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Patients with posttraumatic stress disorder (PTSD) exhibit smaller regional brain volumes in commonly reported regions including the amygdala and hippocampus, regions associated with fear and memory processing. In the current study, we have conducted a voxel-based morphometry (VBM) meta-analysis using whole-brain statistical maps with neuroimaging data from the ENIGMA-PGC PTSD working group.
Methods
T1-weighted structural neuroimaging scans from 36 cohorts (PTSD n = 1309; controls n = 2198) were processed using a standardized VBM pipeline (ENIGMA-VBM tool). We meta-analyzed the resulting statistical maps for voxel-wise differences in gray matter (GM) and white matter (WM) volumes between PTSD patients and controls, performed subgroup analyses considering the trauma exposure of the controls, and examined associations between regional brain volumes and clinical variables including PTSD (CAPS-4/5, PCL-5) and depression severity (BDI-II, PHQ-9).
Results
PTSD patients exhibited smaller GM volumes across the frontal and temporal lobes, and cerebellum, with the most significant effect in the left cerebellum (Hedges’ g = 0.22, pcorrected = .001), and smaller cerebellar WM volume (peak Hedges’ g = 0.14, pcorrected = .008). We observed similar regional differences when comparing patients to trauma-exposed controls, suggesting these structural abnormalities may be specific to PTSD. Regression analyses revealed PTSD severity was negatively associated with GM volumes within the cerebellum (pcorrected = .003), while depression severity was negatively associated with GM volumes within the cerebellum and superior frontal gyrus in patients (pcorrected = .001).
Conclusions
PTSD patients exhibited widespread, regional differences in brain volumes where greater regional deficits appeared to reflect more severe symptoms. Our findings add to the growing literature implicating the cerebellum in PTSD psychopathology.
Background: Traumatic brain injury (TBI) patients exhibit variable post-injury recovery trajectories. Days at Home (DAH) is a patient-centered measure that captures healthcare transitions and offers a more nuanced understanding of recovery. Here, we use DAH to characterize longterm recovery trajectories for moderate to severe TBI (msTBI) survivors. Methods: This multicenter retrospective cohort study utilized population health data from Ontario to identify adults sustaining isolated msTBI hospitalized between 2009-2021. DAH were calculated in distinct 30-day intervals from index admission to 3 years post-injury; latent class mixed modeling identified unique recovery trajectories and trajectory attributes were quantified. Results: There were 2,510 patients eligible for latent class analysis. Four DAH trajectories were identified: early recovery (69.9%), intermediate recovery (11.4%), late recovery (2.9%), and poor recovery (15.8%). Patients in the poor recovery group were older, more frail, and had lower admission GCS scores, while those in early recovery exhibited lower acute care needs. Intermediate and late recovery groups exhibited protracted transitions home, with near-complete reintegration by 24 months. A prediction model distinguished unfavorable trajectories with good accuracy (C-index=0.824). Conclusions: Despite high initial institutional care requirements, 85% of patients reintegrated into the community within three years of msTBI. These findings shed light on post-injury care requirements for brain-injured patients.
OBJECTIVES/GOALS: To examine the individual and combined association between preoperative sleep disturbance (SD) and depression and 12-month disability, back pain, and leg pain after lumbar spine surgery (LSS). METHODS/STUDY POPULATION: We analyzed prospectively collected multi-center registry data from 700 patients undergoing LSS (mean age=60.9 years, 37% female, 89% white). Preoperative SD and depression were assessed with PROMIS measures. Established thresholds defined patients with moderate/severe symptoms. Disability (Oswestry Disability Index) and back and leg pain (Numeric Rating Scales) were assessed preoperatively and at 12 months. We conducted separate regressions to examine the influence of SD and depression on each outcome. Regressions examined each factor with and without accounting for the other and in combination as a 4-level variable. Covariates included age, sex, race, education, insurance, body mass index, smoking status, preoperative opioid use, fusion status, revision status, and preoperative outcome score. RESULTS/ANTICIPATED RESULTS: One hundred thirteen (17%) patients reported moderate/severe SD alone, 70 (10%) reported moderate/severe depression alone, and 57 (8%) reported both moderate/severe SD and depression. In independent models, preoperative SD and depression were significantly associated with 12-month outcomes (all p’s<0.05). After accounting for depression, preoperative SD was only associated with disability, while preoperative depression adjusting for SD remained associated with all outcomes (all p’s<0.05). Patients reporting both moderate/severe SD and moderate/severe depression had 12.6 points higher disability (95%CI=7.4 to 17.8) and 1.5 points higher back (95%CI=0.8 to 2.3) and leg pain (95%CI=0.7 to 2.3) compared to patients with no/mild SD and no/mild depression. DISCUSSION/SIGNIFICANCE: Preoperative SD and depression are independent predictors of 12-month disability and pain when considered in isolation. The combination of SD and depression impacts postoperative outcomes considerably. The high-risk group of patients with moderate/severe SD and depression could benefit from targeted treatment strategies.
Maternal fish consumption exposes the fetus to beneficial nutrients and potentially adverse neurotoxicants. The current study investigated associations between maternal fish consumption and child neurodevelopmental outcomes. Maternal fish consumption was assessed in the Seychelles Child Development Study Nutrition Cohort 1 (n 229) using 4-day food diaries. Neurodevelopment was evaluated at 9 and 30 months, and 5 and 9 years with test batteries assessing twenty-six endpoints and covering multiple neurodevelopmental domains. Analyses used multiple linear regression with adjustment for covariates known to influence child neurodevelopment. This cohort consumed an average of 8 fish meals/week and the total fish intake during pregnancy was 106·8 (sd 61·9) g/d. Among the twenty-six endpoints evaluated in the primary analysis there was one beneficial association. Children whose mothers consumed larger quantities of fish performed marginally better on the Kaufman Brief Intelligence Test (a test of nonverbal intelligence) at age 5 years (β 0·003, 95 % CI (0, 0·005)). A secondary analysis dividing fish consumption into tertiles found no significant associations when comparing the highest and lowest consumption groups. In this cohort, where fish consumption is substantially higher than current global recommendations, maternal fish consumption during pregnancy was not beneficially or adversely associated with children’s neurodevelopmental outcomes.
This article is a clinical guide which discusses the “state-of-the-art” usage of the classic monoamine oxidase inhibitor (MAOI) antidepressants (phenelzine, tranylcypromine, and isocarboxazid) in modern psychiatric practice. The guide is for all clinicians, including those who may not be experienced MAOI prescribers. It discusses indications, drug-drug interactions, side-effect management, and the safety of various augmentation strategies. There is a clear and broad consensus (more than 70 international expert endorsers), based on 6 decades of experience, for the recommendations herein exposited. They are based on empirical evidence and expert opinion—this guide is presented as a new specialist-consensus standard. The guide provides practical clinical advice, and is the basis for the rational use of these drugs, particularly because it improves and updates knowledge, and corrects the various misconceptions that have hitherto been prominent in the literature, partly due to insufficient knowledge of pharmacology. The guide suggests that MAOIs should always be considered in cases of treatment-resistant depression (including those melancholic in nature), and prior to electroconvulsive therapy—while taking into account of patient preference. In selected cases, they may be considered earlier in the treatment algorithm than has previously been customary, and should not be regarded as drugs of last resort; they may prove decisively effective when many other treatments have failed. The guide clarifies key points on the concomitant use of incorrectly proscribed drugs such as methylphenidate and some tricyclic antidepressants. It also illustrates the straightforward “bridging” methods that may be used to transition simply and safely from other antidepressants to MAOIs.
We present the first Southern-Hemisphere all-sky imager and radio-transient monitoring system implemented on two prototype stations of the low-frequency component of the Square Kilometre Array (SKA-Low). Since its deployment, the system has been used for real-time monitoring of the recorded commissioning data. Additionally, a transient searching algorithm has been executed on the resulting all-sky images. It uses a difference imaging technique to enable identification of a wide variety of transient classes, ranging from human-made radio-frequency interference to genuine astrophysical events. Observations at the frequency 159.375 MHz and higher in a single coarse channel ($\approx$0.926 MHz) were made with 2 s time resolution, and multiple nights were analysed generating thousands of images. Despite having modest sensitivity ($\sim$ few Jy beam–1), using a single coarse channel and 2-s imaging, the system was able to detect multiple bright transients from PSR B0950+08, proving that it can be used to detect bright transients of an astrophysical origin. The unusual, extreme activity of the pulsar PSR B0950+08 (maximum flux density $\sim$155 Jy beam–1) was initially detected in a ‘blind’ search in the 2020 April 10/11 data and later assigned to this specific pulsar. The limitations of our data, however, prevent us from making firm conclusions of the effect being due to a combination of refractive and diffractive scintillation or intrinsic emission mechanisms. The system can routinely collect data over many days without interruptions; the large amount of recorded data at 159.375 and 229.6875 MHz allowed us to determine a preliminary transient surface density upper limit of $1.32 \times 10^{-9} \text{deg}^{-2}$ for a timescale and limiting flux density of 2 s and 42 Jy, respectively. In the future, we plan to extend the observing bandwidth to tens of MHz and improve time resolution to tens of milliseconds in order to increase the sensitivity and enable detections of fast radio bursts below 300 MHz.
Optimal maternal long-chain PUFA (LCPUFA) status is essential for the developing fetus. The fatty acid desaturase (FADS) genes are involved in the endogenous synthesis of LCPUFA. The minor allele of various FADS SNP have been associated with increased maternal concentrations of the precursors linoleic acid (LA) and α-linolenic acid (ALA), and lower concentrations of arachidonic acid (AA) and DHA. There is limited research on the influence of FADS genotype on cord PUFA status. The current study investigated the influence of maternal and child genetic variation in FADS genotype on cord blood PUFA status in a high fish-eating cohort. Cord blood samples (n 1088) collected from the Seychelles Child Development Study (SCDS) Nutrition Cohort 2 (NC2) were analysed for total serum PUFA. Of those with cord PUFA data available, maternal (n 1062) and child (n 916), FADS1 (rs174537 and rs174561), FADS2 (rs174575), and FADS1-FADS2 (rs3834458) were determined. Regression analysis determined that maternal minor allele homozygosity was associated with lower cord blood concentrations of DHA and the sum of EPA + DHA. Lower cord blood AA concentrations were observed in children who were minor allele homozygous for rs3834458 (β = 0·075; P = 0·037). Children who were minor allele carriers for rs174537, rs174561, rs174575 and rs3834458 had a lower cord blood AA:LA ratio (P < 0·05 for all). Both maternal and child FADS genotype were associated with cord LCPUFA concentrations, and therefore, the influence of FADS genotype was observed despite the high intake of preformed dietary LCPUFA from fish in this population.
The association of MeHg exposure through fish consumption on human autoimmunity remains unclear. Fish also contain n-3 long chain polyunsaturated fatty acids (LCPUFA) that are known to regulate inflammation and mitigate autoimmune disease symptoms. We studied the association of low-level exposure to methylmercury (MeHg) through fish consumption in the SCDS. We examined this association at age 19 years in the SCDS Main Cohort (n = 497). We measured MeHg exposure at 3 time points [prenatal, weighted average (6 months to 19 years) and concurrent (19 years) and LCPUFA status and a panel of 13 autoimmune markers at age 19 years. The autoimmune markers included antinuclear antibodies (ANA), anti-dsDNA and anti-RNP, and total (non-specific) immunoglobulins (Ig) IgG, IgA, and IgM. A combined ANA variable was also calculated based on being within or above reference range for any of the ANA markers; 56% of the subjects met this criterion. Multivariable regression models adjusted for prenatal MeHg, sex and waist circumference, with and without adjustment for LCPUFA, were fit for the three MeHg exposure metrics and each immune marker. Mean (SD) prenatal, weighted average and concurrent MeHg was 6.84 (4.55), 7.46 (2.82), and 10.23 (6.02) ppm, respectively. Combined ANA was positively associated with concurrent MeHg following adjustment for the n6:n3 LCPUFA ratio (β = 0.036, 95%; CI: 0.001, 0.073). Prenatal and average MeHg exposures were not significantly associated with any individual ANA. IgM was negatively associated with concurrent (β = -0.016, 95%CI: -0.016, -0.002), and average (β = -0.042, 95%CI: -0.042, -0.009) MeHg exposure in the models adjusted for n-3, n-6 LCPUFA and when separately adjusted for the n6:n3 LCPUFA ratio. Total (19-year) n-3 PUFA status was negatively associated with anti-RNP (β = -20.355, 95%CI: -36.89, -4.34) and IgG (β = -1.384, 95%CI: -2.682, -0.087). Total n-3 LCPUFA was associated with lower markers of autoimmunity. MeHg exposure at 19 years was associated with higher ANA and lower IgM but only following adjustment for LCPUFA. The clinical significance of these findings is unclear and further research is warranted to determine if these associations precede autoimmune disease development.
Optimal maternal polyunsaturated fatty acid (PUFA) status is essential for foetal development. The desaturase enzymes, encoded by the fatty acid desaturase (FADS) genes, are involved in the endogenous synthesis of long chain (LC)PUFA and influence maternal LCPUFA concentrations. The minor allele of various FADS SNPs has been associated with increased maternal concentrations of the precursors linoleic acid (LA) and α-linolenic acid (ALA), and lower concentrations of the LCPUFA arachidonic acid (AA) and docosahexaenoic acid (DHA); however, there is limited research to date on the influence of FADS genotype on cord PUFA status. The aim of the current study was to investigate the influence of maternal and child genetic variation on cord blood PUFA status in a high fish-eating cohort.
Cord blood samples collected from mother-child pairs (n = 1088) taking part in the Seychelles Child Development Study (SCDS) Nutrition Cohort 2 (NC2) were analysed for total serum PUFA. Maternal (n = 1088) and child genotype (n = 592) were determined for the FADS SNPs rs174537, rs174561, rs174575, and rs3834458. Regression analysis determined associations between maternal and child FADS genotype and cord PUFA status. In all regression models, the major allele homozygote genotype for each SNP was used as the reference group.
Directions of significant associations were as predicted. In mothers, the minor allele homozygote genotype for SNPs rs174537, rs174561 and rs3834458 was associated with lower cord DHA and lower total n-3 PUFA when compared to the major allele homozygous genotype (p < 0.05 for all). The heterozygous genotype was associated with increased concentrations of LA compared to the reference genotype for rs174561 (p = 0.021) and rs383448 (p = 0.023). In children, the heterozygous genotype was associated with lower AA concentrations and lower cord n-6:n-3 ratio for all SNPs (p < 0.05 for all) compared to those with the major allele homozygous genotype. A lower cord AA:LA ratio was also observed for children heterozygous for rs174547, rs174561 and rs174575 (p < 0.05 for all). Contrary to expected, there were no associations between cord PUFA concentrations and child minor allele homozygous genotype.
The current study indicates that variation in maternal and child FADS genotype influences cord PUFA concentrations, despite the high intake of preformed dietary LCPUFA from fish in this population. The sample size for minor allele homozygous children was likely too small to observe any statistically significant associations in the current analysis. Further research is needed to determine whether increased dietary intake can compensate for lower PUFA status as a result of FADS genotype.
Having discussed the basic theory and approaches to phased array receiver modeling, as well as figures of merit and system characterization, we now turn to specific details of the design and fabrication of the front end aperture itself. A wide variety of element types and configurations have been explored. Chief examples include the wideband sinuous element of the early explorations of PAFs at NRAO [1], dipole elements for PAFs [2], [3] as well as aperture arrays [4], tapered slot antennas or Vivaldi elements [5], [6], derivatives of the TSA element such as the egg-crate array, the checkerboard array [7]–[9] and other current-sheet implementations, horn elements [10], and of course the ubiquitous microstrip patch antenna [11] and the patch excited cup antenna designed by RUAG Space [12]. Many of these designs were surveyed in Chapter 1. In this chapter, we review considerations on selecting an appropriate element type, methods for design optimization, and fabrication issues. Receiver electronics is also discussed, with a specific focus on low noise amplifiers. Signal transport is also briefly addressed. The chapter concludes with an overview of downconversion and sampling, as well as the analog filters which these processes require.
Frequency and Bandwidth
Perhaps the most fundamental criteria in selecting an element type for a phased array system are the operating frequency and bandwidth. Frequency of operation might be considered the initial point in selecting an element, but because a given antenna type can be scaled, within fabrication limitations, to resonate or operate over a wide range of frequencies, bandwidth is in some ways the more critical driver. Element types can be divided most simply into narrowband, resonant antennas (dipole, patch) and wideband antennas (sinuous antenna, Vivaldi, checkerboard, and others). The division between narrowband and wideband is of course not a precise cutoff, but 10% to 20% relative bandwidth (i.e., bandwidth divided by the design center frequency), might be considered the upper limit of narrowband antenna types, and antennas with wider relative bandwidth would be considered to be wideband or ultrawideband. Bandwidth limitations are discussed further in Sec. 9.4.
The general disciplines of calibrating phased arrays, constructing beam weighting coefficients, and performing computations on the output signals from a phased array system, all belong to broad field known as array signal processing. Basic topics from array signal processing, as well as advanced topics such as radio frequency interference mitigation, are surveyed in this chapter. For phased arrays used in demanding applications like radio astronomy, a priori array calibration methods generally are insufficiently accurate. In practice, array calibration generally involves measured signal responses or correlations with bright sources, so calibration is included here in the same treatment as beamforming and signal processing.
Beamforming
In the context of antenna array receivers, beamforming is the process of linearly weighting and combining signals from array elements in order to form a desired spatial response pattern. An example of response pattern is shown in Fig. 10.1. Beamforming can be viewed as spatial filtering where the discrete-in-space samples of the propagating wavefront (i.e., the outputs of the distinct antenna elements of the array, each in a different position) are used as inputs to a linear filter. Typically the beamformer is designed by adjusting the element weights to achieve higher gain, directivity, sensitivity, and signal to noise ratio than is possible from any single array antenna element. In the process, the high gain field of view is narrowed to a relatively small directional region know as the beam main lobe, or simply the beam. The lower response peaks outside this main lobe region are undesirable artifacts of the beamforming process and are pattern sidelobes.
Beams may be steered to a desired direction by inserting time delays in the signal path of each element to compensate for differential propagation delays across the array for wavefronts arriving from that direction. These time aligned signals sum coherently in the beamformer and so higher gain is achieved in the desired steering direction. For narrowband signals this steering time delay may be replaced by simply multiplying element signal streams by the equivalent complex phase shift e−jωkτi where ωk is the narrowband subband center radian frequency for the kth channel and τi is the alignment time delay correction for the ith element (this is equivalent to the phase shift derived in Sec. 4.1).
In common with many other fields of electrical and electronic engineering, real-time digital signal processing (DSP) has revolutionized the processing of datastreams from phased arrays. As will be appreciated from the discussions in this book, modern radio telescopes such as LOFAR and MWA include beamformed stations (comprising individual elements) which are then correlated with each other to form the interferometric array; similarly, the ASKAP and APERTIF designs have PAF feeds on dishes, which again are correlated. In this chapter, we consider several threads of real-time DSP for correlation, beamforming and frequency channelizing.
We start by addressing real-time DSP for interferometers; here, the major cost is at the correlator stage, and this is the first topic considered, following the presentation in [1] for the theoretical background. On the one hand, many of the operations required are relatively simple – multiply and accumulate (integrate) – but there is also the requirement to perform very rapid Fourier transforms. Of course, the fast Fourier transform (FFT) is the key tool here. Aperture arrays and phased array feeds typically require Fourier transforms and correlators for array calibration and for observation-mode array signal processing, so these computational blocks have applications to all of the types of arrays considered in this book.
We then consider beamforming. Beams can be computed in real time, or if accumulated beam power estimates per channel rather than beamformer voltage time series sample outputs are sufficient for a given observation, then the array outputs can be correlated, followed by post-correlation beamforming. The major computational load for real time beamforming is the formation of weighted sums of array outputs. Array calibration with a correlator is computationally intensive, but the calculation of the beamformer weights themselves is generally negligible from a loading perspective. In most current applications, beamformer weights are computed infrequently, and this is done offline, not in real time. As the array response changes due to instrumental electronic drift, structural deformations, or ionospheric effects, beamformer weights may need to be updated at periods ranging from weeks at L band to minutes at mmwave frequencies. In the RFI mitigation scenario, fast relative motion between the SoI and interfering sources implies the need for rapid recalculation of weights (on the order of 1 to 500 ms).
Phased arrays date back to the very earliest days of radio. The German physicist Karl Ferdinand Braun constructed a three element, switchable array in 1909 to enhance radio transmission in one direction. Early phased arrays achieved beam steering through applying a progressive phase to each element of a one- or two-dimensional array; the concept may be found in almost every book on antenna theory, e.g. [1]. The contemporary usage extends to include control of both the amplitude and phase (or time-delay) excitations of each radiating element in a multiantenna system [2].
While the analytical tools covered in this book are applicable to phased array antennas for all applications, the concepts and examples in the book are organized around the design and optimization of high-sensitivity radio frequency and microwave receivers. Radio astronomy is an especially challenging application of this technology, and will feature strongly in this book. Although parabolic dishes have dominated antenna technology since the early 1960s, to the point where dishes have become largely synonymous with radio telescopes in the popular imagination,1 many early discoveries in radio astronomy were made using phased arrays [3]. The same is true for the large dishes (often over 30 m in diameter) used by telecommunication ground stations and for deep space tracking in the same timeframe; but again, phased arrays were far from forgotten, playing an important role in the first Approach and Landing System (ALS) and post- WWII early warning systems.
Parabolic dishes have probably reached the apogee of their design in recent years, and since they are fundamentally large mechanical systems, their cost is dominated by the cost of materials and labour – neither of which is likely to change dramatically in the foreseeable future. In the radio astronomy community, the currently accepted guideline is that the cost of a dish scales since the area only increases as, building ever-larger steerable dishes is clearly not a viable method for increasing sensitivity, which is directly proportional to collecting area. Additionally, steerable dishes in particular involve moving parts, bringing significant maintenance requirements. Phased arrays, on the other hand, are fundamentally electronic systems, whose cost is increasingly dominated by processing. Moore's Law provides the prospect of continuing – and dramatic – reductions in processing costs.
The classical approach to array antenna analysis is to represent the field radiated by the array as a product of the radiation pattern of one element and an array factor that includes the locations and excitations of each element in the array. This approach has been used for many decades to design phased arrays for many applications, from radar and terrestrial communications to satellite systems and radio telescopes.
For high performance receiving arrays, the approximate factorization of the array radiation pattern into an element pattern and array factor may not be accurate enough to use when designing for stringent performance requirements. Mutual coupling causes element radiation patterns to differ across the array, and this must be taken into account in the design process from the beginning. For this reason, we will only briefly consider the classical array factor technique in this chapter, and move instead to a more sophisticated analysis method based on overlap integrals and network theory.
The array factor method certainly has enduring value. The array factor provides an intuitive way to analyze, understand, visualize, and design steered beams and array radiation pattern. It can be taught in a simple way to students of array theory, yet is useful in designing highly sophisticated multiantenna systems. Optimal designs, such as the Chebyshev array, can be readily treated within this framework.
For the high sensitivity applications of interest in this book, the array factor method is only useful for rough designs, and a more advanced approach is needed. The overlap integral and network theory approach comes at a price. It relies on numerical approximations or full wave simulations of embedded element patterns, and is not amenable to pencil and paper treatments. The analysis methodology used in this book is intended from the ground up to be used with numerical methods and optimization tools. As a middle ground between the array factor method and full wave numerical modeling, we will also develop the lossless, resonant, minimum scattering approximation.
The standard approach to antenna theory is to treat transmitting antennas first, followed by the receiving case. After reviewing the classical array factor method and other basic concepts of simple array antennas, we will develop the overlap integral and network theory first for a transmitting array.
The treatment of single antennas in Chapter 2 introduced key concepts for receivers, including gain, directivity, effective area, impedance matching, noise figure, equivalent noise temperature, signal to noise ratio, and sensitivity. The treatment was then extended in Chapter 4 to arrays of transmitting elements. We now turn our attention to the main focus of the book, modeling high-sensitivity receiving antenna arrays.
For transmitters, the distribution of the signal power radiated by the antenna system is the primary consideration. Noise radiated by a transmitter is usually of secondary importance. For receivers, both the signal and noise response of the system are important, and the ultimate figure of merit for the performance of the system is the ratio of received signal of interest to the system noise (SNR). For this reason, the treatment of receiving arrays is more complicated than transmitters, as system noise must be brought into the analysis.We will begin by extending the network theory treatment developed in Chapter 4 to receiving arrays, and then bring in the noise modeling concepts that were introduced in Chapter 2.
Receiving Array Network Model
As a model for a receiving array, we will consider a basic narrowband active receive array architecture consisting of antenna elements terminated by low noise amplifiers, followed by receiver chains and a beamforming network which applies a complex gain constant (magnitude scaling and phase shift) to the signal from each element and sums the weighted signals to form a single scalar output, as in Fig. 5.1.
The canonical block diagram shown in Fig. 5.1 can represent many different types of antenna array receiver systems used in a variety of applications, and there are many variations on this basic architecture. Signals may be combined with an analog network, or the beamforming can be done using sampling followed by digital signal processing. For broadband applications, beamforming can be done with a time delay network, but more commonly the signal is processed digitally in frequency subbands using a narrowband beamformer architecture. Digital signal processing systems can form many simultaneous beams, so that the beamformer block is repeated in parallel for each formed beam.