shown for V(j.9 = OV in Fig. 1. The initial I-V for each device is given by the solid curve, while the dashed curve represents the sec- ond I-V taken in the dark. The latter corresponds to the fully col- lapsed I-V, where all of the traps have been filled. I-Vs taken under light illumination will appear somewhere in between the solid and dashed curves, as reflected by the amount of drain cur- rent recovery. which depends upon the amount of light applied.
1000 MBE/OMCVD MESFET
2ool
0 0 OMCVD GaN MESFET(x4) / - 4 I IFx”
10 I 20 30 drain voltage, V1467/11
Fig. 1 Typicul I- V curve,! for Jour devices studiedCollapsed I-Vs are shown by dashed curves
The two OMCVD HEMTs in Fig. 1 ((i) and (ii)) are represent- ative of the broad range of behaviour that we have observed from these devices, which were fabricated on materials grown under varied process condhons. The collapse in this particular MBE- grown MESFET appears much smaller than that seen in the OMCVD-grown MESFET. 10-13 10-14 I o b . “E 10-15
-
5
10-16 _..--- OMCVO 1047 10-16 10-19 I I .._.- i E M T 1.0 1.5 2.0 2.5 3.0 3.5 4.0 energy, eVFig. 2 Photoionisution spcctru f o r , j h r devices studied
The two HEMT devices are labelled (i), (ii) to correspond to the I-V curves in Fig. I
The photoionisation spectra of these devices, S(hv), are shown in Fig. 2. The spectrum of the OMCVD MESFET was discussed in [3], and appears as the solid circles. The two broad absorptions, associated with photoionisation at two distinct traps (labelled TRAP(i) and TRAP@)), were identified [3] with traps in the HR GaN buffer layer. The absorptions could only be fitted (dashed lines) assuming large lattice relaxation [5], and yielded absorption thresholds at 1.8 and 2.85eV. This identifies TRAP(i) as a mid-gap level and TRAP(ii) as a very dcep acceptor/electron trap. The solid lines in the Figure are linear combinations of the fitted absorptions. The spectra of the OMCVD HEMTs (solid and open squares) and the MBE-on-OMCVD MESFET (open circles) exhibit the same spectral features as those of the OMCVD GaN MESFET, suggesting that they are due to the same traps. In addi- tion to the trap-related absorptions, all four spectra show a clear increase at the bandgap of GaN, corresponding to the optical
cxcitation of free carriers. This increase is smaller in the case of the MESFETs because much of the above-gap light is absorbed in the 200nm GaN layer that lies above the H R GaN. This, coupled with the similarity of the spectra to that of the OMCVD GaN MESFET, clearly indicates that current collapse in the HEMT devices occurs in the H R GaN layer, and that the responsible traps are identical to those in the OMCVD MESFET.
The collapse in the MBE device could be due to similar traps associated with the growth. Altenmtively, if these traps are associ- ated with dislocations, it is possible that current collapse in the MBE-grown device results from dislocations that propagate into the MBE layer from the OMCVD template. Detailed studies of MBE-grown materials are needed to better characterise the role of current collapse in these devices.
Conclusions: Current collapse in OMCVD-grown HEMTs has been shown to result from the same traps that produce current collapse in OMCVD GaN MESFETs. As in the MESFETs, these traps are located in the H R GaN buffer layer.
Acknowledgments: The authors would like to thank H.B. Dietrich and W. Kruppa for several valuable discussions. This work was supported in part by the Ofice of Naval Research.
o
- TEE ._ - 2001 -. . . I 1 March 2001 Electronics Letters Online Nu.- 20010434D OI: IO. 1049/el:200 10434
P.B. Klein, S.C. Binari, K. Ikossi-Anastasiou, D.D. Koleske, R.L. Hcnry and D.S. Katzer (Naval Research Luborutory, 4555 Overlook Avenue S W, Wushington DC 20375-5347, USA)
E-mail: [email protected]
A.E. Wickenden (Army Re.rearch Laboratory, Adelphi M D 20783-1197, USA)
References
BINAKI, S.C., KRUPPA. W., DIETRICH, H.B., KELNEK, G.,
WICKENDEN, A.E., and PKEITAS. J.A., Jr.: ‘Fabrication and
characterization of G a N FETs’, Solid-State Electron., 1997, 41,
(IO), pp. 1549-1554
KHAN, M.A., SEIUR, M.S., CHEN, Q., and KUZNIA, J.N.: ‘CUrl.ent/VOlta!& characteristic collapse in AlGaN/GaN heterostructure insulated
gate field effect transistors at high drain bias’, Electron. Lett., 1994, 30, (25), pp. 2115-2116
‘Observation of deep traps responsible for current collapse in GaN metal semiconductor field effect transistors’, Appl. Phy.r. Lett., 1999, 75, (25), pp. 40164018
KLEIN, P.B., R I N A R I , s . ~ , I’KEII’AS, J.A., ~ r . , and WICKENDEN, A.E.:
‘Photoionization spectroscopy of traps in GaN metal semiconductor field e l k c t transistors’, J . Appl. Phjw., 2000, 88, ( 5 ) ,
pp. 2843-2852
JAROS: M.: ‘Wave functions and optical cross sections associated
with deep ccnters in semiconductors’, Phys. Rev. B, 1977, 16, (8), pp. 36943706
KLEIN, P.B., FREITAS, J.A., Jr., BINARI, S.C., and WICKENDEN, A.E.:
Constrained
VQ codebook design for noisy
channels
Wen-Whei Chang and Heng-Iang Hsu
A codebook design approach for constrained vector quantisation using the Hadamard transform of channel transition probabilities
is proposed. It is examined for quantisation of Gauss-Markov sources over channels with memory and compared with the
gcncralised Lloyd algorithm.
Introduction: Vector quantisation (VQ) is an efficient speech and image compression method. However, transmitting VQ data over noisy channels changes the index bits and consequently leads to severe distortions in the reconstructed output. Forward error con- trol could be used to protect VQ data, but it would be more efi- cient to design a VQ codebook with inherent good channel robustness properties. Among many design approaches to be con-
sidered [I, 21, constrained VQ codebooks given by a linear map- ping of a block code (LMBC) [I] are particularly attractive in that there exists an explicit correspondence between the codevectors and the index bits transmitted on the channel. The usefulness of the LMBC-VQ may be restricted because it was originally derived for the memoryless binary symmetric channels. But transmission errors encountered in most real communication channels exhibit various degrees of statistical dependencies. It is therefore believed that further improvement can be realised through a more precise characterisation of the channel on which the codebook design is based.
dverage distortion: The central component of a VQ system is a codebook consisting of
M
= 2"' codevectors with dimension d. The VQ encoder searches through the codebook for the codevector ci that best matches the input vector x, and then transmits the corre- sponding index i to the decoder in binary format. Here, the index i is regarded as an integer representing the decimal equivalent of a binary codeword, Mi) = (bn,-l(ij, bm-2(i),...,
bo(i)j. Commonly, the input b(i) and output b(j) of a channel differ in the presence of anerror pattem b(e). Let llci - cjI12 represent the squared error distor- tion and let P(b(e)) represent the probability of receiving the index
j given that the transmitted index is i. The overall distortion
D
=qiix - can be viewed as the sum of quantiser distortion
Dq
=411x
- ciIl2] and channel distortion4.
= E[llci - cj112]. Following Hagen [I], an LMBC codebook can be formulated by applying a mapping matrix T on a vector gi to produce its codevector cir i.e.n
1=1
where tr denotes column 1 of T and gi = (I, g j , l , ..., g,,,) is chosen from a block code of length n. The degree of channel robustness
heavily depends on the arrangements for the selecting of block code. A unconstrained VQ employs a block code with maximum codelength n =
M
- 1, whereas a constrained VQ incorporatesonly a subset of block code components. For unconstrained VQ, it was observed in [l] that gi = hi representing coluinn i of a Syl- vester-style Hadamard matrix with elements {h,,}. Assuming that
all the codevectors are equiprobable, the channel distortion is expressed as
M - 1 M ~ l
1M-I
where Iltii12 is the norm of tl and QJb(l)] =
2zj1
P(b(e))h,,r can be viewed as the scalar Hadamard transform of channel transition probabilities P(b(e)). It is readily understood from eqn. 2 that for lowD,,
we must ensure the mapping is such that highm(l)]
cor- responds to high-norm tr vectors, as they make a large contribu- tion to the channel distortion.Block code selection: Compared with unconstrained VQ, con- strained VQ codebooks are more appropriate where complexity and channel robustness are primary considerations. Design of a constrained VQ codebook involves selecting a good block code as well as an optimisation of the mapping matiix for that specific block code. Its codevectors are
(3) where C, specifies the set of block code components from which the codebook is generated. For memoryless binary symmetric channels, it suffices to select short block codes incorporating only compoiients with low Hamming weights [l]. But for channels
with
memory, a reasonable practice is to select block code components associated with highm(l)]
instead of those with low Hamming weights. In addition, it can .be shown that block code components are divided into M/2 disjunct classes and that all elements within each class have the same value ofm(l)].
Following this, we rank the classes by descending order of Mb(l)] and then denoteQi
as the class which has the ith largest value of QJb(l)]. Relevant aspects of the proposed selection scheme are summarised as fol- lows:(i) Set k = 1 and select Cl, as an initial block code C,.
(ii) Optimise the mapping matrix T corresponding to thc block code C,.
(iii) .If channel distortion 0,. is sufficiently small, then terminate. Otherwise, set k = k
+
1, update the block code by C, = C, U ( 2 ~ and go to step(ii).
Mapping matrix optinzisation algorithm: To optimise the mapping
matrix to a given block code, we chose to minimise the quantiser distortion directly using a genetic algorithm as an optimisation technique. The main attraction of a genetic algorithm [3] is that the given search space is explored in parallel by means of iterative modifications of a population of chromosomes. The d (n
+
1) elements of T define the solution and hence can be encoded into a chromosome as a list of real numbers. The fitness values of all chromosomes were ranked with respect to the inverse of quantiser distortionD4.
Crossover among the selected chromosomes then proceeded by exchanging substrings of two chromosomes between two randomly selected crossover points. After crossover, mutation was applied to each chromosome by replacing one of its genes with a random number. When 30 generations were reached, the best chromosome in the final population was taken as the optimal mapping matrix. The parameter values used for the population size, the crossover probability, and the mutation probability were empirically determined to be 50, 0.8, and 0.1, respectively.6 - 5 -
k3
4 -5
3 - a- 2 - B't
01 " " " " " I -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0log,,, (bit error rate)
Fig. 1 SNR performance of various codehooks on Gilhrrt chiinnel
---.O-.- GLA
+
BSA -3- new algorithm0 . GLA
Experimental results: The proposed method was examined for quantisation of a first-order Gauss-Markov source, with correla- tion coefficient 0.5, over the Gilbert channel [4] with bit error rates ranging from 1 t 3 to l@'. Fig. 1 shows the SNR performances of a vector quantiser with a codebook size and vector dimension of
( M ,
d,
= (256, 8). Our method was compared with the generalised Lloyd algorithm (GLA) [2] and GLA with binaiy switching algo- rithm (BSA) [5]. The results obtained using the proposed methodclearly demonstrate an improvement over those obtained using the GLA, even with a post-processing index assignment. The investi- gation further showed that the improvement is more noticeable for higher bit error rates.
Acknololedgment: This work was supported by the National Sci- ence Council, Republic of China, under contract NSC 88-2218- E009-035.
Conclusions: We have explored the benefits of Hadamard trans- form of channel transition probabilities for use in designing a con- strained VQ codebook. Experimental results indicate that the proposed method yields codebooks which more closely match the channel error statistics.
0 IEE 2001
Electronics Letters Online No: 20010419 DOI: I0.1049/el:20010419
Wen-Whei Chang and Heng-Iang Hsu (Department of Comrnunic~itinn Engineering, Nfitionul Chiao Tung Uniiwsity, iJsinchu, Taiwan, Republic qf China)
E-mail: [email protected]
26 October 2000
References
1 H A G E N , R., and HHDELIN, I?: ‘Robust vector quantization by a linear mapping of a block code’. IEEE Trans. I f ?‘hem-y, 1999, 45, ( I ) ,
pp. 200-218
2 LINDE, Y . , R ~ J Z O , A., and GRAY, R.M.: ‘An algorithm for vector quantizer design’, IEEE Trans. Conzniwi., 1980, 28, ( I ) , pp. 84-95
3 GOLDBERG. D.E.: ‘Genetic algorithm in search, optimization and
machine learning’ (Addison-Wesley, New York, 1989)
4 GILBERT, EN.: ‘Capacity of a burst-noise channel’, Bell Sjsst. T d i .
J., 1960, 39, pp. 1253-1265
5 ZECitK, K . , and GtKSHO, A.: ‘PseudoGray coding’, IEEE Trur1.S.
Conimun., 1990, 38. (12) pp, 2147-2158
Efficient real-time correlator for CDMA2000
searcher
J. Kim a n d
M.
BondarowiczA very eKicienl structurc Tor a real-time scdrchcr in thc CDMA2000 system is proposed. The advantages of using this scheme are the small amount of memory required, the processor s p e d per unit timc. and an inherent parallel proccssing strncture. This concept can he applied to other CYDMA systems.
Introduction: Timing recovery. which is a combined function of
searching (or initial acquisition) and tracking, is very important for the overall performance of CDMA systems, which have more than a hundred-fold faster symbol transmission rates than other wireless personal communications systems (PCSs). A searcher measures the pilot energy of possible path delays with sub-chip interval resolution, and sends them to a finger assignment logic device. The searcher needs to operate in real time Lo save niemory and assign fingers promptly. Sincc this is a very high-speed proc- ess, the processors must be used efficicntly. In principle. matclicd filtering or cross-correlation represent optimum searching methods [l]. However, they are not optimum for implementation. In this Letter, we discuss a very efficient method ol‘ designing real-time correlation circuits and describe the implementation of a searcher for a CDMA2000 base station using the proposed method.
addition
I
4
C(0) C(1) C(2) ... C(W-1)
1411111
Fig. 1 Real-time correlutor using matcked jilterEf$ccient real-time correlation: Searching is basically a correlation process. Pilot signal samples with different tinie-delay hypotheses are correlated with a reference signal. The function of the correla- tor is defined as follows. Let the known reference scquencc bep(i). r(i), the addition of the N time-unit delayed version of p(i) and noise n(i), is then
r ( i ) = p ( i - N)
+
, r , ( i ) i E {..,: - 3 , - 2 : -1. U. 1, 2 , 3 , ...} (1:) wherc z is a discrete time index. The correlator calculates C(k) aswhere M i s the coherent integration length and Wis the maximum time delay, or search window length. IT C(K) is the largest or all {C(O), C(l), C(2),
...,
CyQ, ..., C(W- l)}, thcn K is the cstimatcd time delay. From eqns. 1 and 2, we haveM-1 .bl - 1
C ( k ) = p ( i
+
x:
- X ) p @ )+
rr(i+
k)P(’i) ( 3 )i = U ?-I)
The first term is thc signal component and the second term is the
noise component. The signal component has its largcst value when
k is N . As the value of A4 increases, o m estimation becomes more reliable.
Therc are scveral ways of implementing the correlator. r(i) can be considered as the noise-corrupted and time-delayed version of a knowii sequence p(zJ First, we briefly describe two conventional schemes, ,store and measure and mutcheddfilter, and then derive the efficient real-time correlation.
Store ancl ineusure is conceptually simple. Input signals are
stored in memory and cross-correlated with a rcference signal. If we assume that r(i) has E bits and p(i) has H bits, then we need
( M
+
W)B+
MH bits of memory. Furthermore, this is not a real-time process because the calculation will start after the arrival of
the last sample r(M
+
W - 1). We can make this a real-time proc- ess using the mutched,filter schcme.1Matcliedfiltrr uscs an Mth order finite impdse response (FIR) filter having p(i) as its coefficients, which is illustrated in Fig. 1. There is no calculation until r(A4 - 1) arrives. There are then M multiplications and M - 1 additions per iuput sample. This scheme requires M . (5
+
H)
bits of memory. The necessary condition for real-time operation is that the processor is fast enough to support12.I multiplications and M - 1 additions per input sample period. This is not a time-efficient processor because it is active only Tor the last W of M
+
W - 1 sample limes. For example, if the coher- ent integration length M is 1000 and the search window CV is 100 (in general, M is much larger than W for a CDMA2000 base sta-tion), this system is active for only 9% of the time. Compared with
store cirztl measure, the required amount of memory is reduced by W B bits.
We propose a new real-time correlator that uniformly distrib- utes the calculation load over timc. In addition to this, our scheme requires far less memory than the previous two schemes. Our scheme is derived as follows. LetJ = i
+
k in cqn. 2, whercj E (0, I , 2, . . . j M+
IV- I}. ThenM + il - 1
q k ) = r . ( j ) p ( j - k ) k E { 0 , 1 , 2 , ...,
M/’-
l} (4)r=li
From cqn. 4, given input r(i), we need Wprevious values of p(i). Fig. 2 shows the implenientation of this circuit. We nccd size W
shift registers for pfi) (total memory size is LVH)), W’ registers for
C(k), and no memory for rG). For each new received signal r(i), there is a new reference signal p(i) for the shift register. Wmulti- plication results are then accumulated in W registers. There are W multiplications and additions per input sample. In other words, the necessary condition Lor real-time operation is that the proces- sor is fast enough to support W multiplications and additions per input sample pcriod. This is a time-cfficient system because thcrc is no idle period. For examplc; if M is 1000 and W is 100, the
required system speed for real-time operation is only 10% of the
iiintck filter method, which is achieved by uniformly distributing
the calculation load over time. Furthermore, this scheme requires only WH bits of memory. For example, if H is I bit (PN codes have 1 bit values) and B is 4 bits. the required amount of memory is only 2% or that required by the mutched.filtu scheme. The mer- its of this scheme are as follows:
(i) No memory is required for input sample rb].
(ii) Small memory size rcquirement for reference sample
PO].
(iii) Uniform distribution of calculation load over time: there is no idlc timc and thc processor spccd requirements per unit time for real-time processing are minimised.
(iv) Inherent parallel processing structure: In Fig. 2, there is sepa- rate processing per each C(k). We may have W separate parallel processors, or wc caii group multiple C’(k)s and assign one fastcr processor.
