CMOS radio frequency circuits for short-range direct-conversion receivers

The research described in this thesis is focused on the design and implementation of radio frequency (RF) circuits for direct-conversion receivers. The main interest is in RF front-end circuits, which contain low-noise amplifiers, downconversion mixers, and quadrature local oscillator signal generation circuits. Three RF front-end circuits were fabricated in a short-channel CMOS process and experimental results are presented. A low-noise amplifier (LNA) is typically the first amplifying block in the receiver. A large number of LNAs have been reported in the literature. In this thesis, wideband LNA structures are of particular interest. The most common and relevant LNA topologies are analyzed in detail in the frequency domain and theoretical limitations are found. New LNA structures are presented and a comparison to the ones found in the literature is made. In this work, LNAs are implemented with downconversion mixers as RF front-ends. The designed mixers are based on the commonly used Gilbert cell. Different mixer implementation alternatives are presented and the design of the interface between the LNA and the downconversion mixer is discussed. In this work, the quadrature local oscillator signal is generated either by using frequency dividers or polyphase filters (PPF). Different possibilities for implementing frequency dividers are briefly described. Polyphase filters were already introduced by the 1970s and integrated circuit (IC) realizations to generate quadrature signals have been published since the mid-1990s. Although several publications where the performance of the PPFs has been studied either by theoretical calculations or simulations can be found in the literature, none of them covers all the relevant design parameters. In this thesis, the theory behind the PPFs is developed such that all the relevant design parameters needed in the practical circuit design have been calculated and presented with closed-form equations whenever possible. Although the main focus was on twoand three-stage PPFs, which are the most common ones encountered in practical ICs, the presented calculation methods can be extended to analyze the performance of multistage PPFs as well. The main application targets of the circuits presented in this thesis are the short-range wireless sensor system and ultrawideband (UWB). Sensors are capable of monitoring temperature, pressure, humidity, or acceleration, for example. The amount of transferred data is typically small and therefore a modest bit rate, less than 1 Mbps, is adequate. The sensor system applied in this thesis operates at 2.4-GHz ISM band (Industrial, Scientific, and Medical). Since the sensors must be able to operate independently for several years, extremely low power consumption is required. In sensor radios, the receiver current consumption is dominated by the blocks and elements operating at the RF. Therefore, the target was to develop circuits that can offer satisfactory performance with a current consumption level that is small compared to other receivers targeted for common cellular systems. On the other hand, there is a growing need for applications that can offer an extremely high data rate. UWB is one example of such a system. At the moment, it can offer data rates of up to 480 Mbps. There is a frequency spectrum allocated for UWB systems between 3.1 and 10.6 GHz. The UWB band is further divided into several narrower band groups (BG), each occupying a bandwidth of approximately 1.6 GHz. In this work, a direct-conversion RF front-end is designed for a dual-band UWB receiver, which operates in band groups BG1 and BG3, i.e. at 3.1 – 4.8 GHz and 6.3 – 7.9 GHz frequency areas, respectively. Clearly, an extremely wide bandwidth combined with a high operational frequency poses challenges for circuit design. The operational bandwidths and the interfaces between the circuit blocks need to be optimized to cover the wanted frequency areas. In addition, the wideband functionality should be achieved without using a number of on-chip inductors in order to minimize the die area, and yet the power consumption should be kept as small as possible. The characteristics of the two main target applications are quite different from each other with regard to power consumption, bandwidth, and operational frequency requirements. A common factor for both is their short, i.e. less than 10 meters, range. Although the circuits presented in this thesis are targeted on the two main applications mentioned above, they can be utilized in other kind of wireless communication systems as well. The performance of three experimental circuits was verified with measurements and the results are presented in this work. Two of them have been a part of a whole receiver including baseband amplifiers and filters and analog-to-digital converters. Experimental circuits were fabricated in a 0.13-µm CMOS process. In addition, this thesis includes design examples where new circuit ideas and implementation possibilities are introduced by using 0.13-µm and 65-nm CMOS processes. Furthermore, part of the theory presented in this thesis is validated with design examples in which actual IC component models are used.Tässä väitöskirjassa esitetty tutkimus keskittyy suoramuunnosvastaanottimen radiotaajuudella (radio frequency, RF) toimivien piirien suunnitteluun ja toteuttamiseen. Työ keskittyy vähäkohinaiseen vahvistimeen (low-noise amplifier, LNA), alassekoittajaan ja kvadratuurisen paikallisoskillaattorisignaalin tuottavaan piiriin. Työssä toteutettiin kolme RF-etupäätä erittäin kapean viivanleveyden CMOS-prosessilla, ja niiden kokeelliset tulokset esitetään. Vähäkohinainen vahvistin on yleensä ensimmäinen vahvistava lohko vastaanottimessa. Useita erilaisia vähäkohinaisia vahvistimia on esitetty kirjallisuudessa. Tämän työn kohteena ovat eritoten laajakaistaiset LNA-rakenteet. Tässä työssä analysoidaan taajuustasossa yleisimmät ja oleellisimmat LNA-topologiat. Lisäksi uusia LNA-rakenteita on esitetty tässä työssä ja niitä on verrattu muihin kirjallisuudessa esitettyihin piireihin. Tässä työssä LNA:t on toteutettu yhdessä alassekoittimen kanssa muodostaen RF-etupään. Työssä suunnitellut alassekoittimet perustuvat yleisesti käytettyyn Gilbertin soluun. Erilaisia sekoittajan suunnitteluvaihtoehtoja ja LNA:n ja alassekoittimen välisen rajapinnan toteutustapoja on esitetty. Tässä työssä kvadratuurinen paikallisoskillaattorisignaali on muodostettu joko käyttämällä taajuusjakajia tai monivaihesuodattimia. Erilaisia taajuusjakajia ja niiden toteutustapoja käsitellään yleisellä tasolla. Monivaihesuodatinta, joka on alunperin kehitetty jo 1970-luvulla, on käytetty integroiduissa piireissä kvadratuurisignaalin tuottamiseen 1990-luvun puolivälistä lähtien. Kirjallisuudesta löytyy lukuisia artikkeleita, joissa monivaihesuodattimen toimintaa on käsitelty teoreettisesti laskien ja simuloinnein. Kuitenkaan kaikkia sen suunnitteluparametreja ei tähän mennessä ole käsitelty. Tässä työssä monivaihesuodattimen teoriaa on kehitetty edelleen siten, että käytännön piirisuunnittelussa tarvittavat oleelliset parametrit on analysoitu ja suunnitteluyhtälöt on esitetty suljetussa muodossa aina kuin mahdollista. Vaikka työssä on keskitytty yleisimpiin eli kaksi- ja kolmiasteisiin monivaihesuodattimiin, on työssä esitetty menetelmät, joilla laskentaa voidaan jatkaa aina useampiasteisiin suodattimiin asti. Työssä esiteltyjen piirien pääkohteina ovat lyhyen kantaman sensoriradio ja erittäin laajakaistainen järjestelmä (ultrawideband, UWB). Sensoreilla voidaan tarkkailla esimerkiksi ympäristön lämpötilaa, kosteutta, painetta tai kiihtyvyyttä. Siirrettävän tiedon määrä on tyypillisesti vähäistä, jolloin pieni tiedonsiirtonopeus, alle 1 megabitti sekunnissa, on välttävä. Tämän työn kohteena oleva sensoriradiojärjestelmä toimii kapealla kaistalla 2,4 gigahertsin ISM-taajuusalueella (Industrial, Scientific, and Medical). Koska sensorien tavoitteena on toimia itsenäisesti ilman pariston vaihtoa useita vuosia, täytyy niiden kuluttaman virran olla erittäin vähäistä. Sensoriradiossa vastaanottimen tehonkulutuksen kannalta määräävässä asemassa ovat radiotaajuudella toimivat piirit. Tavoitteena oli tutkia ja kehittää piirirakenteita, joilla päästään tyydyttävään suorituskykyyn tehonkulutuksella, joka on vähäinen verrattuna muiden tavallisten langattomien tiedonsiirtojärjestelmien radiovastaanottimiin. Toisaalta viime aikoina on kasvanut tarvetta myös järjestelmille, jotka kykenevät tarjoamaan erittäin korkean tiedonsiirtonopeuden. UWB on esimerkki tällaisesta järjestelmästä. Tällä hetkellä se tarjoaa tiedonsiirtonopeuksia aina 480 megabittiin sekunnissa. UWB:lle on varattu taajuusalueita 3,1 ja 10,6 gigahertsin taajuuksien välillä. Kyseinen kaista on edelleen jaettu pienempiin taajuusryhmiin (band group, BG), joiden kaistanleveys on noin 1,6 gigahertsiä. Tässä työssä on toteutettu RF-etupää radiovastaanottimeen, joka pystyy toimimaan BG1:llä ja BG3:lla eli taajuusalueilla 3,1 - 4,7 GHz ja 6,3 - 7,9 GHz. Erittäin suuri kaistanleveys yhdistettynä korkeaan toimintataajuuteen tekee radiotaajuuspiirien suunnittelusta haasteellista. Piirirakenteiden toimintakaistat ja piirien väliset rajapinnat tulee optimoida riittävän laajoiksi käyttämättä kuitenkaan liian montaa piille integroitua kelaa piirin pinta-alan minimoimiseksi, ja lisäksi piirit tulisi toteuttaa mahdollisimman alhaisella tehonkulutuksella. Työssä esiteltyjen piirien kaksi pääkohdetta ovat hyvin erityyppisiä, mitä tulee tehonkulutus-, kaistanleveys- ja toimintataajuusvaatimuksiin. Yhteistä molemmille on lyhyt, alle 10 metrin kantama. Vaikka tässä työssä esitellyt piirit onkin kohdennettu kahteen pääsovelluskohteeseen, voidaan esitettyjä piirejä käyttää myös muiden tiedonsiirtojärjestelmien piirien suunnitteluun. Tässä työssä esitetään mittaustuloksineen yhteensä kolme kokeellista piiriä yllämainittuihin järjestelmiin. Kaksi ensimmäistä kokeellista piiriä muodostaa kokonaisen radiovastaanottimen yhdessä analogisten kantataajuusosien ja analogia-digitaali-muuntimien kanssa. Esitetyt kokeelliset piirit on toteutettu käyttäen 0,13 µm:n viivanleveyden CMOS-tekniikkaa. Näiden lisäksi työ pitää sisällään piirisuunnitteluesimerkkejä, joissa esitetään ideoita ja mahdollisuuksia käyttäen 0,13 µm:n ja 65 nm:n viivanleveyden omaavia CMOS-tekniikoita. Lisäksi piirisuunnitteluesimerkein havainnollistetaan työssä esitetyn teorian paikkansapitävyyttä käyttämällä oikeita komponenttimalleja.reviewe

Receiver Front-Ends in CMOS with Ultra-Low Power Consumption

Historically, research on radio communication has focused on improving range and data rate. In the last decade, however, there has been an increasing demand for low power and low cost radios that can provide connectivity with small devices around us. They should be able to offer basic connectivity with a power consumption low enough to function extended periods of time on a single battery charge, or even energy scavenged from the surroundings. This work is focused on the design of ultra-low power receiver front-ends intended for a receiver operating in the 2.4GHz ISM band, having an active power consumption of 1mW and chip area of 1mm². Low power consumption and small size make it hard to achieve good sensitivity and tolerance to interference. This thesis starts with an introduction to the overall receiver specifications, low power radio and radio standards, front-end and LO generation architectures and building blocks, followed by the four included papers. Paper I demonstrates an inductorless front-end operating at 915MHz, including a frequency divider for quadrature LO generation. An LO generator operating at 2.4GHz is shown in Paper II, enabling a front-end operating above 2GHz. Papers III and IV contain circuits with combined front-end and LO generator operating at or above the full 2.45GHz target frequency. They use VCO and frequency divider topologies that offer efficient operation and low quadrature error. An efficient passive-mixer design with improved suppression of interference, enables an LNA-less design in Paper IV capable of operating without a SAW-filter

Ultra-low power receivers for wireless sensor networks

In wireless sensor network applications, low-power operation of the wireless receiver is critical. To address this need an ultra-low power Binary Frequency Shift Keying (BFSK) receiver using the super-regenerative architecture is developed. A prototype receiver is built and tested for operation in the 900 MHz ISM band. Lab measurements show power consumption as low as 244 μW with a sensitivity of -84 dBm while operating at 250 kbps. A second test chip designed to operate at 2.4 GHz improves on the previous design by adding full digital control and calibration. The 2.4 GHz receiver consumes 215 μW while operating at 250 kbps and shows a 12 dB improvement in sensitivity over the original design. The entire receiver has an energy consumption of only 0.175 nJ/b while operating at 2 Mbps

Analog baseband circuits for sensor systems

This thesis is composed of six publications and an overview of the research topic, which also summarizes the work. The research presented in this thesis focuses on research into analog baseband circuits for sensor systems. The research is divided into three different topics: the integration of analog baseband circuits into a radio receiver for sensor applications; the integration of an ΔΣ modulator A/D converter into a GSM/WCDMA radio receiver for mobile phones, and the integration of algorithmic A/D converters for a capacitive micro-accelerometer interface. All the circuits are implemented using deep sub-micron CMOS technologies. The work summarizes the design of different blocks for sensor systems. The research into integrated analog baseband circuits for a radio receiver focuses on a circuit structures with a very low power dissipation and that can be implemented using only standard CMOS technologies. The research into integrated ΔΣ modulator A/D converter design for a GSM/WCDMA radio receiver for mobile phones focuses on the implications for analog circuit design emerging from using a very deep sub-micron CMOS process. Finally, in the research into algorithmic A/D converters for a capacitive microaccelerometer interface, new ways of achieving a good performance with low power dissipation, while also minimizing the silicon area of the integrated A/D converter are introduced

Ultra Small Antenna and Low Power Receiver for Smart Dust Wireless Sensor Networks

Wireless Sensor Networks have the potential for profound impact on our daily lives. Smart Dust Wireless Sensor Networks (SDWSNs) are emerging members of the Wireless Sensor Network family with strict requirements on communication node sizes (1 cubic centimeter) and power consumption (< 2mW during short on-states). In addition, the large number of communication nodes needed in SDWSN require highly integrated solutions. This dissertation develops new design techniques for low-volume antennas and low-power receivers for SDWSN applications. In addition, it devises an antenna and low noise amplifier co-design methodology to increase the level of design integration, reduce receiver noise, and reduce the development cycle. This dissertation first establishes stringent principles for designing SDWSN electrically small antennas (ESAs). Based on these principles, a new ESA, the F-Inverted Compact Antenna (FICA), is designed at 916MHz. This FICA has a significant advantage in that it uses a small-size ground plane. The volume of this FICA (including the ground plane) is only 7% of other state-of-the-art ESAs, while its efficiency (48.53%) and gain (-1.38dBi) are comparable to antennas of much larger dimensions. A physics-based circuit model is developed for this FICA to assist system level design at the earliest stage, including optimization of the antenna performance. An antenna and low noise amplifier (LNA) co-design method is proposed and proven to be valid to design low power LNAs with the very low noise figure of only 1.5dB. To reduce receiver power consumption, this dissertation proposes a novel LNA active device and an input/ouput passive matching network optimization method. With this method, a power efficient high voltage gain cascode LNA was designed in a 0.13um CMOS process with only low quality factor inductors. This LNA has a 3.6dB noise figure, voltage gain of 24dB, input third intercept point (IIP3) of 3dBm, and power consumption of 1.5mW at 1.0V supply voltage. Its figure of merit, using the typical definition, is twice that of the best in the literature. A full low power receiver is developed with a sensitivity of -58dBm, chip area of 1.1mm2, and power consumption of 2.85mW

Design of a 2.4 Ghz BAW-Based CMOS Transmitter

In recent years, bulk acoustic wave resonators (BAW) in combination with RF circuits have shown a big potential in achieving the low-power consumption and miniaturization level required to address wireless sensor nodes (WSN) applications. A lot of work has been focused on the receiver side, by integrating BAW resonators with low noise amplifiers (LNA) and in frequency synthesis with the design of BAW-based local oscillators, most of them working at fixed frequency due to their limited tuning range. At the architectural level, this has forced the implementation of several single channel transceivers. This thesis aims at exploring the use of BAW resonators in the transmitter, proposing an architecture capable of taking full advantage of them. The main objective is to develop a transmitter for WSN multi-channel applications able to cover the whole 2.4 GHz ISM band and enable the compatibility with wide-spread standards like Bluetooth and Bluetooth Low Energy. Typical transmissions should thus range from low data rates (typically tens of kb/s) to medium data rates (1 Mb/s), with FSK and GFSK modulation schemes, should be centered on any of the channels provided by these standards and cover a maximum transmission range of some tens of meters. To achieve these targets and circumvent the limited tuning range of the BAW oscillator, an up-conversion transmitter using wide IF is used. The typical spurs problems related to this transmitter architecture are addressed by using a combined suppression based on SSB mixing and selective amplification. The latter is achieved by cointegration of a high efficiency power amplifier with BAW resonators, which allows performing spurs filtering while preserving the efficiency. In particular the selective amplifier is designed by including in the PA analysis the BAW resonator parameters, which allows integrating the BAW filter into the passive network loading the amplifier, participating in the drain voltage shaping. Finally, the frequency synthesis section uses a fractional division plus LC PLL filtering and further integer division to generate the IF signals and exploit the very-low BAW oscillator phase noise. The transmitter has been integrated in a 0.18 µm standard digital CMOS technology. It allows addressing the whole 80 MHz wide 2.4 GHz ISM band. The unmodulated RF frequency carrier demonstrates a very-low phase noise of –136 dBc/Hz at 1 MHz offset. The IF spurs are maintained lower than –48 dBc, satisfying the international regulations for output power up to 10 dBm without the use of any quadrature error compensation in the transmitter. This is achieved thanks to the rejection provided by the SSB mixer and the selective amplifier, which can reach drain efficiency of up to 24% with integrated inductances, including the insertion losses of the BAW filter. The transmitter consumes 35.3 mA at the maximum power of 5.4 dBm under 1.6 V (1.2 V for the PA), while transmitting a 1 Mb/s GFSK signal and complying with both Bluetooth and Bluetooth Low Energy relative and absolute spectrum requirements

Energy Aware RF Transceiver for Wireless Body Area Networks (WBAN)

Ph.DDOCTOR OF PHILOSOPH

Transceiver architectures and sub-mW fast frequency-hopping synthesizers for ultra-low power WSNs

Wireless sensor networks (WSN) have the potential to become the third wireless revolution after wireless voice networks in the 80s and wireless data networks in the late 90s. This revolution will finally connect together the physical world of the human and the virtual world of the electronic devices. Though in the recent years large progress in power consumption reduction has been made in the wireless arena in order to increase the battery life, this is still not enough to achieve a wide adoption of this technology. Indeed, while nowadays consumers are used to charge batteries in laptops, mobile phones and other high-tech products, this operation becomes infeasible when scaled up to large industrial, enterprise or home networks composed of thousands of wireless nodes. Wireless sensor networks come as a new way to connect electronic equipments reducing, in this way, the costs associated with the installation and maintenance of large wired networks. To accomplish this task, it is necessary to reduce the energy consumption of the wireless node to a point where energy harvesting becomes feasible and the node energy autonomy exceeds the life time of the wireless node itself. This thesis focuses on the radio design, which is the backbone of any wireless node. A common approach to radio design for WSNs is to start from a very simple radio (like an RFID) adding more functionalities up to the point in which the power budget is reached. In this way, the robustness of the wireless link is traded off for power reducing the range of applications that can draw benefit form a WSN. In this thesis, we propose a novel approach to the radio design for WSNs. We started from a proven architecture like Bluetooth, and progressively we removed all the functionalities that are not required for WSNs. The robustness of the wireless link is guaranteed by using a fast frequency hopping spread spectrum technique while the power budget is achieved by optimizing the radio architecture and the frequency hopping synthesizer Two different radio architectures and a novel fast frequency hopping synthesizer are proposed that cover the large space of applications for WSNs. The two architectures make use of the peculiarities of each scenario and, together with a novel fast frequency hopping synthesizer, proved that spread spectrum techniques can be used also in severely power constrained scenarios like WSNs. This solution opens a new window toward a radio design, which ultimately trades off flexibility, rather than robustness, for power consumption. In this way, we broadened the range of applications for WSNs to areas in which security and reliability of the communication link are mandatory

Design of a Dual Band Local Positioning System

This work presents a robust dual band local positioning system (LPS) working in the 2.4GHz and 5.8GHz industrial science medical (ISM) bands. Position measurement is based on the frequency-modulated continuous wave (FMCW) radar approach, which uses radio frequency (RF) chirp signals for propagation time and therefore distance measurements. Contrary to state of the art LPS, the presented system uses data from both bands to improve accuracy, precision and robustness. A complete system prototype is designed consisting of base stations and tags encapsulating most of the RF and analogue signal processing in custom integrated circuits. This design approach allows to reduce size and power consumption compared to a hybrid system using off-the-shelf components. Key components are implemented using concepts, which support operation in multiple frequency bands, namely, the receiver consisting of a low noise amplifier (LNA), mixer, frequency synthesizer with a wide band voltage-controlled oscillator (VCO) having broadband chirp generation capabilities and a dual band power amplifier. System imperfections occurring in FMCW radar systems are modelled. Effects neglected in literature such as compression, intermodulation, the influence of automatic gain control, blockers and spurious emissions are modeled. The results are used to derive a specification set for the circuit design. Position estimation from measured distances is done using an enhanced version of the grid search algorithm, which makes use of data from multiple frequency bands. The algorithm is designed to be easily and efficiently implemented in embedded systems. Measurements show a coverage range of the system of at least 245m. Ranging accuracy in an outdoor scenario can be as low as 8.2cm. Comparative dual band position measurements prove an effective outlier filtering in indoor and outdoor scenarios compared to single band results, yielding in a large gain of accuracy. Positioning accuracy in an indoor scenario with an area of 276m² can be improved from 1.27m at 2.4GHz and 1.86m at 5.8GHz to only 0.38m in the dual band case, corresponding to an improvement by at least a factor of 3.3. In a large outdoor scenario of 4.8 km², accuracy improves from 1.88m at 2.4GHz and 5.93m at 5.8GHz to 0.68m with dual band processing, which is a factor of at least 2.8.Die vorliegende Arbeit befasst sich mit dem Entwurf eines robusten lokalen Positionierungssystems (LPS), welches in den lizenzfreien Frequenzbereichen für industrielle, wissenschaftliche und medizinische Zwecke (industrial, scientific, medical, ISM) bei 2,4GHz und 5,8GHz arbeitet. Die Positionsbestimmung beruht auf dem Prinzip des frequenzmodulierten Dauerstrichradars (frequency modulated continuous wave, FMCW-Radar), welches hochfrequente Rampensignale für Laufzeitmessungen und damit Abstandsmessungen benutzt. Im Gegensatz zu aktuellen Arbeiten auf diesem Gebiet benutzt das vorgestellte System Daten aus beiden Frequenzbändern zur Erhöhung der Genauigkeit und Präzision sowie Verbesserung der Robustheit. Ein Prototyp des kompletten Systems bestehend aus Basisstationen und mobilen Stationen wurde entworfen. Fast die gesamte analoge hochfrequente Signalverarbeitungskette wurde als anwendungsspezifische integrierte Schaltung realisiert. Verglichen mit Systemen aus Standardkomponenten erlaubt dieser Ansatz die Miniaturisierung der Systemkomponenten und die Einsparung von Leistung. Schlüsselkomponenten wurden mit Konzepten für mehrbandige oder breitbandige Schaltungen entworfen. Dabei wurden Sender und Empfänger bestehend aus rauscharmem Verstärker, Mischer und Frequenzsynthesizer mit breitbandiger Frequenzrampenfunktion implementiert. Außerdem wurde ein Leistungsverstärker für die gleichzeitige Nutzung der beiden definierten Frequenzbänder entworfen. Um Spezifikationen für den Schaltungsentwurf zu erhalten, wurden in der Fachliteratur vernachlässigte Nichtidealitäten von FMCW-Radarsystemen modelliert. Dazu gehören Signalverzerrungen durch Kompression oder Intermodulation, der Einfluss der automatischen Verstärkungseinstellung sowie schmalbandige Störer und Nebenschwingungen. Die Ergebnisse der Modellierung wurden benutzt, um eine Spezifikation für den Schaltungsentwurf zu erhalten. Die Schätzung der Position aus gemessenen Abständen wurde über eine erweiterte Version des Gittersuchalgorithmus erreicht. Dieser nutzt die Abstandsmessdaten aus beiden Frequenzbändern. Der Algorithmus ist so entworfen, dass er effizient in einem eingebetteten System implementiert werden kann. Messungen zeigen eine maximale Reichweite des Systems von mindestens 245m. Die Genauigkeit von Abstandsmessungen im Freiland beträgt 8,2cm. Positionsmessungen wurden unter Verwendung beider Einzelbänder durchgeführt und mit den Ergebnissen des Zweiband-Gittersuchalgorithmus verglichen. Damit konnte eine starke Verbesserung der Positionsgenauigkeit erreicht werden. Die Genauigkeit in einem Innenraum mit einer Grundfläche von 276m² kann verbessert werden von 1,27m bei 2,4GHz und 1,86m bei 5,8GHz zu nur 0,38m im Zweibandverfahren. Das entspricht einer Verbesserung um einen Faktor von mindestens 3,3. In einem größeren Außenszenario mit einer Fläche von 4,8 km² verbessert sich die Genauigkeit um einen Faktor von mindestens 2,8 von 1,88m bei 2,4GHz und 5,93m bei 5,8GHz auf 0,68m bei Nutzung von Daten aus beiden Frequenzbändern