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Spread spectrum

Spread spectrum is a class of techniques used in communications wherein a signal is deliberately spread across a significantly wider than that required to transmit the original , thereby enhancing to , , and while enabling multiple users to share the same frequency band. This approach contrasts with transmission by distributing the signal energy over a broad spectrum, often using pseudo-random codes or frequency shifts, which allows the receiver to despread the signal using synchronized codes for extraction. The core advantage lies in the processing gain, defined as the ratio of the spread to the data , which provides robustness against and deliberate disruption. The origins of spread spectrum trace back to early 20th-century concepts, but a pivotal development occurred during when actress and composer patented a frequency-hopping system in to secure radio-guided torpedoes against by rapidly switching frequencies in a synchronized manner between transmitter and receiver. Although initially overlooked by the U.S. Navy, this invention laid foundational principles for modern spread spectrum applications, with broader techniques evolving through military research in the and , including direct-sequence methods explored by the U.S. Department of Defense for secure communications. Regulatory advancements, such as the U.S. Federal Communications Commission's 1985 rules permitting unlicensed spread spectrum use in the ISM bands, spurred civilian adoption. Key variants include direct-sequence spread spectrum (DSSS), which multiplies the data signal with a high-rate pseudo-noise code to spread it across the ; frequency-hopping spread spectrum (FHSS), which rapidly switches the carrier frequency according to a pseudorandom sequence; and hybrid forms like time-hopping or modulation. These techniques offer low probability of intercept (LPI) for covert operations, anti-jam capabilities through signal dispersion, and support for (CDMA), allowing simultaneous transmissions without interference. Spread spectrum underpins numerous modern technologies, including the (GPS) for precise navigation via pseudorandom codes, cellular networks employing CDMA for efficient spectrum use, and short-range devices like (using DSSS in early standards such as ) and (using FHSS) for interference-resistant wireless connectivity. In military contexts, it enables secure, jam-resistant tactical radios, while commercial applications extend to wireless sensor networks and anti-collision systems in RFID. Ongoing research focuses on integrating spread spectrum with emerging paradigms like and beyond, including networks as of , for enhanced capacity and in dense environments.

Fundamentals

Definition and Principles

Spread spectrum is a wireless communication technique that intentionally spreads the transmitted signal across a significantly wider than the minimum required for the rate, typically using pseudo-random (PN) sequences to modulate the and achieve a low power that resembles . This spreading process allows the signal to occupy a much larger band, enhancing by making it difficult for unintended receivers to detect or intercept without knowledge of the PN . The core idea, originating in the amid efforts to secure , leverages transmission to provide robustness against various challenges in the radio environment. At the heart of spread spectrum principles is the concept of processing , defined as the ratio of the spread B_{ss} to the R_b, mathematically expressed as G_p = \frac{B_{ss}}{R_b}. This quantifies the system's ability to suppress , as the receiver despreads the signal using the synchronized PN sequence, concentrating the energy back into the original narrowband while noise and remain spread out, effectively improving the signal-to-noise ratio by a factor of G_p. Resistance to arises from this wideband approach, where the low per frequency bin makes the signal less susceptible to or multipath , as the energy is distributed rather than concentrated. Additionally, spread spectrum enables multiple access capabilities, such as (), where multiple users share the same using orthogonal PN codes to distinguish signals without mutual . In contrast to narrowband systems, which transmit at the minimum dictated by the to maximize and , spread spectrum deliberately expands the to mimic , thereby reducing detectability and mitigating effects like selective that plague concentrated transmissions. This intentional over-expansion trades for enhanced security, anti-jamming, and coexistence with other signals, forming the foundational advantage of the technique across various implementations.

Key Concepts

In spread spectrum systems, a represents the smallest unit of the signal, consisting of a single in the pseudonoise () with duration T_c, where the is defined as the , R_c = [1](/page/1) / T_c, determining the at which these are generated. The is significantly higher than the data R_b = [1](/page/1) / T_b, where T_b is the duration, allowing multiple per information to achieve the spreading effect. Spreading occurs by multiplying the baseband information signal b(t) with a high-rate PN code c(t), producing a modulated signal m(t) = b(t) \cdot c(t) that occupies a much wider than the original signal. At the receiver, despreading reverses this process: the incoming signal is multiplied by a synchronized of the PN code, collapsing the back to that of the original data since c^2(t) = 1 for binary codes, thereby recovering b(t) while rejecting outside the despread . Pseudo-noise (PN) sequences are codes designed to mimic random , exhibiting key properties that enable effective spreading. The balance property ensures that the number of +1s and -1s in each differs by at most one, providing near-equal . The run-length property dictates that runs of identical bits follow a specific : half are of length one, one-quarter of length two, one-eighth of length three, and so on, as long as these fractions represent meaningful numbers of runs, promoting uniformity. is another critical property, where the sequence correlates ideally with itself—yielding a peak value equal to the sequence length N at zero shift and -1 for other shifts—resulting in noise-like behavior that enhances rejection. The jamming margin quantifies a spread spectrum system's resilience to intentional interference, calculated as M_j = G_p - (E_b / N_0)_{\min} - L, where G_p is the processing gain, (E_b / N_0)_{\min} is the minimum required signal-to-noise ratio for reliable demodulation, and L accounts for implementation losses, all in decibels. This margin indicates the maximum tolerable jamming power relative to the signal power while maintaining performance, with higher values derived from greater processing gain providing superior anti-jam capability. The expansion factor, often denoted as G_p = T_b / T_c = R_c / R_b, measures the ratio of the spread signal to the original data , directly equating to the number of chips per bit and serving as the processing gain. This expansion distributes the signal's total power over a wider range, reducing the power (PSD) to levels below the ambient , which improves by lowering detectability and enhances robustness against .

History

Early Inventions

The origins of spread spectrum techniques trace back to the early , with initial concepts focused on enhancing communication secrecy through bandwidth manipulation. In 1909, German radio pioneer Jonathan Zenneck proposed varying transmission wavelengths to evade interception in , an idea applied by the Company in early systems. Building on this, a 1920 U.S. patent by engineers Otto B. Blackwell, De Loss K. Martin, and Gilbert S. Vernam (granted in 1926 as U.S. Patent 1,598,673) described a secrecy system using random frequency shifts controlled by perforated telegraph tape. Similarly, Harvard physicist Emory-Leon Chaffee filed for a 1922 patent (granted 1927 as U.S. Patent 1,642,663) on erratically wobbling carrier frequencies to obscure radiocommunications. In 1929, Dutch inventor Willem Broertjes patented (U.S. Patent 1,869,959, granted 1932) a method for randomly varying frequencies to prevent . These pre-World War II inventions laid foundational ideas for spreading signals across frequencies, though they were not fully implemented as modern spread spectrum systems. The first practical method emerged during amid urgent military needs. In 1942, actress and composer received U.S. Patent 2,292,387 for a "Secret Communication System" designed to guide radio-controlled torpedoes without interference. Their invention employed frequency hopping across 88 channels, synchronized using a piano-roll mechanism analogous to technology, ensuring the transmitter and receiver shifted frequencies in unison. This approach, developed in response to observed jamming of Allied naval communications by forces, aimed to counter interference by rendering the signal unpredictable and difficult to detect or disrupt. The unpredictability provided secrecy, as an adversary would struggle to jam a signal rapidly changing across a wide , protecting torpedo guidance from enemy detection. Lamarr and Antheil donated the patent to the U.S. Navy, though it saw limited immediate use due to technological constraints of the era. Post-war, spread spectrum techniques remained shrouded in military secrecy, with developments classified to maintain strategic advantages in secure communications. By the , partial and independent reinvention by government-funded researchers sparked broader recognition, drawing academic interest in applications beyond wartime resistance. This era marked the transition from isolated inventions to systematic exploration, influencing subsequent military and civilian advancements.

Modern Developments

In the , spread spectrum technology advanced significantly through research on (DSSS), with Robert A. Scholtz and collaborators developing key (PN) codes that enabled robust signal spreading for interference resistance and secure transmission. These PN sequences, formalized in Scholtz's early work on correlation properties, laid the groundwork for modern DSSS implementations by allowing signals to be modulated with noise-like codes that could be synchronized at the receiver. Concurrently, the U.S. military adopted spread spectrum systems for secure communications, deploying electronic versions that handled all classified U.S. transmissions during the , marking a shift from theoretical concepts to practical anti-jamming applications in defense. During the 1970s and , commercialization efforts accelerated with the founding of in 1985 by and Andrew J. Viterbi, who pioneered (CDMA) as a DSSS-based multiple-access scheme for cellular networks. Qualcomm's innovations addressed capacity limitations in analog systems, culminating in a public demonstration of a digital CDMA cellular radio on November 7, 1989, which showcased spread spectrum's potential for efficient spectrum reuse. This led to the standardization of CDMA in the IS-95 specification in 1993 by the , enabling widespread deployment in second-generation () mobile networks and transitioning spread spectrum from military secrecy to civilian telecommunications infrastructure. A pivotal regulatory occurred in with the U.S. Federal Communications Commission's allocation of unlicensed Industrial, Scientific, and Medical () bands (902–928 MHz, 2.4–2.4835 GHz, and 5.725–5.850 GHz) for spread spectrum operations under Part 15 rules, fostering civilian innovation by allowing low-power, interference-tolerant devices without licenses. This enabled the integration of spread spectrum into consumer standards during the 1990s, including direct-sequence variants in IEEE 802.11b (ratified 1999) for 2.4 GHz wireless LANs and (FHSS) in (released 1999) for short-range personal area networks, driving explosive growth in unlicensed wireless ecosystems. Key educational resources, such as the 1989 second edition of by Horowitz and Winfield Hill, further disseminated practical insights into spread spectrum circuits within its high-frequency discussions, aiding engineers in implementing these techniques. From the 2000s onward, spread spectrum evolved with broader adoption in wireless standards and recent enhancements for emerging networks. Hybrid spreading approaches, combining DSSS with (OFDM), are being explored in research for New Radio (NR) to improve uplink coverage in (NB-IoT) and enhanced machine-type communication, potentially boosting reliability in dense deployments. Similar hybrid techniques are under exploration for to support frequencies and ultra-reliable low-latency communications. In the , research has emphasized anti-jamming applications for , leveraging adaptive spread spectrum to counter dynamic threats in ecosystems, with frequency-hopping and DSSS variants demonstrating up to 20–30 dB jamming resistance in low-power sensor networks.

Techniques

Frequency-Hopping Spread Spectrum

Frequency-hopping spread spectrum (FHSS) operates by rapidly switching the carrier frequency among a set of predefined channels according to a pseudorandom noise (PN) sequence, thereby spreading the signal energy across a wider bandwidth than required for the data alone. The PN sequence determines the hopping pattern, ensuring that the transmitter and receiver follow the same sequence of frequencies to maintain communication. The hop rate, defined as the number of frequency changes per second, and the dwell time, the duration spent on each frequency before hopping, are key parameters that control the spreading effect and system performance. Synchronization in FHSS involves two primary phases: acquisition for initial alignment of the hop timing and , and tracking to maintain precise during transmission. Acquisition can employ sequential methods, where the scans frequencies one by one until the correct is detected, or methods using multiple correlators to check several frequencies simultaneously for faster lock-in. Tracking then refines the timing using loops to adjust for drifts in the PN sequence phase. The hop T_h, the time per frequency , relates to the bit T_b and the number of hops per bit N_h by the equation: T_h = \frac{T_b}{N_h} This relationship determines how frequently the signal hops relative to the data rate, influencing both interference rejection and implementation feasibility. FHSS systems are categorized as slow-hopping, with one or a few hops per data bit (N_h \leq 1), or fast-hopping, with multiple hops per bit (N_h > 1), offering distinct practical advantages. Slow hopping simplifies hardware but provides moderate jamming resistance, while fast hopping enhances robustness against interference by distributing energy across more frequencies per bit. A key benefit is resistance to partial-band jamming, where an adversary targets only a fraction of the spectrum; since hops visit all channels pseudorandomly, the probability of jamming a given hop is low, allowing the system to avoid affected bands entirely in many cases. A practical example is , which employs FHSS in the 2.4 GHz ISM band using 79 one-MHz channels and a hop rate of 1600 hops per second, achieved by changing frequencies every 625 μs time slot. This configuration yields a spectral occupancy where the signal intermittently occupies the full 79 MHz , with the fraction of time any single channel is used given by $1/N, where N = 79 is the number of channels, promoting efficient spectrum sharing. Despite these strengths, FHSS introduces drawbacks, particularly the higher complexity required for frequency synthesizers to achieve rapid, precise hopping with minimal between frequencies. This demands advanced phase-locked loops or direct digital synthesis capable of switching in microseconds, increasing power consumption and design challenges compared to fixed-frequency systems.

Direct-Sequence Spread Spectrum

Direct-sequence spread spectrum (DSSS) is a technique in which the original signal is multiplied by a high-rate pseudo-noise () to spread the signal across a wider . This spreading is typically achieved using binary phase-shift keying (BPSK) , where the bits are XORed (modulo-2 added) with the sequence, effectively flipping the phase of the carrier for each of the . The operates at a much higher than the , with the sequence length (number of chips per data bit) determining the spreading factor; for example, longer sequences provide greater expansion. At the receiver, despreading recovers the original data by correlating the received spread signal with a locally generated replica of the PN code, using either a or an active correlator. The aligns the code phases, compressing the signal back to its original while the remains spread, resulting in an output (SNR) improvement equal to the processing gain G_p, defined as the ratio of the chip rate to the rate. This gain enhances resistance to and , as the despreading process suppresses disturbances by approximately G_p. PN codes in DSSS are selected for their autocorrelation properties, which are ideal for a single-user : the autocorrelation R(\tau) is approximately N (the code ) when the time \tau = 0, and -1 otherwise, enabling sharp peaks and low . For multi-user environments, such as (CDMA), Gold codes are commonly used due to their balanced autocorrelation and low between different users' codes, allowing multiple signals to share the same with minimal . In CDMA systems, orthogonal codes (or near-orthogonal sets like Walsh codes combined with PN spreading) further improve user separation, though non-ideal cross-correlations can still cause multi-access . A key challenge in multi-user DSSS is the near-far problem, where a strong signal from a nearby transmitter overwhelms weaker signals from distant ones, degrading detection for the latter due to unequal received powers. This is mitigated through mechanisms, which dynamically adjust transmit powers to equalize received signal strengths at the , ensuring fair levels across users. An illustrative example of DSSS is the (GPS) coarse/acquisition (C/A) code, which uses a 1023-chip m-sequence generated at a chip rate of 1.023 MHz to spread the 50 bps navigation data, repeating every 1 millisecond. This configuration provides a processing gain of about 43 , enabling robust signal acquisition in noisy environments.

Other Variants

Time-hopping spread spectrum (THSS) is a where data symbols are transmitted using short pulses placed in pseudo-randomly selected time slots within a larger frame, enabling multiple access and interference mitigation in impulse-based systems. This method spreads the signal energy over time rather than frequency or code, making it particularly suitable for (UWB) communications where precise timing control allows coexistence with narrowband systems. Chirp spread spectrum (CSS) employs linear , where the carrier frequency sweeps continuously across a using up-chirps (increasing frequency) or down-chirps (decreasing frequency) to encode data symbols. The rate, defined as \mu = \frac{\Delta f}{T} where \Delta f is the () and T is the chirp duration, determines the sweep speed and impacts the signal's robustness to Doppler shifts and multipath . CSS achieves processing gain through of the received chirp with a replica, supporting long-range, low-power applications like () networks. Hybrid spread spectrum methods combine multiple techniques to leverage their strengths, such as (DS) with frequency-hopping (FH) in DS/FH systems, where a (PN) code modulates the within each hop to enhance and resistance in radios. These hybrids, including time-frequency hopping variants, allow flexible bandwidth allocation by varying hop rates and code lengths, improving performance in contested environments over single-method approaches. Emerging variants like spread spectrum utilize non-periodic, noise-like signals generated from chaotic dynamical systems to modulate data, offering enhanced security through unpredictable spreading sequences that resist and better than traditional periodic codes. Post-2010 research has focused on challenges and chaotic implementations, demonstrating improved bit error rates in low signal-to-noise environments via encoding schemes.
VariantBandwidth UsageComplexity Level
THSSUltra-wide (UWB, >500 MHz)Low (timing-based)
CSSWide (chirp-dependent, 100s kHz to MHz)Medium ( )
(DS/FH)Variable (hop + code combined)High (multi-layer )
Wide (noise-like, )High (chaotic generator and sync)

Applications

Telecommunications

Spread spectrum techniques form the backbone of several key commercial telecommunications standards, particularly in cellular networks where code-division multiple access (CDMA) enables efficient spectrum sharing. In 3G Universal Mobile Telecommunications System (UMTS), wideband CDMA (W-CDMA) utilizes direct-sequence spread spectrum (DSSS) to overlay multiple user signals within a 5 MHz carrier bandwidth, allowing simultaneous voice and data transmission while improving resistance to multipath fading and interference. This approach, standardized by 3GPP, supported peak data rates up to 384 kbps in early deployments and facilitated the transition from 2G GSM networks. For 4G, while Long-Term Evolution (LTE) shifted to orthogonal frequency-division multiple access (OFDMA) for downlink and single-carrier FDMA for uplink, CDMA-based systems like CDMA2000 evolved through enhancements such as EV-DO Revision A, achieving data rates up to 3.1 Mbps and serving as a bridge for CDMA operators toward LTE compatibility via evolved high-rate packet data (eHRPD) interworking. In 5G New Radio (NR), low-density parity-check (LDPC) codes replace turbo codes for channel coding on data channels, providing superior error correction for high-throughput scenarios, while elements of spread spectrum persist in random access preambles to enhance synchronization in dense networks. Wireless local area networks (WLANs) and short-range devices also leverage spread spectrum for robust operation in unlicensed bands. The IEEE 802.11b standard employs DSSS with complementary code keying (CCK) modulation to deliver data rates up to 11 Mbps across a 22 MHz channel in the 2.4 GHz band, enabling reliable connectivity in environments with moderate interference. Early telephones, operating under FCC Part 15 rules, adopted (FHSS) in the 900 MHz and 2.4 GHz bands to meet requirements for digital modulation and hopping across at least 75 channels, which permitted higher transmit power (up to 1 W ) while minimizing interference in shared spectrum. This FHSS implementation ensured clear voice quality over ranges of 100-300 meters indoors by rapidly switching frequencies to avoid interferers. The industrial, scientific, and medical (ISM) bands, especially the 2.4 GHz allocation, host unlicensed applications like Wi-Fi and Zigbee, where spread spectrum mitigates co-channel interference from diverse devices such as microwaves and Bluetooth. Wi-Fi in its early DSSS mode and Zigbee, based on IEEE 802.15.4, use DSSS with offset quadrature phase-shift keying (O-QPSK) across 16 channels in the 2.4-2.4835 GHz ISM band, spreading signals over 2 MHz to achieve processing gains of 9-15 dB for better coexistence. These techniques allow Zigbee networks to maintain low-power operation at 250 kbps while rejecting narrowband noise, supporting applications in home automation and sensor meshes. Spread spectrum's capacity advantages are evident in systems like cdmaOne (IS-95), where 1.25 MHz channels support up to 64 simultaneous users through orthogonal Walsh codes and a processing gain of approximately 21 dB, enabling three to six times higher user density compared to TDMA or FDMA equivalents in the same bandwidth. This multiplexing via unique spreading codes allows efficient reuse of spectrum, reducing the need for frequency planning in dense urban deployments. As of 2025, research proposals integrate massive with spread spectrum overlays, such as frequency hopping or DSSS, to enhance anti-jamming resilience and in bands, targeting peak rates exceeding 1 Tbps while supporting ultra-dense connectivity for integrated sensing and communication.

Military and Secure Communications

Spread spectrum techniques have been integral to since the mid-20th century, primarily due to their robustness against adversarial in contested environments. In anti- applications, these methods employ signals that distribute across a broad frequency , allowing receivers to correlate the desired signal while rejecting . This resistance stems from the processing gain achieved through despreading, where military systems typically target gains exceeding 20 dB to maintain link integrity under jamming conditions up to 40 dB above the signal level. For instance, (DSSS) systems can suppress tone jammers—narrowband continuous-wave interferers—by factors proportional to the chip rate, forcing adversaries to expend significantly more for effective disruption. A key advantage in military operations is the low probability of intercept (LPI) and low probability of detection (LPD) provided by spread spectrum's noise-like power spectral density (PSD), which blends the signal into background noise, complicating enemy detection and geolocation. (FHSS), a primary variant, rapidly switches carrier frequencies according to a pseudorandom sequence, further enhancing LPI by limiting dwell time on any single channel. The (Single Channel Ground and Airborne Radio System), a VHF tactical radio fielded by the U.S. Army in the , exemplifies this through its FHSS mode, hopping up to 100 times per second across 2,325 channels to achieve LPI/LPD while supporting encrypted voice and data at rates up to 16 kbps. In tactical scenarios, such as rapid environmental assessments, spread spectrum waveforms have demonstrated reliable LPI over 10-20 nautical miles with low transmit power (e.g., 1 W), minimizing emissions for covert operations. Secure modes in spread spectrum leverage encrypted pseudonoise (PN) sequences to protect hopping patterns and spreading codes, ensuring only authorized receivers can synchronize and demodulate. The protocol, developed for U.S. in the late , uses FHSS with time-of-day synchronized pseudorandom hopping across the UHF band (225-400 MHz), compatible with external devices like the KY-57 for securing air-to-air and air-to-ground links. By encrypting the PN sequence at the chip level, these systems prevent sequence reconstruction by adversaries, adding layers of (TRANSEC) beyond basic frequency agility. Historical deployments underscore spread spectrum's evolution in warfare. During the (1955-1975), early frequency hoppers and spread spectrum networks, such as the Wabash Independent Networks, were employed for resilient command-and-control communications, countering North Vietnamese jamming and interception attempts through distributed signal power and rapid hopping. This laid groundwork for modern systems like the (JTRS), a initiative from the early 2000s that integrates spread spectrum waveforms for LPI, anti-jam protection, and networking across 2 MHz to 2 GHz, supporting data rates over 5 Mbps in contested battlespaces. In the 2020s, spread spectrum continues to enable countermeasures in emerging threats, particularly for unmanned systems. Drone swarms in military operations rely on FHSS and DSSS for jam-resistant inter-drone and command links, allowing coordinated maneuvers under . For example, quantum random number generator (QRNG)-enhanced FHSS in UAV communications generates unpredictable hopping sequences, improving resistance to predictive while maintaining swarm cohesion over wide areas. These adaptations ensure scalable, secure networking for swarm tactics, where tone resistance allows sustained operations despite partial-band interference. Spread spectrum techniques play a pivotal role in global satellite systems (GNSS), enabling precise signal acquisition and ranging in challenging environments. The (GPS), developed by the , primarily employs (DSSS) modulation for its civilian signals. The coarse/acquisition (C/A) code, a (PRN) sequence generated at a chip rate of 1.023 MHz, modulates the L1 carrier frequency of 1575.42 MHz to spread the signal across a wider , facilitating robust and interference resistance. This DSSS structure allows receivers to despread the signal using the same PRN code, recovering the navigation message while rejecting noise and multipath effects. For applications, the precision (P) code, encrypted as the Y-code, operates at a higher chip rate of 10.23 MHz on both L1 and L2 frequencies, providing enhanced accuracy for authorized users through finer time resolution and anti-jamming capabilities. Signal acquisition in GPS relies on delay-lock loops (DLLs) to achieve synchronization, where the receiver correlates the incoming spread-spectrum signal with locally generated replicas of the or P(Y) code. The DLL maintains alignment by adjusting the to minimize the between early, , and late correlator outputs, enabling precise estimation of the . This yields pseudorange measurements, which represent the apparent distance from the to the receiver, incorporating clock biases and atmospheric delays; these measurements form the basis for to compute position. In practice, the spread-spectrum process ensures high , allowing acquisition even at low signal-to-noise ratios typical of signals attenuated by distance and . Other GNSS constellations integrate variant spread-spectrum approaches to complement GPS. The Russian system traditionally uses (FDMA) with or BPSK for civil signals, assigning unique carrier frequencies to each satellite within the L1 and bands (centered around 1602 MHz and 1246 MHz, respectively), which provides frequency diversity to mitigate interference. Modern GLONASS-K satellites introduce (CDMA) signals using for enhanced with GPS through shared spreading codes. The European Galileo system employs a hybrid spreading modulation known as Alternate Binary Offset Carrier (AltBOC) for its E5 signal at 1191.795 MHz, which combines four components—data and pilot channels on in-phase and quadrature carriers—into a constant-envelope spanning 51.15 MHz . This AltBOC structure optimizes power efficiency and multipath resistance by leveraging subcarrier offsets for better spectral separation. Enhancements to spread-spectrum GNSS signals address security and environmental challenges. Anti-spoofing measures in GPS include via encrypted codes, such as the P(Y)-code's (SAASM), which verifies by correlating against known patterns, preventing deception by counterfeit transmissions. For indoor positioning, (UWB) systems utilize time-hopping spread spectrum (THSS), where short pulses are transmitted in pseudorandom time slots across a multi-gigahertz (typically 3.1–10.6 GHz), enabling centimeter-level accuracy in non-line-of-sight conditions through precise time-of-arrival measurements. These techniques extend GNSS principles to enclosed spaces, where traditional signals are unavailable. Accuracy in spread-spectrum is bolstered by inherent signal properties that counter errors. Multipath leverages the sharp peak of spreading codes, such as the GPS code, where correlators discriminate direct signals from delayed reflections; narrow-correlator spacing (e.g., 0.1 chip) in DLLs further suppresses multipath-induced biases by rejecting off-peak correlations, reducing errors to sub-meter levels in urban settings. Ionospheric delay compensation exploits multi-frequency transmissions, as delays are inversely proportional to the square of the carrier frequency; dual-frequency receivers (L1 and L2) compute an iono-free [linear combination](/page/linear combination) of pseudoranges, eliminating up to 90% of first-order ionospheric effects without external models. In Galileo, the AltBOC E5 signal's wide further aids in modeling higher-order ionospheric distortions for precise positioning.

Advantages and Limitations

Benefits

Spread spectrum techniques offer significant rejection, enabling reliable operation in noisy environments through the achieved by spreading the signal over a wider . This , typically quantified as the of the spread to the data rate, provides 10-30 dB of jamming resistance, allowing the system to maintain performance even when interferers overpower the signal by that margin. In multipath environments, spread spectrum systems, particularly direct-sequence variants, exhibit strong resistance by exploiting delayed signal paths for constructive combining. The correlates multiple multipath components using the known spreading code, yielding diversity gain that improves and mitigates effects. A key advantage is support for multiple access without traditional frequency or time division, as in (CDMA) where orthogonal or pseudo-random codes enable simultaneous transmissions from multiple users over the same band. This allows efficient sharing of spectrum resources, accommodating more users per unit compared to . Security is enhanced by low probability of intercept (LPI) properties, as the spread signal's low power resembles , making it difficult for unauthorized receivers to detect or intercept without the spreading . This inherent anti-eavesdropping feature, combined with resistance to , suits secure communications. Spread promotes spectrum efficiency in unlicensed bands by enabling low-power operations that minimize while reusing frequencies across devices. This approach supports battery-powered applications, such as sensors, by transmitting at reduced power levels without compromising range or reliability.

Challenges and Drawbacks

Spread spectrum techniques, while offering robustness against , introduce significant in and requirements. Generating pseudonoise (PN) codes and maintaining demand specialized circuitry, such as correlators and code generators, which increase system design challenges compared to systems. acquisition, in particular, can be time-consuming due to the need to search over a large phase for long spreading sequences, leading to delays in initial link establishment. In (CDMA) systems based on (DSSS), the near-far effect poses a critical limitation, where signals from nearby transmitters overpower those from distant ones at the receiver, degrading overall performance. This power imbalance requires sophisticated mechanisms to adjust transmit powers dynamically, mitigating the issue but adding further complexity to the system. Spread spectrum signals inherently occupy a much wider than the information they carry, resulting in lower and potential conflicts with regulatory spectrum allocation constraints. This bandwidth expansion, essential for spreading gain, can limit the number of concurrent users or applications in bandwidth-scarce environments. Self-interference arises in multi-user or dense network scenarios due to imperfect properties of spreading codes, treating other users' signals as and reducing capacity. In (FHSS) networks, simultaneous hops can exacerbate this, particularly in multihop topologies. Implementation of spread spectrum systems often incurs higher costs due to the need for precise analog components in early designs or advanced processors in modern variants, making them less economical for low-power or consumer applications. Additionally, while digital implementations alleviate some analog precision issues, they remain vulnerable to that overwhelms the entire spread , unlike systems.

Mathematical Foundations

Spreading Sequences and Codes

Spreading sequences, also known as pseudonoise () codes, are or polyphase sequences used to spread the signal in spread spectrum systems. These sequences are generated to exhibit randomness-like properties while being deterministic and periodic, enabling effective signal modulation and despreading at the . Linear feedback shift registers (LFSRs) are a primary mechanism for generating such sequences, particularly maximal-length sequences (m-sequences), which achieve the longest possible period of $2^n - 1 for an n-stage register when driven by a primitive over . For instance, the x^4 + x^3 + 1 = 0 corresponds to a primitive polynomial that produces an m-sequence of length 15 when implemented in an LFSR with feedback taps at positions 4 and 3. Code families extend m-sequences to support multiple users in systems like (CDMA) by providing sets with low . M-sequences form the basis, with their period $2^n - 1 ensuring maximal length and desirable statistical properties. Gold codes, constructed by modulo-2 addition of two m-sequences from preferred pairs of primitive s of degree n, yield $2^n + 1 sequences with three-valued magnitudes bounded by $2^{(n+2)/2} + 1 for even n, making them suitable for multiuser environments. Kasami codes offer even lower , with small sets of size $2^{n/2} derived from m-sequences of periods $2^n - 1 and $2^{n/2} - 1, achieving values at most $2^{n/2 + 1}. Generation algorithms prioritize balanced codes to approximate ideal randomness; for example, a 7-chip m-sequence generated by an LFSR with x^3 + x^2 + 1 = 0 is 1110010, containing four 1s and three 0s. Key properties of these codes include , where the number of 1s and 0s in a period differs by at most 1 (e.g., $2^{n-1} ones and $2^{n-1} - 1 zeros for m-sequences), ensuring uniform power distribution. They also exhibit two-level , with in-phase value $2^n - 1 and out-of-phase value -1 for m-sequences, ideal for . For aperiodic applications like , the merit M_f = \frac{2E^2}{\sum_{k=1}^{N-1} R^2(k)} (where E is the and R(k) the aperiodic autocorrelation) quantifies sidelobe suppression, with m-sequences achieving an asymptotic merit factor of approximately 3. Security aspects stem from the sequences' long periods and linear , resisting attacks unless the LFSR taps are known; cryptographically strong variants, such as those based on nonlinear feedback, enhance resistance to correlation-based sequence estimation in adversarial settings.

Signal Processing and Correlation

In spread spectrum receivers, signal processing relies heavily on correlation techniques to despread the received signal and detect the information bits, exploiting the orthogonality or low cross-similarity of spreading codes to suppress and . The core operation involves computing the between the incoming signal and a locally generated of the spreading , which compresses the spread back to the original data rate while enhancing the (SNR). This process is fundamental to (DSSS) systems, where the receiver aligns the code phase before . The autocorrelation function quantifies the similarity of the spreading code with a time-shifted version of itself, serving as a key metric for code synchronization and despreading performance. For a binary spreading code \{c_i\} of length N, the normalized autocorrelation is given by R(\tau) = \frac{1}{N} \sum_{i=0}^{N-1} c_i c_{i+\tau}, where \tau is the time shift in chip intervals and indices are modulo N for periodic correlation. Ideal pseudonoise (PN) sequences exhibit an autocorrelation peak of 1 at \tau = 0 and sidelobes approaching -1/N for \tau \neq 0, enabling sharp detection thresholds and minimal self-interference after despreading. This property arises from the balanced nature of PN codes, ensuring near-white noise-like behavior in the time domain. In multi-user scenarios, such as code-division multiple access (CDMA), cross-correlation between different users' codes determines the level of inter-user interference after despreading. The cross-correlation function C_{xy}(\tau) between two distinct codes x and y is defined analogously to autocorrelation, and low values are essential to minimize multiple-access interference (MAI). The Welch bound provides a theoretical lower limit on the maximum possible cross-correlation magnitude for a set of K codes of length N, stated as \max |C_{xy}(\tau)| \geq \sqrt{\frac{K-1}{K(N-1)}}, achieved when codes are equi-correlated, guiding the design of code families for practical systems. Sequences meeting or approaching this bound, like Gold codes, support higher user capacities with acceptable interference levels. Matched filtering implements the correlation process optimally in additive white Gaussian noise (AWGN), maximizing the SNR at the decision instant. The filter's impulse response is the time-reversed conjugate of the spreading code waveform, h(t) = c(-t), producing an output peak proportional to the code energy when the input aligns with the code. For a DSSS signal with energy E, the peak SNR after matched filtering is $2E/N_0, where N_0 is the noise power spectral density, independent of the spreading factor but enhanced by despreading gain. This structure rejects out-of-phase components, yielding a narrow mainlobe for precise timing. Code acquisition, the initial phase alignment step, often employs search strategies, where the receiver correlates the incoming signal against locally shifted code replicas until the peak exceeds a . The complexity of exhaustive search is O(N^2), as it requires testing up to N phase shifts with over N each, though parallel or partial searches can reduce this in hardware-constrained systems. Once acquired, fine tracking maintains alignment using a (DLL), which compares early and late code correlations to adjust phase dynamically. The DLL's steady-state tracking error, or , is typically on the order of a of the duration, bounded by \sigma_\tau \approx \frac{1}{\rho \sqrt{2 B_L T}}, where \rho is the carrier-to-noise , B_L the , and T the time, ensuring robust operation under moderate dynamics. Performance in AWGN channels is characterized by the (BER), which benefits from the processing gain G_p = N of the spreading code. For binary (BPSK) modulated DSSS, the BER is P_b = Q\left(\sqrt{\frac{2 G_p E_b}{N_0}}\right), where E_b is the per bit and Q(\cdot) is the ; this reflects the effective SNR boost by G_p, allowing reliable communication at low pre-despreading SNR. This metric underscores the anti-jam resilience, with G_p typically 20–60 in practical systems.

References

  1. [1]
    Spread Spectrum Communication Techniques | www.dau.edu
    A means of communicating by purposely spreading the spectrum (frequency extent or bandwidth) of the communication signal well beyond the bandwidth of the ...Missing: definition | Show results with:definition
  2. [2]
    [PDF] Federal Communications Commission Record
    BACKGROUND. 2. Spread spectrum communications systems use special. modulation techniques that spread the energy of the sig- nal being transmitted over a very ...
  3. [3]
    [DOC] gsfc-std-9001-cancelled.doc - NASA Standards
    Spread Spectrum (SS) is a family of communications techniques in which the RF bandwidth used to transmit a given data signal is much wider (typically several ...
  4. [4]
    Actress/Inventor Hedy Lamarr – and How Far Wireless ... - IEEE SA
    Jun 23, 2023 · ... spread spectrum technology. Lamarr and Antheil's invention, named in 1942 in US patent 2,292,387A as “Secret Communication System,” aimed to ...
  5. [5]
    Further Notes and Anecdotes on Spread-Spectrum Origins
    This sequel to R. A. Scholtz's monograph of May 1982, in this TRANSACTIONS, adds to the early history of spread-spectrum communications from circa 1900 ...
  6. [6]
    [PDF] Direct Sequence Spread Spectrum - DTIC
    Jan 18, 2001 · The most well-known and widely employed spread spectrum modulation technique, direct sequence makes use of noise-like sequences in order to ...
  7. [7]
    [PDF] The application of spread-spectrum communications to real tactical ...
    Spread-spectrum techniques offer such features as interference rejection, anti-jam capability and lowdensity power spectra for covert operations: field tests of ...
  8. [8]
    Spread Spectrum Communications - 525.783 | Hopkins EP Online
    This course presents an analysis of the performance and design of spread-spectrum communication systems. Both direct-sequence and frequency-hopping systems ...<|control11|><|separator|>
  9. [9]
    [PDF] Fundamentals of spread-spectrum techniques - Elsevier
    The spread-spectrum concept has developed from the principle of Shannon theorem. If data is transmitted at a rate of Rb over a channel occupying a bandwidth ...
  10. [10]
    An Introduction to Spread-Spectrum Communications
    Feb 18, 2003 · Applied at the LO stage, FHSS PRN codes force the carrier to change or "hop" according to the pseudo-random sequence. If the PRN acts as an on/ ...An Introduction To... · Spread Spectrum Allows Cdma · Different Modulation...
  11. [11]
  12. [12]
    Spread Spectrum Technology & Communications - EE Times
    All spread spectrum systems have a threshold or tolerance level of interference beyond which useful communication ceases. This tolerance or threshold is related ...
  13. [13]
    [PDF] Spread Spectrum Signals for Digital Communication
    Dec 15, 2015 · Definition: Spread spectrum is a means of transmission in which the signal occupies a bandwidth in excess of the minimum necessary to send ...
  14. [14]
    [PDF] unit v- spread spectrum modulation - Sathyabama
    The ratio J/P is termed jamming margin. Jamming Margin is expressed in decibels as. jamming margin dB = Processing gain dB − 10 log10. Eb. N0 min. Where. Eb. N0.Missing: expansion | Show results with:expansion
  15. [15]
    Random Paths to Frequency Hopping | American Scientist
    Most of the research into spread-spectrum transmission took place in anticipation of war, or during war itself.
  16. [16]
    US2292387A - Secret communication system - Google Patents
    This invention relates broadly to secret communication systems involving the use of carrier waves of different frequencies, and is especially useful in the ...
  17. [17]
    Hedy Lamarr and George Antheil submit patent for radio frequency ...
    Hedy Lamarr and George Antheil patented a torpedo guidance system using frequency hopping, a spread spectrum technology, using a mechanism similar to piano ...Missing: origin | Show results with:origin
  18. [18]
  19. [19]
    The Origins of Spread-Spectrum Communications | Semantic Scholar
    This monograph reviews events, circa 1920-1960, leading to the development of spread-spectrum communication ... The Simulation Study of the Spread-Spectrum System.Missing: declassification | Show results with:declassification<|control11|><|separator|>
  20. [20]
    [PDF] Spread Spectrum − Secret Military Technology to 3G
    Spread spectrum is a technique that takes a narrow band radio signal and spreads it over a broader portion of the radio frequency spectrum. This has the.
  21. [21]
    Spread Spectrum - an overview | ScienceDirect Topics
    Spread spectrum technology Conceived of by Hedy Lamarr and George Antheil in 1940 ... Spread spectrum first achieved widespread use in military applications ...
  22. [22]
    (PDF) A Secure Telecommunication Link using Spread Spectrum ...
    In this paper, a novel central dogma based symmetric key frequency hopping spread spectrum circuit is proposed to increase the security of data within the ...
  23. [23]
    (PDF) Jamming and anti-jamming solutions for 5G and IoT
    The paper covers the different types of jamming attacks, their impact on network performance, and the various anti-jamming techniques such as frequency hopping, ...Missing: 2020s | Show results with:2020s
  24. [24]
    [PDF] Spread Spectrum (SS)
    Spread Spectrum. 4. Frequency Hopping Spread Spectrum. A pseudo-noise sequence pnt generated at the modulator is used in conjunction with an M-ary. FSK ...
  25. [25]
    [PDF] Performance Study of Hybrid Spread Spectrum Techniques
    In frequency hopping spread spectrum, the frequency of the carrier is periodically modified (hopped) following a specific sequence of frequencies obtained using ...
  26. [26]
    [PDF] Tracking of Spread Spectrum Signals
    The first stage is often termed acquisition and typically obtains initial, coarse timing synchronization. The second is termed tracking and involves fine tuning ...
  27. [27]
    [PDF] Physical Layer Design for a Spread Spectrum Wireless LAN
    Sep 12, 1996 · Frequency hopping spread spectrum (FHSS) is similar to DSSS in the sense of spreading the signal energy over a wider bandwidth than the ...<|control11|><|separator|>
  28. [28]
    [PDF] california state university, northridge frequency-hopping spread ...
    FHSS: Frequency Hopping Spread Spectrum. FSK: Frequency Shift Keying. LAN ... In this example, the chip duration is equal to the bit duration. One of the ...
  29. [29]
    [PDF] ULTRA FAST FREQUENCY HOPPING TRANSCEIVER DESIGN ...
    In this chapter two type of spread spectrum communication techniques namely Direct Sequence Spread Spectrum (DSSS) and Frequency Hopping. Spread Spectrum (FHSS) ...
  30. [30]
    [PDF] 13 Wireless Communications Using Bluetooth
    Because each time slot has a 625-μs duration, the nominal hopping frequency is 1600 hops per second. All devices that are part of the same piconet hop in ...
  31. [31]
    [PDF] Frequency Hopped Spread Spectrum
    In this chapter we describe a second common form, namely frequency hopped spread spectrum. Additionally, we will also briefly describe other techniques ...
  32. [32]
    [PDF] DESIGN OF FREQUENCY SYNTHESIZERS FOR SHORT RANGE ...
    The choice of a particular type of frequency synthesizer depends on the design needs. Complexity, power consumption and frequency resolution are some of the ...
  33. [33]
    [PDF] Lecture 190 – All Digital Frequency Synthesizer for Bluetooth
    - Spectrum spreading: FHSS (Frequency Hopping Spectrum Spreading). • fk ... - Advantage: high frequency resolution, fast switching time. - Disadvantage ...Missing: drawbacks | Show results with:drawbacks
  34. [34]
    [PDF] Spread Spectrum (SS)
    DEFINITION OF SPREAD SPECTRUM (SS) ... Viterbi, 'CDMA Principles of Spread Spectrum Communication', Addison-Wesley, 1995.<|control11|><|separator|>
  35. [35]
    Direct Sequence Spread Spectrum - an overview - ScienceDirect.com
    While the despreading process does not improve the S/N in random noise, it does reduce narrow band interference by the value of the processing gain. Once ...
  36. [36]
    [PDF] Simulated Assessment of Interference Effects in Direct Sequence ...
    Mar 11, 2014 · The SNR improvement from the input (SNRsim) to the output of the spreading filter (SNRDS ) was approximately 19.8 dB and the processing gain ...<|separator|>
  37. [37]
    [PDF] PN Sequences for Use in Direct Sequence Spread Spectrum
    The following formulae hold for. Gold sequences (and can be derived from [3] with relative ease). In the following equations we use this approximation: N ≈ 2n.<|separator|>
  38. [38]
    [PDF] Multi-user detection for DS-CDMA communications
    So instead we look for codes that are nearly orthogonal, that is, have as low cross-correlation as possible (e.g., [11, 12]). Power Control The use of power ...
  39. [39]
    [PDF] Solving the near–far problem in CDMA-based ad hoc networks
    The near-far problem in MANETs is addressed by a distributed CDMA protocol using collision avoidance information to bound interfering nodes' power.
  40. [40]
    Signal Existence Verification (SEV) for GPS Low Received Power ...
    C(k) is the 1023-chip coarse/acquisition (C/A) code sequence with a chip rate of 1.023 MHz assigned to satellite number k. The C/A code is also called the ...
  41. [41]
  42. [42]
  43. [43]
  44. [44]
    [PDF] Design, Implementation, and Evaluation of a Hybrid DS/FFH Spread ...
    Based on the hopping rate, an HSS system is classified into a hybrid direct-sequence/slow frequency hopping (DS/SFH) system or direct-sequence/fast frequency ...
  45. [45]
  46. [46]
    20 Years – a promising start - 3GPP
    Dec 12, 2018 · Vote 1. On the creation of a 3GPP (92,62% in favour). · Vote 2. Whether 3GPP includes UTRA - W-CDMA in FDD mode and TD-CDMA in TDD mode (95,9% in ...
  47. [47]
    [PDF] Evolution of the 3GPP System
    Jun 1, 2010 · What will LTE-Advanced deliver? • Support for wider Bandwidth (Up to. 100MHz). • Up link transmission scheme.
  48. [48]
    Smooth Evolution from CDMA to LTE - ZTE
    Jun 11, 2010 · LTE has been chosen by major CDMA operators as their path to 4G evolution because of its open standards, sound industrial chain, and high- ...
  49. [49]
    Five wireless inventions that define 5G NR — the global 5G standard
    Dec 17, 2017 · Although Turbo codes have been well suited for 3G and 4G, Qualcomm Research has demonstrated that low-density parity check (LDPC) codes, and ...<|separator|>
  50. [50]
    Wi-Fi: Overview of the 802.11 Physical Layer and Transmitter ...
    The 802.11b, 802.11g, and the low-frequency part of the 802.11n standards utilize the 2.400 – 2.500 GHz spectrum located in the ISM band. The 802.11a, 802.11n ...
  51. [51]
    Cordless telephone - HFUnderground
    Oct 22, 2024 · ... FHSS cordless phones became available for the 900MHz band. If FHSS technology is used, base stations may transmit up to 1 watt ERP. This ...
  52. [52]
    FCC ID ACJ96NKX-TG2356 2.4GHz FHSS Cordless Telephone ...
    Application: 2.4GHz FHSS Cordless Telephone System · Equipment Class: DSS - Part 15 Spread Spectrum Transmitter · Short Link: fcc.id/ACJ96NKX-TG2356 · Sources: FCC ...
  53. [53]
    IEEE 802.15.4
    ### Summary of IEEE 802.15 WPAN™ Task Group 4 (TG4)
  54. [54]
  55. [55]
    [PDF] IS-95 (cdmaone) - University of Pittsburgh
    – Pair of 1.25 MHz radio channels (up/downlink). – Several users share a ... • FDMA – breaks up licensed spectrum into 1.25 MHz channels. • CDMA ...
  56. [56]
    [PDF] Processing Gain in Spread Spectrum Signals.
    The paper describes the benefits of processing gain and the reasons that the PG properties have been attractive for both military and commercial applications.
  57. [57]
    [PDF] Performance Evaluation of Different Jamming Strategies Over ... - DTIC
    Frequency–hopping spread–spectrum protects against a hostile jammer by increasing the bandwidth that the information signal occupies far more than required. By.
  58. [58]
    None
    Summary of each segment:
  59. [59]
    HAVE QUICK - Crypto Museum
    Mar 31, 2010 · HAVE QUICK is the codename of an American Frequency Hopping system. It is used for the protection of military UHF radio traffic, such as air-to- ...
  60. [60]
    Frequency Hopping Spread Spectrum Security Improvement with ...
    A new method based on encryption algorithm applied over spreading codes, named hidden frequency hopping is proposed to improve the security of FHSS.
  61. [61]
  62. [62]
    Joint Tactical Radio System Underway - AFCEA International
    Aug 1, 2002 · By using spread spectrum modulation, the system also supports low-probability-of-intercept and antijam capabilities, transmit power controls ...
  63. [63]
    Enhancing Communication Security in Drones Using QRNG ... - MDPI
    This paper enhances drone communication security by using QRNGs in FHSS to generate truly random frequency hopping sequences, improving resistance against ...
  64. [64]
    How Frequency Hopping Spread Spectrum (FHSS) Enhances ...
    May 22, 2025 · FHSS is a military-grade wireless technique that rapidly switches frequencies to avoid jamming, reduce interference, and maintain stable connections.
  65. [65]
    [PDF] Introduction to GPS and other Global Navigation Satellite Systems
    Jun 7, 2012 · ▫ Two L-band carrier frequencies. L1 = 1575.42 MHz L2 = 1227.60 MHz. ▫ Two PRN Codes – Uniquely Identify. Each Satellite. ❑ C/A: Coarse ...
  66. [66]
    Global Positioning System Overview - GPS INFO - CNMOC
    The satellites transmit on two L-band frequencies: L1 = 1575.42 MHz and L2 = 1227.6 MHz. ... The coarse/acquisition (C/A) code has a 1.023 MHz chip rate, a ...Missing: DSSS | Show results with:DSSS
  67. [67]
    Code Tracking and Pseudoranges - Inside GNSS
    Jan 13, 2012 · GNSS receivers estimate signal propagation time, which becomes pseudoranges due to time scale differences. These are generated by a delay lock ...
  68. [68]
    Lesson 1: The GPS Signal
    Many GPS receivers use the pseudorange code observable as sort of the ... Once correlation of the two codes is achieved with a delay lock loop (DLL) ...
  69. [69]
    GLONASS Signal Plan - Navipedia - GSSC
    The system now uses only 14 primary frequency channels with k values ranging from –7 to +6, including two channels for testing purposes (currently –5 and –6).GLONASS L1 Band · GLONASS L2 Band · GLONASS L3 Band · L3OCdMissing: elements | Show results with:elements
  70. [70]
    Galileo Signal Plan - Navipedia - GSSC
    AltBOC(15,10) is a wideband signal that is transmitted at 1191.795 MHz. Next figure shows the Galileo E5 signal modulation diagram: Figure 6: Modulation ...Missing: hybrid | Show results with:hybrid<|separator|>
  71. [71]
    [PDF] Detection Strategy for Cryptographic GNSS Anti-Spoofing
    Encryption codes such as the GPS W code serve a dual purpose: they both authenticate and deny unauthorized access to the signals they encrypt ...
  72. [72]
    [PDF] Ultra-Wide Bandwidth Time-Hopping Spread-Spectrum Impulse ...
    Low transmission-power and short-range operation with ultra-wide bandwidth (UWB) results in an ex- tremely low transmitted power spectral density, which insures.
  73. [73]
    Overview of multipath mitigation technology in global navigation ...
    In using narrow correlation techniques, a wrong locking point in the code tracking loop discriminator will likely lead to missed or false detections. Therefore, ...
  74. [74]
    Step 1 — Satellites - NovAtel
    The P(Y) code is for military use. It provides better interference rejection than the C/A code, which makes military GPS more robust than civilian GPS. The ...Satellite Orbits · Satellite Signals · Satellite Errors
  75. [75]
    A double sideband combined tracking method for Galileo E5 AltBOC ...
    Oct 16, 2023 · The spectrum of the Galileo E5 signal spreads over two adjacent frequency bands, E5a and E5b. While the E5 signal has a bandwidth of 51.15 MHz, ...
  76. [76]
    [PDF] Spread Spectrum Systems - DTIC
    Spread spectrum developments actually began in the 1940 as the result of ''clever engineering'' on a selected basis, with most applications involving ...
  77. [77]
    [PDF] 3 Point-to-point communication: detection, diversity, and channel ...
    For now, we focus on how DS spread-spectrum systems can achieve frequency diversity. The Rake receiver. Suppose we transmit one of two n-chips long pseudonoise ...
  78. [78]
  79. [79]
  80. [80]
    ABCs of Spread Spectrum - A Technology Introduction and Tutorial
    Spread Spectrum (SS) dates back to World War II. A German lady scientist was granted a patent on a simple frequency hopping CW system. The allies also ...Missing: pre- | Show results with:pre-
  81. [81]
    The End of Spectrum Scarcity
    Mar 1, 2004 · The first of these, spread spectrum, replaces ancient high-power, undifferentiated narrowband transmissions with modern low-power, coded ...Missing: experiments spreading<|separator|>
  82. [82]
  83. [83]
    Near-far problem in direct-sequence code-division multiple-access ...
    The effects of the 'near-far' problem on the Direct Sequence Code Division Multiple Access (DS/CDMA) system performance is investigated, for nonfading and ...
  84. [84]
  85. [85]
    Spectrally Efficient Spread Spectrum System Design - IEEE Xplore
    However, the spectral efficiency of existing FH systems is very low due to inappropriate use of the total available bandwidth. To improve the system capacity, ...
  86. [86]
    Optimum transmission ranges in a direct-sequence spread-spectrum ...
    Jun 30, 1990 · ... spread-spectrum multihop packet radio network. In the analysis, they model the network self-interference as a random variable which is equal ...
  87. [87]
    Spread-spectrum technology for commercial applications
    Apr 30, 1994 · Only recently has our technology advanced to the point that commercial application of spread-spectrum signaling is economically feasible.
  88. [88]
  89. [89]
    Shift Register Sequences : Solomon W. Golomb - Internet Archive
    Aug 16, 2022 · Shift Register Sequences. by: Solomon W. Golomb. Publication date: 1967. Publisher: Holden-Day. Collection: internetarchivebooks; inlibrary ...
  90. [90]
    [PDF] shift register sequences
    The purpose of this book is to collect and present in a single volume a thorough treatment of both the linear and nonlinear theory, with a guide to the area of ...
  91. [91]
    Optimal binary sequences for spread spectrum multiplexing (Corresp.)
    Optimal binary sequences for spread spectrum multiplexing (Corresp.) Published in: IEEE Transactions on Information Theory ( Volume: 13 , Issue: 4 , October ...
  92. [92]
    [PDF] WEIGHT DISTRIBUTION FORMULA FOR SOME CLASS OF ... - DTIC
    WEIGHT DISTRIBUTION FORMULA. 9'. FOR SOME CLASS OF CYCLIC CODES. Tadao Kasami. REPORT R- 285. APRIL, 1966 ! I. 1 i! I. Page 3. IL. This work was supported in ...
  93. [93]
  94. [94]