Advanced signal-processing algorithms for energy ... - IEEE Xplore

Advanced Signal-Processing Algorithms for Energy-Efficient Wireless Communications CARLO LUSCHI, MEMBER, IEEE, MAGNUS SANDELL, MEMBER, IEEE, PAUL STRAUCH, MEMBER, IEEE, JIAN-JUN WU, COSTEL ILAS, PING-WEN ONG, MEMBER, IEEE, ROMAIN BAERISWYL, FREDERIC BATTAGLIA, SPYROS KARAGEORGIS, AND RAN-HONG YAN Substantial progress has been made in the receiver signal-processing algorithms for wireless communications to minimize the requirements on signal-to-noise (and/or interference) power ratio and computational complexities for the same quality of service. In cellular infrastructure systems, one of the key system design objectives in the base stations is to maximize the receiver sensitivity, so that the required signal level from the mobile stations can be minimized. The use of advanced signal-processing algorithms, based on maximum a posteriori (MAP) estimation, iterative (turbo) channel estimation, equalization, and decoding, allows for a reduction of the required transmitter power by one-third to one-half. Lower computational complexities in the terminals, which implies a reduced power drain on the digital circuits, can be achieved by using techniques that adapt the state complexity of the receiver to the propagation channel. We give an in-depth review of these algorithms, and discuss their performance and implementation requirements. Keywords—Iterative channel estimation, iterative decoding, MAP equalization and decoding, wireless communications.

I. INTRODUCTION Power consumption is of major concern in wireless transmission systems. Wireless communications between a fixed base station (BS) and a number of mobile terminals or mobile stations (MSs) take place within a certain coverage area, defined by the maximum distance beyond which the Manuscript received December 31, 1999; revised June 1, 2000. C. Luschi, M. Sandell, P. Strauch, J.-J. Wu, and C. Ilas are with Global Wireless Systems Research, Bell Laboratories, Lucent Technologies, Swindon, SN5 7YT Wiltshire, U.K. (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). P.-W. Ong is with High-Speed Circuits and Systems Research, Bell Laboratories, Lucent Technologies, Holmdel, NJ 07733-3030 USA (e-mail: [email protected]). R. Baeriswyl, F. Battaglia, and S. Karageorgis are with Global Wireless Systems Research, Bell Laboratories, Lucent Technologies, Holmdel, NJ 07733-3030 USA (e-mail: [email protected]; [email protected]; [email protected]). R.-H. Yan is with Global Wireless Systems Research and High-Speed Circuits and Systems Research, Bell Laboratories, Lucent Technologies, Swindon, SN5 7YT Wiltshire, U.K., and Holmdel, NJ 07733-3030 USA (e-mail: [email protected]). Publisher Item Identifier S 0018-9219(00)09136-2.

quality of the radio link becomes unacceptably poor. For a given transmission technique, this area is determined by the transmitted power level, the propagation medium, and by the receiver implementation. Portable wireless terminals are usually powered by battery, and, therefore, the transmission power is a scarce resource. In the basic design of a wireless system, the required transmitter power for a given coverage depends on the minimum received signal-to-noise ratio (SNR), which guarantees a certain quality of service measured, e.g., in terms of bit error rate (BER). Hence, the required transmitter power from the MS can be reduced by a BS receiver design that corresponds to improved error performance, and, therefore, to lower requirements in terms of minimum acceptable SNR. Given a certain SNR threshold, adaptive RF power control is then often employed at both MS and BS to minimize the transmit power and reduce interference to co-channel users, while maintaining the quality of the radio link. Power consumption in a mobile terminal can also be reduced by reducing the implementation complexity of the MS receiver. In fact, lower computational complexities imply a decreased power drain on the digital circuits. The two requirements of lowering the SNR threshold and reducing the complexity very often conflict with each other, and various tradeoffs should be made according to the overall system design objective. This paper addresses recent progress in the receiver signalprocessing algorithms for wireless communications, to minimize the requirements on SNR and/or computational complexity for a fixed quality of service. In Section II, we introduce the relevant parameters of the wireless propagation channel [1], [2]. Short-term signal fading due to multipath propagation causes frequency selective distortion, which requires the implementation of suitable signal-processing techniques at the receiver. Without an effective countermeasure, this distortion produces a degradation of the receiver SNR threshold [3]. On the other hand, for a fixed SNR threshold, the statistics of long-term and medium-term signal variations (path loss

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and shadowing) determine the coverage corresponding to a given transmitter power [4]. The basic principles of the link power-budget design are reviewed in Section III. In cellular systems like GSM, one of the key design objectives in the BSs is to maximize the receiver sensitivity, defined as the RF signal power at the receiver input for which a defined quality of service is achieved. Maximizing the BS sensitivity corresponds to minimize the required signal power from the terminals. Advanced signal-processing algorithms based on maximum a posteriori probability (MAP) data estimation, soft-in/soft-out decoding and iterative (turbo) channel estimation, equalization, and decoding can be employed at the BS to achieve this objective. The algorithms can be implemented either in a single-channel receiver or with multiple antennas, which provides an additional advantage in sensitivity performance [3]. The price to pay is the increased computational complexity of these techniques, which implies higher implementation costs for the BS. A complexity reduction of both MS and BS receivers can be achieved by adapting the state complexity of the trellis equalizer to the characteristics of the propagation channel. This allows a lower average power consumption of the digital circuits. GSM receivers are introduced in Section IV, and the above signal-processing techniques are discussed in Sections V and VI, where we analyze their performance and implementation requirements. Section VII addresses the application of the algorithms to next-generation cellular standards. Finally, conclusions are drawn in Section VIII. II. WIRELESS PROPAGATION CHANNEL IMPAIRMENTS In wireless communications, the transmitted signal is corrupted by the time-varying propagation channel. In this respect, three physical mechanisms can be identified [1], [3]: 1) long-term signal fading or path loss; 2) medium-term signal variations, due to shadowing; and 3) short-term signal fading, due to multipath propagation. Each of these phenomena is caused by a different underlying physical principle and must be taken into account, at different levels, when designing and evaluating the performance of the system. Path loss or inverse distance power loss accounts for slow variations of average signal strength caused by varying distances between transmitter and receiver. Signal variations due to shadowing are often modeled as log-normal fading. Path loss and shadowing information is essential in determining the size of the coverage area for radio communications and in selecting optimum locations for base antennas. Multipath fading results in rapid variations in the envelope of the received signal. Typically, the received envelope can vary by as much as 30–40 dB over a fraction of a wavelength [1]. In wide-band transmission systems, multipath propagation causes frequency selective distortion, which results in intersymbol interference (ISI). Over the typical duration of one burst in a wireless system, both inverse power loss and shadowing correspond to a simple attenuation of the received signal. Therefore, the receiver design and the 1634

choice of the proper digital signal-processing algorithms depend essentially on the characterization of the multipath process. A. Multipath Fading In a multipath propagation channel, the superposition of the arriving paths at a given value of delay induces destructive and constructive interference, which varies as a function of the position. As the antenna moves through this interference pattern, its spatial variation results in a time variation of the received signal. In addition, due to the motion of the antenna, the signal on each path undergoes a Doppler shift that depends on the path’s arrival angle. At a given time , the channel impulse response can be modeled as a densely tapped delay line with delay index [3] (1) Under the assumption of wide sense stationary uncorrelated scatterers (WSSUS), from the central limit theorem one can assume Gaussian statistics. Therefore, the channel is . As a characterized by the mean and correlation of can first-order statistical description of the fading, be decomposed into a specular and diffuse component. The specular component, corresponding to line-of-sight or and specular reflection, is defined by is known as the channel mean. The diffuse component is and is Rayleigh given by distributed [1], [3]. A second-order statistical description is given by the tap-gain cross-corof the process , relation function is the normalized autocorrelation function, and where is the delay power of density profile [3]. The Fourier transform is the Doppler spectrum of the fading process [1], [2]. The is essentially nonzero range of values of over which is the multipath delay spread of the channel. For mobile radio channels, the multipath delay spread ranges from a few microseconds up to tens of microseconds. B. Shadowing and Path Loss While the impulse response approach is useful in characterizing the short-term or local variations of the channel, the long-term or global statistics are described by path loss models, which account for the reduction of the received power with the distance from the transmitter. The classical free space model predicts that the received power decays with the square of the radio path length , , where is the carrier wavelength and is the transmitted power [1], [3]. Free space propagation does not apply in a mobile radio environment and the propagation path loss depends not only on the distance and wavelength, but also on the antenna heights of the MSs and the BSs and on the local radio environment [1]. The simplest path loss model assumes that the received power is given by dBm (2) PROCEEDINGS OF THE IEEE, VOL. 88, NO. 10, OCTOBER 2000

where the term gives the received signal power (in dBm) at a known reference distance from the transmitting antenna [1], [4]. The parameter is the path loss exponent, which depends on the cell size and the characteristics of the local environment. ranges from 3 to 4 for a typical urban macrocellular environment and from 2 to 8 for a microcelin (2) is a lular environment [1], [4]. The parameter zero-mean random variable that represents the error between the actual and estimated path loss. This statistical variation is caused by shadowing, and is generally modeled of by a log-normal distribution with mean dBm (3)

generated within the receiver. Hence, the total noise power in the receiver bandwidth results , where indicates the total noise density at the receiver input. If denotes the received signal power, the , or in dB received SNR is then given by (4) . Define now , and let be the value of (in dB) on the cell fringe, defined by . Taking into account that is log-normally distributed, the probability at a distance results [1], [4]

with

. For macrocells, typically and standard deviation dB being a typical ranges from 5 to 12 dB, with value [4]. C. Thermal Noise and Co-Channel Interference The characterization of the wireless channel includes the thermal noise power received at the antenna, which depends on the temperature and bandwidth of the system. Additionally, circuit noise is generated within the RF and IF stages of the receiver. Besides the noise, wireless receivers are affected by interference from other communications operating in the same frequency band. In cellular systems, the reuse of the same carrier frequencies in different cells (frequency reuse) causes co-channel interference (CCI). Frequency reuse also introduces adjacent channel interference (ACI), when neighboring cells use frequencies that are spectrally adjacent to each other. Although interference determines the system capacity, it has little impact on the link-power budget, and, therefore, it will be not considered in this paper. III. LINK POWER BUDGET Radio links often exhibit a threshold effect, such that the link quality is acceptable provided that both the average reand the average signal-to-interference ratio ceived SNR exceed certain thresholds, denoted by and , (SIR) respectively. These thresholds depend on many parameters of the radio link, including the particular modulation and coding scheme, and the receiver design [4]. The performance of a radio system can be measured in terms of the outage proband . abilities In the basic design of a wireless system, the required transis mitter power can be determined once the probability known. Likewise, the required co-channel reuse factor of a of cellular system can be obtained from the probability the acceptable CCI. In this section, we review the basic principles of the link-power budget design. The thermal noise that arises at the receiver front-end is Watt/Hz, where is the Boltzmann’s given by is the noise temperature in degrees Kelvin. constant and The equivalent input noise that accounts for the noise generated in the RF and IF stages of the receiver is conventionally , represented by the receiver noise figure is the equivalent input spectral density of the noise where LUSCHI et al.: ADVANCED SIGNAL-PROCESSING ALGORITHMS

(5)

with tity

. In (5), the quan-

(6) is the SNR margin required to sustain a probability [4]. To obtain a relationship between the outage probability and the area averaged outage probability requires models for the propagation path loss and spatial density of the MSs. Assuming that the MSs are uniformly distributed throughout the cell area, the path loss model [(3)] yields the area averaged probability [1], [4]

(7) and , with . The area averaged probability (7) is, thereon a cell fringe minus fore, given by the probability a correction term. or is specified, (5) or (7) can be solved Once . If is known from theory, exfor can be obtained. Once periments, or simulation, then is known, the minimum required transmitted power can be determined by using knowledge of the path loss, antenna gains, and receiver noise power [4]. The system power budget design is summarized in Fig. 1 for the case of a typical urban macrocellular environment. From the above discussion, we note that it is desirable as small as possible. For a to design radio links having given transmission format (modulation and channel coding is to employ scheme), the only way of decreasing more effective signal-processing algorithms at the receiver. (i.e., for a given We also observe that, for a fixed ), the required received signal power and, hence, the required transmitted power can be decreased by designing a receiver with a reduced noise figure. The quantity defines the sensitivity of the receiver.

where

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duration of a coded bit

, respectively. Then, . In the case of the GSM system, kHz, and kHz. Therefore, we have , or dB. Suppose now that the bits are obtained from the source-encoded bits, or information bits, by means of a rate 1/2 code. , Then, the bit energy for the information bits is and dB. IV. GSM CELLULAR RADIO RECEIVERS

Fig. 1. Power-budget design for a typical urban macrocellular environment. F : receiver noise figure; N W : total equivalent noise power at the receiver input; 0 : SNR threshold; M : required SNR margin for a given outage probability;  : average signal power at distance d;  : average SNR at distance d.

Example 1: As an example, we consider the case of a typical urban GSM macrocell, where typical values and dB. for the path loss model are K Assuming an equivalent noise temperature dB, the total noise and a receiver noise figure spectral density at the antenna connector is dBm/Hz. Therefore, taking into account that the bandwidth of a GSM kHz, the input noise power in the bandreceiver is width results dBm. Suppose that the required (area averaged) outage prob. Then, from (7), we obtain ability is dB. A typical value of the SNR threshold for a GSM receiver is dB, which corresponds to a receiver sensitivity of dBm. dB and This gives dBm. Finally, using , we can derive and the (3) with required transmitted power for the given coverage area. We emphasize that the receiver sensitivity can be im(through a proved by decreasing both the noise floor . In this decreased noise figure) and the SNR threshold paper, we focus on baseband techniques for reducing the SNR threshold, and assume that the noise figure has been minimized by a suitable design of the RF and IF stages of the receiver. It is worth mentioning that the performance of digital communications systems is often specified by the value of required to keep the error-rate performance below a given denotes the required energy per transmitted level, where bit. Depending on the section of the receiver chosen to meais defined with reference to either sure the link quality, coded or uncoded bits (information bits). Example 2: Consider the error performance at the output and denote the energy and of the equalizer, and let 1636

In time division multiple access (TDMA) cellular radio systems, multipath fading causes frequency selective distortion. In GSM, multipath delay spreads are on the order of two to five symbol intervals. In addition, channel characteristics are normally time-varying due to the relative motion of mobile and fixed stations. These channels require the implementation of an equalizer at the receiver. The equalizer performance with respect to interference and noise has implications on the system performance discussed in Section III. ) performance diIn particular, an improved SNR ( rectly translates into an improved receiver sensitivity, i.e., in a lower required transmitter power. GSM specifies a referdBm ( dBm for hand portable ence sensitivity of mobile receivers) [5]. From the analysis in Section III, this implies that the sum (in decibels) of SNR threshold and receiver noise figure should not exceed 17 dB. In a typical GSM receiver, the above sum does not usually exceed 14 dB. This is conventionally achieved by maximum-likelihood equalization (maximum-likelihood sequence estimation, or MLSE), which implements the Viterbi algorithm on the ISI trellis [7]–[9]. A. GSM Radio Link GSM is a TDMA system with 200-kHz carrier spacings. A TDMA frame on one channel is divided into eight time slots, each one reserved to one user. The communication is full-duplex, with transmit and receive frequencies separated by 45 MHz. GSM operates in the paired bands 890–915 MHz (uplink) and 935–960 MHz (downlink), while its derivative system DCS 1800 operates in the bands 1710–1785 MHz (uplink) and 1805–1880 MHz (downlink). The GSM full-rate speech transmission employs a regular pulse excited-long term predictive (RPE-LTP) speech codec [6], [10], which compresses the 64 kb/s speech to 13 kb/s. The encoder produces 260 output bits for every 20-ms speech frame [10]. These 260 bits are then unequally protected by means of channel encoding. The coding scheme for speech transmission is shown in Fig. 2 [6], [11]. After interleaving, the bits are encrypted and assembled according to the burst structure sketched in Fig. 3 [6], [11], [12], prior to Gaussian minimum shift keying (GMSK) modulation and transmission. The modulated signal has s, which corresponds to a raw a bit interval bit-rate of 270.8 kb/s. As shown in Fig. 3, each transmitted burst contains a midamble of 26 bits (training sequence) that is used for channel estimation. The training sequences are designed to exhibit good autocorrelation properties, PROCEEDINGS OF THE IEEE, VOL. 88, NO. 10, OCTOBER 2000

Fig. 2. GSM channel coding scheme for TCH/FS.

Fig. 3.

GSM frame and burst formatting for TCH/FS.

and tolerate 5 bits of delay spread [12]. Carrier and burst synchronization between MS and BS is established prior to data transmission through specific control channels [frequency correction channel (FCCH) and synchronization channel (SCH)] and a unique set of time base counters [12]. To reduce the power transmitted by BS and MSs whilst maintaining the quality of the radio link, GSM employs RF power control. Based on the measured received power level, the transmit power is reduced in steps of 2 dB each 60 ms [13]. In GSM, BSs and MSs are classified according to the maximum transmitter output power. BSs have maximum powers from 34 to 55 dBm (2.5–320 W), while MSs have power classes from 29 to 43 dBm (0.8–20 W). Depending on the power class, the range for uplink power control is between 20 and 30 dB. The range used for downlink is manufacturer dependent, and may be up to 30 dB. The lowest power level for all MSs is 13 dBm (20 mW) [5]. B. GSM Channel Model GSM specifies the multipath channel models for the different propagation environments, in order to provide appropriate test conditions for different implementations of the receiver [5]. For each propagation condition, the GSM wide-band multipath channel is described by the time-varying impulse response (1), with complex tap gains of a given mean power and delay [5], [6]. In the LUSCHI et al.: ADVANCED SIGNAL-PROCESSING ALGORITHMS

GSM channels, the presence of a line-of-sight or specular component is specified only for the first tap of the model for rural area conditions (RA). In all the other cases, including the model for typical urban area (TU), the stochastic processes are characterized by a Rayleigh distribution (classical Doppler spectrum [1], [2]). In terms of multipath delay spread, the rural area response decays fast within one bit interval. The hilly terrain (HT) model has a long-delay part around 15–20 s due to distant reflections. The typical urban (TU) impulse response spreads over a delay interval of 5 s, which corresponds to almost two 3.69 s bit interval duration. These channels result in serious ISI, which require the use of a channel equalizer at the receiver. C. System Model and Receiver It is possible to show [14] that the transmitted GMSK signal, expressed in complex baseband notation, can be approximated by the equivalent linear model (8) where transmitted binary symbols; symbol rate; transmit impulse response or pulse shape. 1637

Fig. 4. Conventional GSM receiver.

The signal (8) is transmitted over a multipath fading , which produces the channel with impulse response . The overall channel response model of the received signal includes the equivalent thermal noise at the antenna connectors, represented by an additive , with zero mean white complex Gaussian noise process . and double-sided power spectral density The received signal is passed through the equivalent receive filter, and the output is sampled at time instants . The GSM signal is substantially bandlimited (zero excess bandwidth). Therefore, with bandwidth Baud-rate sampling provides sufficient statistics for data estimation. Assume an ideal low-pass receive filter, and define the taps of the equivalent discrete-time channel . impulse response as Then, the received signal samples are expressed as , where . At the receiver, a binary modulation is [15]. Therefore, recovered by applying the derotation the signal samples at the input of the equalizer results

(9)

represent the where the complex tap-gains equivalent channel taps at time . A typical implementation of a GSM digital receiver is shown in Fig. 4. GSM channel equalization is conventionally performed by means of an ML trellis processor. The receiver . The must first estimate the channel impulse response initial channel estimation is usually obtained by means of correlative channel sounding [16], [17]. In this case, the estimated channel taps are obtained by correlating the received with bits out of the 26 bits training signal sequence

(10)

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With ML sequence estimation by means of the Viterbi algorithm, the equalizer uses the channel estimate to minimize the Euclidean distance between the received sequence and all the possible transmitted sequences [8], [9], [18]. If the channel cannot be considered approximately constant within one burst, the channel estimate can be updated during the burst by using the decisions at the equalizer output [17]. The equalizer output sequence is finally deinterleaved and decoded. The above discussion refers to the case of singlechannel reception. The different algorithms can be easily generalized to the case of receivers with multiple-antenna [19]. V. ADVANCED SIGNAL-PROCESSING ALGORITHMS MLSE is the optimum detection technique for finite-length ISI and additive white Gaussian noise (AWGN), in the sense that it minimizes the probability of a sequence error. However, it provides only hard decisions on the received symbol sequence. In receivers employing the concatenation of an equalizer and a channel decoder, the performance can be further improved by soft-decision decoding [20], [21]. This requires a reliability information associated with the equalizer output data. In this respect, the optimum equalizer is the symbol-by-symbol maximum a posteriori probability (MAP) estimator [22], which has the advantage of intrinsically providing optimal a posteriori probabilities as soft-output values. Soft-in/soft-out equalization and decoding are reviewed in Section V-A. With both ML or MAP data estimation, the equalizer operation is based on the knowledge of the channel impulse response, which quality has a significant impact on the equalizer performance. The GSM standard employs training symbols to estimate the channel response at the equalizer start-up according to (10). The sensitivity performance of a GSM receiver can be improved by iterating the equalization and channel estimation procedures on a burst-by-burst basis [23]–[25]. In particular, in a first pass the initial channel estimate is obtained by means of the known training sequence. After that, one or more iterations can be performed where hard or soft data symbol decisions at the equalizer output PROCEEDINGS OF THE IEEE, VOL. 88, NO. 10, OCTOBER 2000

are employed, together with the original training symbols, to obtain an improved channel estimate [24]. Iterative channel estimation techniques are discussed in Section V-B. In GSM, the information bits are encoded and interleaved prior to modulation. Therefore, by viewing channel encoder and ISI channel as a serially concatenated coding scheme, one can consider the implementation of iterative equalization and decoding (turbo equalization), as an application of the turbo principle [26]–[30]. In this context, the performance of iterative channel estimation (ICE) is further improved by using the more reliable decisions obtained by interleaving the a posteriori values for the coded bits provided by a softin/soft-out channel decoder [24], [25], [31]. As detailed in Section V-C, for the GSM full-rate speech traffic channel (TCH/FS) [12], the proposed technique provides a significant performance gain after just one iteration. The above techniques allow the operation of the BS receiver at reduced SNRs, thus, lowering the requirements on the power transmitted by the MSs. In the case of speech transmission, another way of reducing the required received signal level corresponding to a given speech quality is to exploit the residual redundancy of the speech encoder by source-controlled channel decoding [32]–[34], which is considered in Section V-D. With this technique, the a priori information about the source statistics is used in the channel decoder to improve the BER of the most significant bits of the speech frame. In the case of the GSM full-rate speech encoder, this scheme allows to significantly improve the speech quality at low SNRs [33], [34]. Power consumption in a mobile terminal can also be reduced by reducing the implementation complexity of the receiver. Conventional receivers implement a trellis equalizer with a fixed state complexity to represent all the relevant ISI terms for the worst case channel delay spread. A considerable saving in complexity can be achieved by adaptively adjusting the number of states of the ISI trellis, in order to match the actual length of the propagation channel [35], [37]. Furthermore, at low SNRs, limiting the channel description to the significant ISI terms reduces the overall channel estimation noise, and can provide improved error performance. Adaptive channel memory truncation techniques are addressed in Section V-E. A. Soft-In/Soft-Out Equalization and Decoding ML sequence estimation implemented by the Viterbi algorithm is the optimum sequence detector [8], [7]. It is widely used in digital mobile receivers for processing both the ISI trellis (equalization) and the channel code trellis (channel decoding). However, the channel decoder performance can be improved by an equalizer which provides soft values at the decoder input [20]. Furthermore, in some advanced schemes implementing iterative equalization and decoding and/or source controlled channel decoding [32], the channel decoder must be able to provide soft outputs for both the coded bits and the information bits [38], [32], [29]. As pointed out in [31], there are several advantages in maintaining soft values as long as possible in a digital receiver. LUSCHI et al.: ADVANCED SIGNAL-PROCESSING ALGORITHMS

In terms of bit error probability, the optimum algorithm for soft-in/soft-out equalization and decoding is the symbol-bysymbol MAP algorithm. Originally proposed by Bahl et al. [22] for decoding of convolutional codes, the MAP algorithm initially received very little attention. In fact, it provides a minimal advantage in BER performance over ML decoders, at a higher implementation cost. However, being an a posteriori probability (APP) calculator, it has the advantage of intrinsically providing optimal soft output values. It has been recently shown that the logarithmic version of the MAP algorithm is equivalent to a combination of a forward and backward Viterbi processors, coupled by a dual maxima computation [39]. The first part of this section reviews the log-likelihood algebra and the formulation of MAP equalization and decoding (Sections V-A1–V-A3). Then we discuss suboptimum processors that provide a substantial complexity reduction at nearly optimum performance (Section V-A4). 1) Log-Likelihood Algebra: Associated with the theory of soft-in/soft-out decoding is the notion of log-likelihood algebra [31], [27]. The log-likelihood value ( -value) of a binary random variable is defined as (11) is the hard decision on , The sign of the soft value is the reliability of this decision. For statistically and independent , we define the sum of two -values as [31]

(12) denotes the modulo-2 addition of biwhere the symbol nary data (exclusive OR operation). The sum defined in (12) and . yields the additional rules 2) Soft-In/Soft-Out Equalization: Consider the binary ISI trellis in Fig. 5 (which represents the channel as a and denote rate 1 convolutional encoder), where and , respectively. The the trellis states at level symbol-by-symbol MAP equalizer [22] computes the conditioned to log-likelihood values of the encoded bits the received sequence

(13) In (13), the sums at the numerator and denominator are to be taken over all the existing transitions from state to state corresponding to or , respectively. 1639

, . Let denote the input log-likegiven the sample lihood value for the coded bits received by the equalizer. Then, from (14) with (18) (19) one obtains [31]

Fig. 5. Trellis structure of the intersymbol-interference channel.

Assuming independent noise samples, the joint probability is expressed as the product of three independent probabilities

(14) and can be calculated by a where the quantities forward and backward recursion, and [29], [31]. can be expressed as The branch transition metrics and a transition the product of a a priori probability . For a MAP equalizer one obtains probability (15) represents the a priori information on the bit where (that is obtained from the channel decoder), and

(20)

(21) The soft-in/soft-out convolutional decoder can be viewed as a nonlinear filter that improves the quality of the -values on encoded bits by using the relationship between them (which is given by the convolutional code) [40]. 4) Suboptimal Soft-In/Soft-Out Schemes: The complexity of the optimal symbol-by-symbol MAP algorithm can be reduced by operating in the log domain, and by exponential observing that the logarithm of a sum of can be efficiently computed as [38], [39] terms

(16) (22) Therefore, using (14)–(16) in (13) the equalizer soft-output results [29], [31]

(17) The above MAP equalizer is easily extended to the case of diversity reception by observing that, in the case of independent input noise . 3) Soft-In/Soft-Out Decoding: The operation of the optimal symbol-by-symbol MAP decoder is similar to that of the equalizer, the difference being that the decoder takes -values about encoded bits as inputs and produces -values about both encoded bits and information bits. Consider the binary convolutional code. The MAP case of a rate for the decoder delivers the log-likelihood values for the encoded bits information bits , and/or 1640

. With with this log-MAP rule, we avoid calculating the exponential , , and , and terms, using replacing the summations by the corresponding modified operation. Further simplification is obtained by ap, which corresponds proximating to the max-log-MAP algorithm [20], [41], [38]. We also observe that the complexity penalty associated with the presence of both the forward and backward recursion is eliminated by a suboptimal log-MAP algorithm limited to the forward recursion, with the introduction of a decision delay depending on the code/channel memory [20], [41]. Among the suboptimal soft-in/soft-out schemes, the softoutput Viterbi algorithm (SOVA) [42] has been often considered for implementation as an alternative to suboptimal MAP algorithms [41], [38]. In evaluating the symbol reliability information, the SOVA only considers one competing path per decoding stage (the survivor of the Viterbi algorithm). Its soft-output is, therefore, noisier than with most of the suboptimal MAP algorithms proposed in the literature. A modified PROCEEDINGS OF THE IEEE, VOL. 88, NO. 10, OCTOBER 2000

Fig. 6. Iterative channel estimation (ICE) with soft or hard feedback from the output of the equalizer and/or channel decoder.

SOVA algorithm with improved soft-output quality has been recently proposed [43]. However, the improved performance is obtained at the expense of additional complexity. The performance of the optimum symbol-by-symbol MAP equalizer and channel decoder has been compared with that of the different suboptimal soft-in/soft-out schemes. In particular, in the case of a GSM receiver, a good tradeoff between complexity and performance is obtained by the max-log-MAP algorithm [41], [38]. The forward max-log-MAP algorithm is shown to provide a negligible degradation with respect to the optimum strategy for MAP equalization of the GSM channel [20]. B. Iterative Channel Estimation The performance of the channel estimator can be improved if the output of the equalizer is fed back to the channel estimator and used as an extended training sequence, as illustrated in Fig. 6 [24], [25]. In fact, it is possible to show that increasing the length of the sounding sequence decreases the estimation error. The gain will be clearly reduced in the presence of decision errors at the equalizer output. The feedback can be performed by employing either hard decisions or soft decisions [24]. As is intuitive, soft decision feedback mitigates the effect of error propagation, and provides robustness at low SNRs. The complexity associated with a least-square (LS) channel estimator with the extended training sequence can be reduced by using correlative channel sounding, which ignores the autocorrelation of the estimated data. The effectiveness of this approximation will depend on the sequence length. With reference to Fig. 6, the initial estimate of the channel is obtained by the known training sequence. Once the first LUSCHI et al.: ADVANCED SIGNAL-PROCESSING ALGORITHMS

data estimation is performed for the entire burst, the output is fed back to the channel estimator to produce an improved channel estimate, which is passed again on to the data estimator. This iterative process may be repeated a number of times. For reasons of implementation complexity, we will consider here only one iteration and not address the problem of determining the optimum number of iterations. As an alternative, also shown in Fig. 6, iterative channel estimation can be performed by using the channel decoder output [24], [25]. This solution provides an additional performance gain, since the error correction code reduces the number of decision errors in the feedback sequence. Hard decision and soft decision feedback schemes are analyzed in Section V-B1 and V-B2. The last part of this section presents simulation results on the performance of these algorithms. 1) Hard Decision Feedback: In a hard decision (HD) feedback scheme, we assume all decisions to be correct and use them as an additional training sequence. The received can be written as signal vector (23) where matrix of the transmitted data bits ; channel vector; channel noise. corresponds to the convolution beThe matrix product and the equivalent impulse retween the data sequence [see (9)]. The above notation assumes the sponse channel to be constant over the block of transmitted data. It 1641

is worth noting that, in case of fast-varying channels, the initial estimate can be updated by means of a suitable tracking algorithm. Assuming the knowledge of the transmitted symbols (by decision feedback), the maximum-likelihood (ML) channel estimator is (24) denotes the probability density function (pdf) where of conditioned to . The ML estimator (24) corresponds to the LS estimator

Therefore, the ML estimator sponds to minimize the quantity

corre-

(28) where the expectation is taken over the bits conditioned on the received sequence . To minimize the cost (28) one differentiates it with respect to the channel vector , obtaining [44]

and (25) denotes Hermitian transpose and we assume that where reveals the inverse exist. A closer look at the matrix that one can reduce the computational complexity, and obtain a suboptimal estimator, by ignoring the off-diagonal are indepenvalues. In fact, by assuming that the bits , the off-diagonal elements dent, and, hence, can be considered small compared to the main diagonal. , This implies that we can take identity mawhere is the trix. Under this assumption, the matrix inversion can be avoided. The simplified LS estimator then becomes , which corresponds to the is a correlative channel sounding (CS) technique (10). If training sequence which is properly chosen (as is the case of can be made diagonal which elimGSM), the matrix inates the matrix inversion and the CS estimator coincides with the LS estimator. 2) Soft Decision Feedback: With soft decision (SD) feedback [24], the soft output of the equalizer is fed back to the channel estimator. The soft output is usually in the form of . This a posteriori probability a log-likelihood ratio from the equalizer can be used as a priori knowledge for the channel estimator. We observe that considering the transmitted bits as random variables, the a posteriori pdf can be written as

(26) where the expectation is taken over the transmitted bits. For one has small values of

(27)

1642

(29) and with inition of -value we compute

. From the def-

(30) Then, we have (31) Hence, similar to the case of hard decision feedback, the can be assumed small as compared to off-diagonals of the main diagonal terms. By ignoring them we have , and obtain the simplified (CS) estimator . Although the equalizer provides the log-likelihood ratios , these can be easily transformed by a lookup table according to (30). The above to produce the quantities analysis also applies to the case where the channel estimator is obtained by feeding back the -values of the coded bits provided by the channel decoder. 3) Performance of Iterative Channel Estimation: The numerical results presented here and in the following sections have been obtained by computer simulation of the GSM system. The simulator includes the time-varying GSM propagation channel. At the receiver, a 16-states forward max-log MAP equalizer is employed, which uses a 5-taps estimated channel response. Soft-in/soft-out decoding is performed by the max-log-MAP algorithm. As a reference, we consider a receiver implementing channel estimation by training sequence, single-pass max-log-MAP equalization and Viterbi decoding. It is worth noting that the error performance of this receiver (at the output of the decoder) is 2.5 dB better than that obtained with an hard-output MLSE equalizer [20]. The performance of the iterative channel estimation (ICE) schemes discussed in this section are compared in Fig. 7. The figure reports the normalized mean square estimation error (mse) in the case of decision feedback from the equalizer output for the GSM hilly terrain profile and a mobile speed of 100 km/h (HT100). As expected, soft-decision feedback provides an advantage at low SNRs. The reduced complexity PROCEEDINGS OF THE IEEE, VOL. 88, NO. 10, OCTOBER 2000

Fig. 7. Normalized mse of iterative channel estimation with decision feedback from the equalizer output (GSM HT100 profile) [24].

Fig. 8. BER performance of iterative channel estimation (GSM HT100 profile).

CS estimators gives a small performance loss at low SNR, where the channel noise is the main cause of error. However, for moderate channel distortion and at high SNRs, the approximation introduces a performance degradation. Figs. 8 and 9 show the BER performance at the output of the equalizer and channel decoder for the class I bits, with LS ICE by soft feedback from the output of equalizer (equalizer feedback) and channel decoder (decoder feedback). Equalizer feedback provides a gain of about 0.7–1 dB, while decoder feedback gives an improvement of 1.5–2 dB in terms of (where denotes the bit energy for the coded bits). C. Iterative Equalization and Decoding The idea of iterative decoding was introduced by Berrou et al. in 1993 [26] with application to parallel concatenated codes, the so called turbo codes. The principle, however, is general and can be applied to any concatenated coding scheme [27]. If the dispersive channel is treated as a rate 1 LUSCHI et al.: ADVANCED SIGNAL-PROCESSING ALGORITHMS

Fig. 9. BER performance of iterative channel estimation (GSM TU50 profile).

convolutional code, one can use the turbo principle to perform iterative equalization and decoding [28]–[31]. A simple block diagram in Fig. 10 illustrates the concept. The equalizer receives the channel output sequence , and delivers soft values on the transmitted (encoded) bits in the form of log[see (17)]. These values are deinlikelihood values terleaved and passed on to the channel decoder. The output of the decoder is given by the log-likelihood values on the coded bits (21). The decoder acts as a nonlinear filter which uses the dependence between the coded bits to produce less noisy estimates of the data. Its output at time can be decomposed into two parts: a) channel information and b) extrinsic information. The former is the input to the decoder and the latter is the incremental information about the bit which derives from all other bits excluding itself. Hence, it represents the new information obtained by the decoder using the dependence between the bits. The extrinsic information is calculated by simply subtracting the decoder input from the decoder output. In an iterative equalization and decoding scheme, these new -values are interleaved and fed back to about the coded the equalizer as a priori information bits . The equalizer now performs a second-pass equalization of the channel output sequence, taking into account the a according to (17). The extrinsic inpriori knowledge formation from the equalizer is then obtained by subtracting the input a priori knowledge from the equalizer output. This iterative process can be performed a number of times, and at the last iteration the decoder produces (possibly soft) estimates of the information bits according to (20). 1) Performance of Iterative Equalization and Decoding: The performance of the receiver that implements iterative equalization and decoding and iterative channel estimation by soft decoder feedback is reported in Fig. 11. For the GSM HT channel, this turbo-ICE scheme offers an . It is worth improvement of about 2 dB at noting that using ICE with decoder feedback provides a more substantial gain than iterative equalization and decoding. After the first iteration, the advantage of using a priori information in the trellis equalizer is limited by the 1643

Fig. 10.

Iterative equalization and decoding scheme with soft-in/soft-out modules.

Fig. 11. BER performance of the turbo-ICE receiver (GSM HT100 profile).

small constraint-length and time-varying characteristics of the GSM channel used as an inner code of the serially concatenated coding scheme. This fact has also been recognized in [29], [30]. However, as will be discussed in Section VI, choosing to implement iterative channel estimation with decoder feedback, there is essentially no extra cost associated with employing iterative equalization and decoding. D. Source-Controlled Channel Decoding The GSM full-rate speech encoder [10] has been designed to obtain a good compromise between the requirements of speech quality, low bit rate, delay, and complexity. As a result, the encoded speech samples are not independent and identically distributed, but maintain a residual redundancy which corresponds to a residual correlation between bits and nonuniformity of the encoded bit streams. Furthermore, the highest residual redundancy has been observed for the most important bits for the speech reconstruction (class Ia of Fig. 2) [33]. If these bits are found to be in error by the CRC code, a whole speech frame will be declared as bad. It has been recently noticed that the above redundancy provides information about the source statistics that can be used as a priori information in the channel decoder 1644

by source-controlled channel decoding (SCCD) [32]. In practice, the redundancy is employed to estimate the log-likelihoods on the information bits , that are then used as a priori information to derive the decoder soft or hard output [see (20)]. At low SNRs, this approach allows to significantly reduce the BER of the most significant bits of the speech frame, and, hence, dramatically improve the speech quality [33], [34]. There are two different types of correlation between bits the informain the encoded speech frame. Denote by tion bit at position in the th encoded speech frame of a given user. Interframe correlation accounts for the correlation between bits of successive encoded speech frames of the , . same user, that is the correlation between bit pairs On the other hand, intraframe correlation represents the correlation between bits inside one encoded speech frame, i.e. and . Hagenauer [32] devised a between the bits very simple and efficient way to calculate the a priori information of the interframe source statistics. His original work exploits the interframe correlation of the 10 most significant bits of the 260 bits GSM full-rate encoded block. Later, Ruscitto and Hindelang [45] showed how to exploit the intraframe correlation by running the channel decoder twice. In [33] the speech quality has been further improved by combining the a priori information derived from the inter- and intraframe correlation. With this approach, the a priori information for both interframe and intraframe correlation is computed during the transmission by a simple probabilistic method which uses the -values from the channel decoder. are The statistics updated on a frame-by-frame basis, and then passed as a priori information to the channel decoder, to be used for processing of the successive frame, according to (20) [33]. The method provides an improvement not only for the 12 most significant bits of the speech frame, but also for the whole class Ia [33]. Source-controlled channel decoding can be employed in conjunction with iterative channel estimation and iterative equalization and decoding. These iterative schemes are based the soft-in/soft-out decoder described in Section V-A. However, the complexity associated to the calculation of the soft-output can be avoided for the last decoding iteration. A low complexity SCCD scheme based on a soft-in/hard-out PROCEEDINGS OF THE IEEE, VOL. 88, NO. 10, OCTOBER 2000

Fig. 12. BER performance with and without source-controlled channel decoding for class Ia bits and for the first 12 bits of the speech block (GSM TU50 profile) [34].

channel decoder has been proposed in [34]. The source statistics are computed by a simple histogram method at the output of a channel decoder implemented by a modified Viterbi algorithm, which accepts a priori information at its input (APRI-VA) [34]. The accumulated metric of the convolutional code results APRI-VA at time for a rate

(32) is the soft input to the decoder for the channel where , and denotes the a priori information encoded bit for the speech encoded bit . 1) Performance of Source-Controlled Channel Decoding: As reported in [33], a SCCD scheme with combined use of inter- and intraframe correlation for the GSM full-rate speech codec can improve the error performance of the 12 most significant bits of the speech frame by 3.5 dB, and the whole class Ia by 1.5 dB. Fig. 12 shows the gain achieved by the low complexity scheme proposed in [34]. SCCD with an APRI-VA decoder is seen to provide an improvement of 1.8 dB for the first 12 bits in class Ia and 0.8 . This result dB for all the bits in class Ia, at a is quite remarkable if compared with those reported in [45]. The improvement achieved in [45] for the first 12 bits is about the same, but running a more expensive (soft-output) channel decoder twice.

section, we address techniques for the reduction of the state complexity of the trellis receiver of both MS and BS. Conventional receivers implement a trellis equalizer with a fixed number of states, in order to correctly represent the ISI terms for the worst case multipath delay spread. In a typical GSM receiver, the initial channel estimate (10) is usually windowed by maximum-energy search, to produce a truncated response of fixed length or [6]. This also provides a bit synchronization with a resolution equal to the sampling period [16]. Consequently, data estimation states. One possible is performed on an ISI trellis of solution to reduce the state complexity of the ISI trellis is to shorten the channel by decision feedback [46]. However, this approach corresponds to a performance degradation. We observe that in propagation environments with moderate to low delay spreads (such as the GSM typical urban environment), a substantial saving in complexity can be realized by adapting the channel model, and the number of states of the equalizer, to the actual channel profile [35]. The selection of the proper channel length not only provides a complexity reduction, but can correspond to a performance gain. In fact, from (9) and (10) we write the estimated channel taps as , , where

(33)

and represents the estimation error. If , from (33) follows . Therefore, at low SNRs, assuming a channel memory higher than required increases the overall noise of the estimated channel response. The selection of the optimum channel length implies a tradeoff between the requirements of matching the length of the actual channel and minimizing the overall channel estimation error. The problem can be addressed by applying statistical rules for model order selection, such as Rissanen’s minimum-description length criterion [36], [44] (see, e.g., [37]). A simple alternative algorithm which operates on a burst-by-burst basis has been proposed in [35]. The procedure is based on the minimization of the squared error of the truncated channel estimate over the possible channel lengths and delays. Denoting by the window of delay and length used to derive the truncated channel, the criterion can be expressed as [35] (34)

E. Adaptive Channel Memory Truncation The improved performance of the BS receiver algorithms discussed in the previous sections corresponds to a lower transmitter power required from the mobile terminals. Power consumption in the terminal can also be reduced by reducing the computational complexity of the mobile receiver. In this LUSCHI et al.: ADVANCED SIGNAL-PROCESSING ALGORITHMS

The statistics on the optimum length selected by the algorithm for the GSM TU profile are shown in Fig. 13 [35]. We coremphasize that a channel truncation to a length responds to a reduction of 3/4 on the state complexity of the equalizer. Simulation results reported in [35] indicate a BER improvement of about 0.7 dB for relatively low delay spread 1645

block ). Slots 0–3 have already been iteratively equalized , so now only four slots need after decoding of block to be processed. This reduces the additional complexity for iterative decoding by half, but also leads to the use of soft values from the decoder for only 50% of the bits. B. Implementation Complexity

Fig. 13. Optimum length of the truncated channel for typical urban propagation conditions (GSM TU profile) [35].

(TU conditions), and no degradation in the presence of significant delay spread (HT conditions). VI. IMPLEMENTATION ISSUES The penalty to be paid for the improved sensitivity performance of the iterative signal-processing algorithms is the increased implementation complexity. As already pointed out, while a lower SNR requirement reduces the power needed for the mobile transmitter, a higher computational cost implies a higher power drain on the digital circuits at the BS. In this section, we give the details on the complexity associated to the different algorithms, and discuss the tradeoff between error performance and complexity. We also address the physical implementation of the above signal-processing techniques. In this respect, considerable gain in terms of circuit size, speed and power consumption has been recently achieved by an analog implementation of soft-in/soft-out equalizers and decoders [47]–[50]. A. Latency Problems The interleaving scheme in GSM causes latency problems with a decoder feedback scheme. Fig. 14 shows the effect of interleaving for three consecutive speech blocks of a single user. In order to iteratively decode block or to use the decoder output for iterative channel estimation, one has to feed . However, this back the soft values of the bits in block output is not available until four slots later, that corresponds to four frames in terms of time, since one user only has one slot per frame. This introduces a delay of 18.5 ms, which is not acceptable for speech applications [51], [52]. One solution to the above problem is to feed back the soft outputs that are available at slot 7 of Fig. 14 (i.e., the information from and block ). With this approach, only 75% block of the bits will have a priori information to be used in the second-pass channel estimation and equalization. Yet another solution is to iteratively equalize only slots 4–7 of Fig. 14 (with soft values from the decoder only for 1646

As a reference for providing a measure of the computational load, we consider a DSP implementation of the digital receiver. The cost will be quantified in terms of number of DSP instruction cycles. More precisely, we will assume that channel estimation and equalization of one GSM burst need to be performed in one time-slot time (i.e., the 0.577 ms duration of one burst). Similarly, we will set the constraint that deinterleaving and decoding for one speech block is performed in one time-slot time. These assumptions are motivated by the latency constraints relative to speech transmission addressed in the previous section. Furthermore, being the number of instruction cycles needed for a given operation dependent on the particular implementation, we will parameterize the complexity estimates by using the implemen– million cycles/s. tation-related quantity 1) Channel Estimation and Equalization: As a soft-in/ soft-out equalizer, we consider the forward max-log MAP algorithm as the best tradeoff between performance and implementation cost. The complexity for one-pass equalization with channel estimation using the 26-bit training sequence is estimated by about one times the quantity defined above. Iterative channel estimation with feedback from the equalizer output requires a second pass max-log MAP equalization and channel estimation using an extended training sequence, which additionally needs a matrix inversion. With iterative equalization and decoding, the latter equalizer also uses a priori information from the decoder in the branch metric. The cost of this equalizer is still approximately given by . 2) Deinterleaving and Decoding: The implementation cost of the max-log MAP convolutional decoder for rate 1/2 and constraint-length 5, taking into account deinter, leaving/interleaving and CRC check, is approximately which is about twice the complexity of a hard-output Viterbi decoder. The latter implementation can be used for the last pass decoding, which does not need to provide soft-output values. Considering an APRI-VA using a priori information on the source statistics (SCCD), the cost increases only marginally. The complexity associated with the estimation of the source statistics is negligible. 3) Complexity of the Iterative Schemes: On the basis of the cost of the individual modules, we are now in a position to compare the implementation complexity of the different iterative receivers. The results are summarized in Table I. As a reference, the overall complexity of a single-pass GSM receiver with forward max-log-MAP equalizer and hard-output Viterbi decoder in million cycles/s results about . In the ICE receiver employing soft-decision feedback from the equalizer output and SCCD, the complexity penalty comes from performing a second-pass channel estimation and equalization, which corresponds to an additional cost . A higher complexity is required in case of feedback from the PROCEEDINGS OF THE IEEE, VOL. 88, NO. 10, OCTOBER 2000

Fig. 14.

Latency for iterative processing due to the GSM interleaving.

Table 1 Computational Complexities for Iterative Processing (5–Taps Channel), as a Function of the Implementation-Dependent Quantity C

decoder output. This is due to the constraint of performing the second-pass channel estimation and equalization for ), and to the need eight bursts within one burst time ( ). On the of a soft-output decoder for the first-pass ( contrary, implementation of SCCD is quite inexpensive. Overall, the turbo-ICE scheme results four to five times more complex than ICE from the equalizer output, and about seven times more than the noniterative MAP receiver. It is worth mentioning here that a possible solution to reduce this complexity is to begin the first-pass decoding after equalization of the seventh burst out of the eight corresponding to the interleaving depth. In this case, the unknown values at the decoder input are declared as erasures. Simulation results show that the performance degradation (after the second-pass decoding) is not significant, while doubling the processing time reduces the implementation complexity by half. We also note that in all the above implementations, the complexity of each equalization pass can be reduced in the presence of moderate to low delay spread by adaptive channel truncation techniques. C. Analog Implementation As follows from the above discussion, the implementation of a probabilistic receiver may require substantial LUSCHI et al.: ADVANCED SIGNAL-PROCESSING ALGORITHMS

computational resources. The capability of resorting to the full performance gain offered by the iterative processing is, therefore, determined by the effectiveness of the hardware implementation. In this respect, it has been recently shown that an analog implementation of soft-in/soft-out decoders can significantly outperform the corresponding digital implementation in terms of speed and/or power consumption. The idea of analog decoding, first introduced by Hagenauer [47], is based on the observation that probabilistic decoding relies on the soft representation of the log-likelihood values and uses computations with real numbers (as opposed to algebraic decoding, which deals with binary values). Moreover, a soft-in/soft-out decoder requires a large dynamic range, which can be provided by a suitable analog design. Finally, the soft decision feedback required in an iterative decoding scheme can be intrinsically realized by the settling behavior of an analog network with continuous-time processing [49]. The problems commonly associated with analog signal processing include sensitivity to component variations, susceptibility to noise and power supply disturbances, and temperature dependencies. However, it has been demonstrated that these problems can be circumvented by exploiting, rather than fighting, the fundamental nonlinearities of transistor physics [49]. In the approach of [47], [48], soft-in/soft-out decoding and equalization are performed by an analog nonlinear network, where the log-likelihood values of the bits are represented by currents and voltages. The network design is based on two fundamental building blocks realized as analog circuits, the , and the box-plus simple addition of -values, , illustrated in Fig. 15. The hyperelement (12), bolic functions in Fig. 15 can be implemented by exploiting the natural exponential characteristics of diodes and BJTs. A fully analog 0.25 m BiCMOS tailbiting MAP decoder for a rate 1/2 code has been recently fabricated and tested [50]. With respect to an equivalent digital circuit, the above implementation provides more than 3.3 times higher speed, 1647

VIII. CONCLUSION

Fig. 15. Box-plus element of the log-likelihood algebra (soft exclusive OR).

eight times lower power consumption, and a size reduction by a factor 5.2 [50]. VII. APPLICATION TO NEXT-GENERATION TDMA WIRELESS SYSTEMS Besides third-generation wireless mobile systems based on code division multiple access (CDMA) technology (UMTS/IMT-2000), future cellular systems include the evolution of existing TDMA systems GSM and IS-136 toward the higher data rate EDGE standard [53]. EDGE will provide an evolutionary path for delivering third-generation services in existing frequency bands. One of the major differences of EDGE with respect to the GSM radio interface is the introduction of an 8-PSK modulation format in order to improve the spectral efficiency of the GMSK transmission. This modification implies that the practical implementation of optimum (full-state) trellis equalizers becomes unrealistic, and suboptimum schemes have to be considered. Possible solutions for EDGE channel equalization are reduced state trellis equalizers employing decision feedback (see, e.g., [54]), and linear or decision feedback equalizers. In both cases, the signal-processing techniques addressed in this paper have the potential for providing significant performance gains, and an important flexibility in designing the best tradeoff between computational complexities and performance, i.e., between power consumption and quality of service. The impact of iterative channel estimation techniques for an EDGE receiver is investigated in [55]. The results show that ICE can greatly improve the receiver block error rate performance. A turbo equalization receiver for 8-PSK modulation has been recently studied in [56], using a simple minimum mean square error (mmse) block decision feedback equalizer. This nonprobabilistic equalizer has been modified in order to operate as a soft-in/soft-out module that accepts a priori information from the channel decoder. Although the receiver uses a suboptimum equalizer, simulation results show a performance improvement of 2–3 dB after the first two iterations [56]. It is worth mentioning here that, compared to the GSM channel, the EDGE ISI channel has been shown to be a better inner convolutional code for an iterative equalization and decoding scheme. Finally, from the implementation point of view, EDGE has the advantage of using an interleaving over four bursts (while the GSM interleaver spreads the data over eight bursts), which allows a reduced implementation complexity for iterative signal-processing techniques. 1648

Substantial progress has been made in the receiver signalprocessing algorithms for wireless communications to minimize the requirements on signal-to-noise and/or computational complexities for a given quality of service. In wireless cellular systems, lower computational costs in the terminals, which implies a reduced power drain on the digital circuits, can be achieved by techniques that adapt the state complexity of the data estimator to the propagation channel. These algorithms realize a complexity reduction of about one-third for a typical MS receiver. An improved BS sensitivity—i.e., a reduced value of minimum SNR that guarantees a given quality of service—allows for a lower transmitter power required from the mobile. Iterative (turbo) signal-processing algorithms based on maximum a posteriori probability data estimation have been presented, which can improve the sensitivity performance of a GSM BS receiver by approximately 2 dB (4.5 dB with respect to hard-input decoding). A further 1–2-dB improvement of the speech quality is achieved by source-controlled channel decoding. The gain of iterative channel estimation with SCCD corresponds to a reduction of about one-third (two-thirds with respect to hard-input decoding) on the required MS transmitter power, with an additional complexity of about 50%. Using iterative processing with feedback from the decoder output allows for an overall reduction of transmitted power by one-half. This performance gain corresponds to an extension of the handset talk time. ACKNOWLEDGMENT The authors would like to thank I. Bar-David, R. Meyer, G. Heinrich, M. Lehnert, T. Beggs, M. Hepworth, B. Royer, and J. Salz. REFERENCES [1] W. C. Jakes, Microwave Mobile Communications. Piscataway, NJ: IEEE Press, 1993. [2] R. H. Clarke, “A statistical theory of mobile-radio reception,” Bell Syst. Tech. J., vol. 47, pp. 957–1000, July 1968. [3] J. G. Proakis, Digital Communications, 3rd ed. New York: Mc Graw-Hill, 1995. [4] G. L. Stüber, Principles of Mobile Communication. Boston, MA: Kluwer, 1996. [5] GSM-05.05, “Digital cellular telecommunications system (Phase ): Radio transmission and reception,” ETSI, 5.2.0 ed., July 1996. [6] R. Steele, Mobile Radio Communications. Piscataway, NJ: IEEE Press, 1996. [7] G. D. Forney Jr., “The Viterbi algorithm,” Proc. IEEE, vol. 61, pp. 268–278, Mar. 1973. [8] , “Maximum likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 363–378, May 1972. [9] G. Ungerboeck, “Adaptive maximum-likelihood receiver for carriermodulated data-transmission systems,” IEEE Trans. Commun., vol. COM-22, pp. 624–636, May 1974. [10] GSM-06.10, “GSM full rate speech transcoding,” ETSI, 5.0.1 ed., May 1997. [11] GSM-05.03, “Digital cellular telecommunications system (Phase ): Channel coding,” ETSI, 5.2.0 ed., Aug. 1996. [12] GSM-05.02, “Digital cellular telecommunications system (Phase ): Multiplexing and multiple access on the radio path.,” ETSI, 5.2.0 ed., Nov. 1996. [13] GSM-05.08, “Digital cellular telecommunications system (Phase ): Radio subsystem link control,” ETSI, 5.1.0 ed., July 1996.

2+

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Carlo Luschi (Member, IEEE) received the Dr. Ing. degree in electronic engineering from the University of Pisa, Pisa, Italy, in 1991. Since 1997, he has been with Global Wireless Systems Research, Bell Laboratories, Lucent Technologies, Swindon, U.K., where he is currently a Member of Technical Staff involved in the research and design of advanced receiver techniques for wireless communications. In 1988, he was affiliated with Telettra SpA, Milan, Italy, where he worked on cross-polarization interference cancellation for digital radio receivers. From 1991 to 1997, he was with the DSP Lab, Alcatel Telecom—Radio, Space, and Defense Division, Milan, Italy, as a Member of the Advanced Research Group. His research interests include digital communication theory, with emphasis on channel equalization, channel coding, and estimation and detection techniques. He has filed 15 patents in the field of digital communications.

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Magnus Sandell (Member, IEEE) received the M.Sc. degree in electrical engineering and the Ph.D. degree in signal processing from Lulea University of Technology, Sweden, in 1990 and 1996, respectively. He spent six months as a Researcher with the Division of Signal Processing, Lulea University of Technology, and then joined Bell Laboratories, Lucent Technologies, Swindon, U.K., in August 1997. His research interests include statistical parameter estimation and algorithms with applications in telecommunications. He primarily works with the physical layer of wireless communication systems. Currently, his focus is on transmit diversity and multiple antenna solutions for wide-band CDMA.

Paul Strauch (Member, IEEE) received the Dipl. Ing. degree in electrical engineering from the University of Applied Sciences, Kiel, Germany, in 1994, and the Ph.D. degree in electrical engineering from the University of Edinburgh, Edinburgh, U.K., in 1997. He was with the Signals and Systems Group at the Department of Electrical Engineering, University of Edinburgh. Since 1997, he has been with the Global Wireless Systems Research Group, Bell Laboratories, Lucent Technologies, Swindon, U.K. His main research interests are in digital communications, signal processing, and communication theory.

Jian-Jun Wu was born in Binzhou, Shandong Province, China. He received the B.Sc. and M.Sc. degrees from Nanjing University of Posts and Telecommunications, Nanjing, China, in 1982 and 1985, respectively, and the Ph.D. degree from King’s College, University of London, London, U.K., in 1996. He is currently with Bell Laboratories, Lucent Technologies, Swindon, U.K. His research interests include equalization, voice over EDGE, RLC/MAC, modulations, and coding techniques in mobile communication systems. He has published more than 40 research papers.

Costel Ilas, photograph and biography not available at the time of publication.

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Ping-Wen Ong (Member, IEEE) received the B.S. degree from National Taiwan University, Taipei, in 1984, and the M.S. and Ph.D. degrees from the Department of Computer Science, New York University, New York, in 1989 and 1992, respectively. He joined the R&D Organization, AT&T, Middletown, NJ, after graduation. In 1994, he joined Bell Labs Research, Holmdel, NJ. Currently, he is a Member of the High Speed Circuits and Systems Research Department, Bell Laboratories, Lucent Technologies, Holmdel, NJ. His research interests include digital signal processing, software radio, computer vision, graphical user interface, fast prototyping, navigation systems, and Internet/World Wide Web infrastructure. He has been involved in the GSM BS receiver enhancement and UMTS BS receiver prototype projects. Currently, he is working in the mobile Internet area.

Romain Baeriswyl, photograph and biography not available at the time of publication.

Frederic Battaglia studied physics at the Swiss Federal Institute of Technology, Lausanne, Switzerland (EPFL) from 1993 to 1995, and received the Dipl. Eng. degree from the same university in 1998. He joined the Communication Systems Department, EPFL, while pursuing his studies. He was also with Eurecom Institute, Sophia Antipolis, France, where he specialized in mobile communications. Since graduation, he has been with the Global Wireless Systems Research Group, Bell Laboratories, Lucent Technologies, Holmdel, NJ, specializing in DSP and FPGA programming for wireless applications.

Spyros Karageorgis, photograph and biography not available at the time of publication.

Ran-Hong Yan has been with Bell Laboratories, Lucent Technologies, since 1990. He was made a Distinguished Member of Technical Staff in 1994 and is currently Department Head for the Global Wireless Systems Research Department, Swindon, U.K. and Utrecht, The Netherlands. He also heads the Wireless Circuits and Systems Research Department, Holmdel, NJ. He has authored or coauthored more than 80 technical papers or conference papers, as well as 16 patents.

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