for the results in Fig. 2. From Fig. 3, we find that for SNR = 9 dB, the TRMAS capacity is thus increased by a factor of three (12 MUI vs. 4 MUI shown in Fig. 2 with the BER ≈ 10−2 ) as a result of the use of time hopping. In addition, comparing the MPMD 12 MUI curve in Fig. 3 to the TR-MAS 12 MUI curve, we see the TR-MAS receiver achieving a 1.5 dB improvement at BER = 10−2 .
YEH and SHABAIK: TIME HOPPED TRANSMITTED REFERENCE WITH MULTIPLE AUTOCORRELATION SAMPLING FOR ULTRA WIDEBAND RADIO 0
characteristics, enables our TR-MAS receiver to far outperform the MPMD scheme that relies on frequency separated chirp signals, as demonstrated by simulation results in a multi user environment.
10
−1
BER
10
R EFERENCES
−2
10
MPMD 12 MUI TR−MAS 50 MUI −3
10
TR−MAS 24 MUI TR−MAS 12 MUI
−4
10
0
769
2
4
6 E /N (dB) Rx
8
10
o
Fig. 3. TR-MAS receiver BER performance for different numbers of system users in a multipath channel (𝑁ℎ = 10, 𝑁𝑝 = 5, 𝑇𝑐 = 103 𝑛𝑠, 𝑁𝑠 = 10, 𝑇𝑠 = 𝑁ℎ 𝑇𝑐 , data rate = 97 kbits/s).
IV. C ONCLUSION We have presented the model for our TR-MAS receiver, which exploits the energy in the ACF side lobes of the received pulses and thus outperforms the traditional TR receiver. In addition, the use of carefully selected pulse shapes, that are both bandwidth efficient and posses favorable autocorrelation
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