EQUALIZING GMSK FOR HIGH DATA RATE WIRELESS LANS
Jose Telladoy, Ellen Khayata, and John M. Cioy Apple Computer, Inc. 1 In nite Loop, MS: 301-4J Cupertino, CA 95014, USA. email:
[email protected] yInformation Systems Lab, Stanford University We simulate the performance of an equalized Gaussian Minimum Shift Keying (GMSK) signal in an indoor radio environment with fading, noise, cochannel interference and Inter Symbol Interference (ISI). We show that data rates of 20 Mbps at Bit Error Rates (BER) 10?4 are possible with rms delay spreads up to 25 ns using a simple limiter-discriminator-integrator receiver and a (6,4) Decision Feedback Equalizer (DFE). In environments with larger rms delay spreads, coherent detection is required for the same performance. We introduce a DFE structure which compensates for both modulator and channel ISI, and yet requires no power-intensive multiplication operations in the feedback section. An (8,8) DFE with 2-level switched (selection) diversity is shown to allow 20 Mbps data transfer at BER 10?4 for rms delay spreads under 150 ns, with cochannel interference. Adding a (26,31) BCH code allows error-free reception of over 90% of packets with rms delay spreads under 150 ns, and up to 70% of packets with rms delays of 150 ns.
I. Introduction
Wireless Local Area Networks (LAN) support computing mobility on a local scale. They allow users to exchange information and retrieve les from the desktop or library as they walk about campus. High data rate radio links (on the order of 20 Mbps) will be needed to support the expected multimedia applications. Interest in these data rates has been reinforced by CEPT's allocation in Europe of 150 MHz of clear spectrum at 5.2 GHz for high data rate wireless LANs. For the past three years, technical subgroups in the European Telecommunications Standards Institute (ETSI) have been de ning a standard for a HIgh PErformance Radio LAN (HIPERLAN) operating in this band. HIPERLAN is being de ned as a 24 Mbps GMSK radio system. Adaptive equalization will be needed to overcome the severe ISI a ecting transmission at such data rates. Clearly, low power consumption is critical in a portable radio communicator. In addition to the ISI due to multipath, spectrally ecient GMSK introduces considerable amount of controlled phase ISI. Schemes to reduce this latter ISI and take advantage of simple noncoherent receivers have been studied [1]. Results have been published on mitigating multipath for linear modulations (QAM or QPSK), using only phase information [2] or amplitude and phase (e.g. [3]). In [4], a receiver is implemented to jointly reduce both ISI components, but is too complex for the proposed data rates. This paper quanti es the equalization needed to transmit 20 Mbps using GMSK in radio environments with various levels
of ISI impairment. We simulate the performance of an equalized GMSK signal in an indoor radio environment with fading, noise, cochannel interference and intersymbol interference. In section 2, we describe the fading radio channel model used in our simulations. Section 3 describes the two receivers we considered for GMSK: Limiter-Discriminator-Integrator and Coherent Detector. Section 4 covers our equalization simulation assumptions. The number and computation complexity of equalizer taps is explored here. We introduce a new structure for training the equalizer to compensate for both modulator and channel ISI. Section 5 shows the performance improvement through the use of two-level switched antenna diversity system. Section 6 introduces the e ect of cochannel channel interference on the equalized system. We show the improvement from applying a (26, 31) BCH code with interleaving. We present our recommendation for equalizing indoor radio channels in section 7.
II. Channel Model
Radio environments are often modeled as a two-ray impulse response system with independent Rayleigh fading. The channel root-mean-square (rms) delay spread, , is set by adjusting the delay separation between the rays. This model yields optimistic BER results and is not an accurate model for large normalized delay spreads [3].
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Figure 1: Several 50 ns rms Delay Spread Channels. The greater the number of rays, the more accurate the model. Here, we use a n-ray model, with a baseband channel impulse response being de ned as
h(t; k) =
Xn i(k)(t ? iTs =8); i=1
(1)
where n is the e ective number of paths, k is the channel number and i (k) is the gain of the i-th path for channel k. There are eight impulse response taps per symbol period, Ts . In our simulation, the number of paths, n, varies between 33 and 194, depending on the value of the delay spread. The individual i (k) are zero mean, complex Gaussian random variables, with an exponentially decaying pro le. The resultant signal envelope has a Rayleigh distribution. The delay spread is adjusted by changing the exponent. The channels have been designed to have zero gain on average, but individual channels deviate from this because of Rayleigh fading. This deviation can be up to 7dB in channels with small values of and 5dB in channels with large values of . Indoor channels change at pedestrian speeds of 1-2 m=s. Since the channel changes slowly relative to the symbol rate it is possible to transmit 20 kbit packets without tracking the channel after initial estimation. Measurements show that most impulse responses have a under 100 ns in typical oce buildings and open-plan factory buildings [3]. To evaluate the performance of the di erent schemes, sets of 50 channels were generated for each of four , 25, 50, 100 and 150 ns. The system symbol rate is set at 20 Mbps, resulting in a normalized delay spread, N = Ts , of .5, 1, 2, and 3 respectively. The impulse response can extend 4-6 times the length of the , to 15 symbols. When the N , becomes greater than 0.1-0.2, some ISI mitigation method, such as equalization, must be applied to achieve Bit Error Rates (BER) under 10?3 , as shown in [5].
III. GMSK Modulation and Receivers
In this section, we describe several GMSK receiver structures. We argue that the optimum detector is too complex for state-ofthe-art DSP speeds, and explore suboptimum detection schemes. The transmitted GMSK signals at carrier frequency fc can be represented as s(t) = RefA exp[j (2fc t + (t))]g; (2) where A is the amplitude and (t) is the modulating phase given by
(t) = 2h
Zt 1 X ak
k=?1
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g( ? nT )d :
(3)
Here, h is the modulation index, ak is the k-th 1data symbol, and T is the symbol duration. The premodulation Gaussian lter g(t) is given by g(t) = 21T fQ(c1 ( Tt )) ? Q(c1 ( t ?T T ))g; (4) 2 where c1 = 2BT ( ln12 ) and Q(t) = t1 p(21 ) e? 2 d . Detectors. The optimal detector for CPM is a Maximum Likelihood Sequence Estimation (MLSE), which can be eciently implemented using the Viterbi algorithm whenever h = 2k=p (k,p integers). However, the complexity of this algorithm grows exponentially with the memory of the modulation (length of g(t)) and of the channel. Several proposed suboptimal structures use an equalizer to shorten the ISI, then apply a Viterbi type algorithm on the resulting shortened sequence, but the structure is still too complex for 20 Mbps at current DSP speeds. Alternatively, an adaptive equalizer can be used alone to mitigate the ISI in combination with a symbol by symbol GMSK detector such as: di erential detection, frequency detection, and coherent detection.
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Di erential and frequency detection are simple to implement, but their performance degrades severely as BT decreases to values of interest for spectrally ecient radio communications (:2 BT :3). Some algorithms have been studied to correct for transmitter phase-ISI in the absence of channel ISI [1]. Mitigating channel ISI using only phase information has been studied for QPSK [2], which does not su er from the additional transmitter ISI. These non-coherent receivers disregard the amplitude of the received signal and therefore perform poorly for N > :5. An adaptive equalizer can be used alone to mitigate the modulator and channel ISI. The results for several equalizer structures, and for both limiter-discriminator-integrator and coherent detectors, are presented in the following section.
IV. Adaptive Equalization
We rst explore the performance impact of using symbol-spaced versus fractionally-spaced DFEs. We then quantify the performance of the simplest receiver: a limiter-discriminator-integrator followed by a DFE. After showing that this system would only yield acceptable performance for < 25ns, we quantify the performance of a coherent receiver followed by a DFE. We end this section with a discussion of equalizer coecients setting.
A. Simulation Assumptions
In this paper, GMSK was simulated with a BT = 0:3, as a compromise between spectral eciency and added ISI. The data rate is 20 Mbps, and each packet is limited to 10 kbits, over which the stationary channel assumption holds. We assumed perfect frequency tracking. The equalizer adjusts to phase lock. The transmitter and receiver have the same timing frequency, but no attempt is made to optimize sampling time. The feedback section of the DFE realistically uses the receiver decision outputs and thus the system su ers from error propagation.
B. Equalizer De nitions
Symbol-Spaced vs. Fractionally-Spaced DFE. Keeping the total number of taps constant, we found that the FS scheme has no performance advantage over the TS scheme in the coherent detector case and only a slight advantage in the limiterdiscriminator-integrator equalization simulation. In all gures the notation LMS(450) refers to using the Least Mean Squares (LMS) algorithm on a 450 bit training sequence. The vertical axis represents the percentage of channels with BER better than the horizontal axis value. See gure 2. The point where the curve intersects the vertical axis gives the number of error-free 10 kbit packets. This representation can be eciently used to evaluate the advantages of using block error correcting codes. Number of DFE Taps. The pairs (n1 ; n2 ) on the graphs represent the number of feedforward and feedback coecients respectively, of the DFE(n1 ; n2 ). Since the radio channel varies on each packet, the (n1 ; n2 ) DFE weights need to be adapted for each incoming packet. In a computer network, variable-length packets often arrive in bursts. This LAN trac pattern dictates that packets be detected in real time which requires n1 +n2 complex multiplications and additions within Ts . Therefore minimizing the number of coecients while maintaining acceptable performance is critical.
C. DFE Following a Limiter-Discriminator-Integrator (LDI)
We rst evaluate the simplest ISI combatting structure: a LDI receiver followed by an adaptive DFE. This structure simpli es the receiver IF. Because the samples after the integrator are real
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numbers, the equalizer only has to perform real arithmetic (one multiplication and add per tap), instead of the complex arithmetic of equalizers following coherent detectors (four multiplications and four additions per tap). This reduced computation translates to considerable power saving. In the absence of multipath and noise, the output of the integrator has a known transmitted ISI that can be e ectively removed, but in the presence of multipath the circuit output is a nonlinear function of the path delays. Figure 2 shows the performance of a FS and TS DFE applied to these samples. For = 25ns over 80% of the channels allow transmission of errorfree 10 kbit packets, but only 38% of the 50ns channels allow that. We notice that there is a slight advantage in the FS case vs. the TS case. Clearly, the performance is poor for large delay spreads, but < 50ns for most oce environments. This scheme allows operation at 10 Mbps with over 80% error-free packets. This could be an e ective low cost alternative to a coherent receiver.
Figure 4: Coherent Detector for DFE(Ff,Fb) and /T=2 (100 ns), LMS(450), and (Eb =No ) = 17dB . larger number of feedback taps, such as (8,16), does not increase the performance when is on the order of 50 ns or 100 ns, as in gure 4. A DFE(8,16) is slightly better in channels with =150 ns. Figure 5 compares several con gurations for the Recursive Least Squares (RLS)(45), = 50ns. We conclude that since the vast majority of indoor radio channels < 150 ns, an DFE(8,8) is a good compromise between performance and complexity. 1 DFE(5,5)
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Figure 2: Performance of LDI LMS(450) DFE(6,4). No noise.
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Figure 5: RLS(45) DFE(Ff,Fb) and 50 ns rms delay spread. (Eb =No ) = 17dB .
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E. Computing Equalizer Coecients
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Figure 3: Coherent Detector for DFE(Ff,Fb) and /T=1 (50 ns), LMS(450), and (Eb =No ) = 17dB .
D. Decision Feedback Equalization for Coherent Detector
This section explores the performance of a coherent detector followed by a DFE. This structure is more complex than the LDI-DFE, but is still implementable with present-day technology. Performance is signi cantly better in the coherent detector case. Figure 3 shows that for = 50ns (8,8) DFE provides error free 10kbit packets approximately 98% of the time. Using a
(t) =
Zt 1 X ak
k=?1
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g( ? nT )d :
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For BT > :25, g(t) can be truncated to 3 symbols and at the optimum sampling instant this becomes
((n + 1)T ) = MSK ((n + 1)T ) + (an+1 ? an )BT ; (6) R 0 g(t)dt. P where MSK ((n + 1)T ) = 2 nk=0 ak and BT = ?1 For MSK, BT = 0 and a coherent receiver su ers no transmitter ISI. For nite values of BT , we can still recover an under ideal conditions since jan+1 ? an jBT < jan j 2 , but now the immunity to disturbances has been reduced. For BT = :3, BT = 160 and the degradation is only about 1dB .
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almost 50% reduction of complexity and power consumption for n1 = n2 and will be greater if n1 < n2 . In noise-free channels with ISI, the coherent detector with DFE(8; 8) is able to achieve error free transmission for all 25, 50 and 100ns channels and 96% of the 150ns channels when the equalizer coecients converge to the optimum solution. The performance with noise is shown in gure 6. This proposed structure is clearly e ective in combatting distortion in ISI limited channels even for very long N . We will study the e ect of limiting the training sequence length and applying realizable adaptive equalization algorithms. 1
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Figure 7: LMS(200) DFE(8,8) for (Eb =No ) = 17dB . 1
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(7) MSK ((n + 1)T ) = (an + 1) 2 + MSK (nT ): For a zero starting angle, exp(j MSK ((n + 1)T )) can only take
1 values, simplifying the feedback additions of the DFE even further. This proposed structure will realize (4 n ) real multiplies and (4 n +2 n ? 3) real additions. The system trained with exp(j ((n + 1)T )) requires (4 (n + n )) real multiplies and (4 (n + n ) ? 4) real additions. This translates into an
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The sequence exp(j ((n +1)T )) will take 12 di erent values in general. If we use this sequence to train the the equalizer, we will mitigate the channel ISI. If, on the other hand, we use exp(j MSK ((n + 1)T )) as the training sequence, then the sequence can only take values f1,j,-1,-jg. This training sequence assumes that the transmitted sequence was actually MSK. This scheme does not require multiplications in the feedback section of the DFE, since multiplying any complex number by any of f1,j,-1,-jg only involves swapping real and imaginary parts and sign changes. Now the feedback section of the DFE can be implemented using adders only. Simulations show that the BER computed using either exp(j ((n+ 1)T )) or exp(j MSK ((n +1)T )) as training sequences are equivalent. Hence we used exp(j MSK ((n + 1)T )) due to its implementation advantages. A further reduction in complexity can be realized if we use a passband equalizer at frequency 41T . In this case,
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Figure 8: LMS(450) DFE(8,8) for (Eb =No ) = 17dB . performance curves for LMS DFE(8,8) for training sequences of length 200 and 450 are presented in gures 7 and 8. Increasing the training sequence to 1000 from 450 only improved the performance slightly. The slow convergence of LMS was due to high eigenvalue spreads present in channels with deep fades. In contrast, RLS achieved LMS(450) performance with a 45 bit training sequence, and approached the asymptotic value of gure 6 at 100 bits.
V. Diversity
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Figure 6: Performance of a DFE(8,8) for (Eb =No ) = 17dB and perfect training. Training Sequence Length. The equalizer must perform correctly across a large range of values of . Using too many equalizer taps degrades the performance under nite training length. Finite training sequences lead to imperfect convergence, introducing noise. Using too few equalizer taps degrades the performance by not compensating for signi cant channel re ection paths. The length of the training sequence should be as small a fraction of the packet size as possible to minimize overhead. The
Diversity techniques are known to reduce the impact of radio channel fades. There are three main ways of processing the signals received from each diversity branch: Maximal Ratio Combining (MRC), Equal Gain Diversity (EGD), and Switched (or Selection) Diversity (SD). Unlike MRC and EGD, SD does not require cophasing and operates with a single equalizer. Maximizing equalized decision point SNR would be an optimum SD criteria, but would require equalizing each branch signal. The simplest and most utilized technique receives on the branch with largest input S + N + I . We simulated selection diversity in all the diversity plots. Figure 9 shows the performance of the system using 2-level selection diversity for each of the .
VI. Performance under Interference
Frequency reuse is necessary to maximize the number of users supported by the wireless system. Cochannel interference is inevitable as a result. Figure 10 shows the performance degradation when the desired signal has passed through a 50 ns rms delay spread channel, and the interfering signals are assumed
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Figure 9: LMS(450) DFE(8,8) Performance Under 2-level Diversity. (Eb =No ) = 17dB . S/Io=17dB
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Figure 11: Error free packet Throughput for several packet sizes using an Interleaved BCH(26,31) and 2-level diversity. LMS(450) DFE(8,8) (Eb =No ) = 17dB .
References
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performance on these channels. Introducing a (26,31) BCH code allows error-free reception of over 90% of packets with rms delay spreads under 150 ns. ASICs have been built providing computation complexity on the order of that of the proposed scheme [8].
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Figure 10: Performance for several Cochannel Interference levels and /T=1. to have passed through a 150 ns channel. This is a worst case interference scenario. As expected, the degradation is worse for longer delay spreads. For the 100 ns case S=Io = 17dB is necessary for good performance, but for 50 ns S=Io = 14dB is acceptable. Note that coding can be e ective here, since the curves are relatively at for BER > 5 10?3 and drop more rapidly after that. Codes. Codes are of limited value when errors are bursty. However, our simulations show that a single-error-correcting BCH(26,31) code with a 31 by 16 matrix interleaver was effective in increasing error-free packet throughput at the output of the DFE to that shown in gure 11.
VII. Conclusions
We have shown that a wireless LAN can provide a 20 Mbps link at a BER 10?4 over highly dispersive and time-varying channels. Power and spectrally ecient GMSK received using a coherent detector was followed by a symbol-spaced DFE(8,8) to reduce the modulator and channel ISI. An LDI receiver followed by DFE(6,4) was shown to provide a BER 10?4 only in environments with rms delay spreads of under 25 ns at these data rates. We introduced a DFE structure which does not require multiplication operations in the feedback section, allowing a signi cant reduction in power consumption relative to a direct DFE implementation. LMS was chosen to train the equalizer because of its robustness and ease of implementation. Powerbased selection antenna diversity was shown to greatly enhance
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