Academic literature on the topic 'Delay spread'

This paper presents results for delay and Doppler spread characterization in high-speed railway (HSR) hilly scenario. To investigate the propagation characteristics in this specific terrain, a measurement campaign is conducted along the “Guangzhou-Shenzhen” HSR in China. A wideband channel sounder with 40 MHz bandwidth is used to collect raw data at 2.4 GHz band. The delay spread and Doppler frequency features are analyzed based on measured data. It is found that there are abundant multipath components (MPCs) in this scenario. We present the relationship between the delay spreads and the transceiver distances. The measured route can be divided into four areas with different delay and Doppler characteristics. Finally, a tapped delay line (TDL) model is proposed to parameterize the channel responses in the HSR hilly environment, which is supposed to provide criterions for evaluations of the radio interface and development of wireless communication system.

Multiple Input Multiple Output (MIMO) technology is a technique that can be used to overcome multipath fading. The multipath fading is caused by signals coming from several paths that experience different attenuations, delays and phases. In a multipath condition, an impulse that sent by the transmitter, will be received by the recipient not as an impulse but as a pulse with a spread width that called delay spread. Delay spread can cause intersymbol interference (ISI) and bit translation errors from the information received. To determine the effect of delay spread on the MIMO system, then MIMO system performance research was performed on flat fading and frequency selective fading channels using the Space Time Block Code (STBC) coding technique. This research was conducted using MatLab 2018a software. The simulation results show that the MIMO STBC system performance on flat fading channels is better than the MIMO STBC system performance on the frequency selective fading channel. This result is analyzed based on the value of BER vs. Eb/No and eye diagram.

ITC/USA 2012 Conference Proceedings / The Forty-Eighth Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2012 / Town and Country Resort & Convention Center, San Diego, California
Radio transmission channel influences greatly the quality of transmitted voice and data signal in terms of data rate and robustness. This degradation is as a result of many factors, notable amongst them are having multiple replica of the transmitted signal at the receiver (multipath), changes of frequency as a result of the movement of the aircraft (Doppler shift) and noise. This paper characterizes the scattered components of the aeronautical channel in terms of delay spread. Geometric representation is used to derive expressions for the maximum delay spread using the 2-ray model and the three dimensional model of the scattered path. Furthermore, the delay and Doppler frequencies are described as a function of the horizontal distance to the specular reflection point between a ground station and a test article. The simulated results are compared to measured data of related articles and the value of the maximum delay spread is compared with the proposed intersymbol guard band for Orthogonal Frequency Division Multiplexing (OFDM) in the Integrated Network Enhanced Telemetry (iNET) program to see if this proposition can be adapted to the aeronautical channel.

Ultrawideband (UWB) is one of the most promising communication technologies in recent times with the promise of high data rates and spectral reuse. This work analyses the outdoor and outdoor-to-indoor propagating characteristics of the UWB pulse, which can be of the order of a few gigahertz in bandwidth. The aim of the thesis is to provide the parameters needed in order to develop a channel model for such cases. The channel model would then play an important role in determining physical layer (PHY) solutions to optimally exploit these characteristics. The measurements carried out on the Virginia Tech campus are used to compute parameters such as path loss, penetration loss and delay statistics. These are carried out in multiple frequency bands and the results are compared across frequency bands to determine effect of different frequency levels on the parameters. Finally the results are analyzed with respect to similar parameters obtained in other measurement campaigns in an attempt to evaluate the performance of Ultrawideband vis-à-vis narrowband systems.
Master of Science

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Nesta dissertação, é apresentado estudo realizado sobre a variabilidade do sinal, da banda de coerência e do espalhamento de retardos em um ambiente de rádio propagação móvel, por meio de medição em campo de um sinal WiMAX propagado ao longo do canal rádio móvel. A análise da estatística do sinal capturado é comparada com valores teóricos. O sinal WiMAX utilizado possui a tecnologia OFDM-256, como base da sua camada física, e frequência central de 3,410 GHz. A partir dos dados coletados durante as medições, são realizadas as análises da variabilidade do sinal, taxa de cruzamento de nível, tempo médio de desvanecimento, verificada a banda de coerência do canal e calculado o espalhamento de retardos (delay spread), por meio de fórmulas teóricas, em ambientes de LOS e NLOS. O nível do sinal medido é apresentado na forma de distribuição de probabilidade cumulativa, comparado com as distribuições cumulativas teóricas Rayleigh e m-Nakagami, sendo possível verificar a satisfatória adaptação dos dados às distribuições teóricas. São apresentados gráficos com a informação de taxa de cruzamento de nível e tempo médio de desvanecimento de determinadas subportadoras do sinal capturado, bem como os valores teóricos dos parâmetros supracitados, de acordo com as distribuições Rayleigh e m-Nakagami. Novamente, é possível verificar a satisfatória adaptação entre as informações teóricas e os dados medidos em campo. Por fim, é realizada a correlação entre as subportadoras, com o intuito de averiguar a banda de coerência definida, neste trabalho, para um valor de correlação igual a 0,5. De posse dessa informação, o cálculo do parâmetro de espalhamento de retardos é realizado, com base em fórmulas presentes na literatura.
This work presents a study of signal variability, coherence bandwidth and delay spread of a WiMAX signal transmitted through a mobile radio propagation environment. The statistical analysis of the received signal is compared with theoretical distributions. The transmitted WiMAX signal has its physical layer based on OFDM-256 and 3.4 GHz as central frequency. Based on the signal received during the measurements campaign some analysis are done: signal variability; level crossing rate; average fade duration; coherence bandwidth; and delay spread calculation, based on theoretical formulas, in LOS and NLOS environment. The received signal amplitude is plotted as a function of the cumulative probability and compared to the theoretical Rayleigh and m-Nakagami cumulative distributions. It’s possible to notice a good characterization of the measured data based on those two distributions. Some graphs show the level crossing rate and average fade duration of a specific subcarrier of the received signal. In the same graphs are also plotted the theoretical values of Nakagami-m and Rayleigh distributions for those two parameters and we are able to see the good agreement. The correlation between subcarriers is also calculated in order to find out the correlation bandwidth for a correlation of 0.5. Once that the correlation bandwidth is known, the delay spread is calculated based on theoretical formulas.

International Telemetering Conference Proceedings / October 27-30, 1997 / Riviera Hotel and Convention Center, Las Vegas, Nevada
A parallel multi-channel receiver for binary phase shift keyed (BPSK) direct-sequence (DS) spread-spectrum (SS) is introduced in this paper. It adopts a Costas carrier frequency-tracking loop which maintains frequency lock rather than phase lock, and the delay-lock error can be noncoherently obtained to track the PN code. For airborne applications, this method will extend effectively the receiver’s tracking dynamics range for the carrier Doppler shift. A erasable programmable logic device (EPLD) is applied to get the advantage of smaller size and higher flexibility. A high speed microprocessor (TMS320C30) which acts as the processing unit of the receiver is used for acquiring and tracking of the carrier and PN code by digital signal processing algorithms. This receiver is more flexible and is easily improved by reconfiguring the EPLD and modifying the software algorithms. Its fundamental principle is described in the paper.

The radio wave propagation prediction is one of the key elements for designing an efficient radio network system. WRAP International has developed a software for spectrum management and radio network planning.This software includes some wave propagation models which are used to predict path loss. Current propagation models in WRAP perform the calculation in a vertical 2D plane, the plane between the transmitter and the receiver. The goal of this thesis is to investigate and implement a 3D wave propagation model, in a way that reflections and diffractions from the sides are taken into account.The implemented 3D wave propagation model should be both fast and accurate. A full 3D model which uses high resolution geographical data may be accurate, but it is inefficient in terms of memory usage and computational time. Based on the fact that in urban areas the strongest path between the receiver and the transmitter exists with no joint between vertical and horizontal diffractions [10], the radio wave propagation can be divided into two parts, the vertical and horizontal part. Calculations along the horizontal and vertical parts are performed independently, and after that, the results are combined. This approach leads to less computational complexity, faster calculation time, less memory usage, and still maintaining a good accuracy.The proposed model is implemented in C++ and speeded up using parallel programming techniques. Using the provided Stockholm high resolution geographical data, simulations are performed and results are compared with real measurements and other wave propagation models. In addition to the path loss calculation, the proposed model can also be used to estimate the channel power delay profile and the delay spread.

International Telemetering Conference Proceedings / October 28-31, 1996 / Town and Country Hotel and Convention Center, San Diego, California
At present, multiple mobile targets will be remote controlled in many remote control and telemetry system, in which multiple access technology will be applied. This paper proposes a communication scheme to remote control multiple mobile targets using Coded-Division Multiple Access(CDMA) technique. It's feasibility, advantage and shortcoming are analyzed. Moreover, the key techniques of Direct-Sequence Spread Spectrum(DS/SS) system, i.e. the correlation detection and delay lock-on techniques, are studied and stimulated on the experimental model. The results of theoretical analysis show that the CDMA system has the peculiar advantage over the conventional multiple access system, such as FDMA and TDMA.

Neurodegenerative dementias, including Alzheimer’s disease (AD), Parkinson’s disease (PD) and Frontotemporal dementia (FTD), pose enormous challenges for our aging society. Genetic and mechanistic studies have revealed common molecular and cellular pathways, including imbalanced proteostasis and aberrant innate immune responses. Key pathogens in AD, PD, and FTD accumulate and spread from one brain region to another, resulting in network dysfunction and cognitive decline. These diseases are multifactorial, caused by interactions among multiple genetic, epigenetic, and environmental factors and pathways. Combination therapies that target multiple pathways may also be needed to stop or delay the dementing conditions in neurodegenerative dementias.

Genitourinary cancers examines the malignancies arising in the kidney, ureter, bladder, prostate, testis, and penis. Renal cancer has high propensity for systemic spread, largely mediated by overexpression of vascular endothelial growth factor (VEGF). Treatments include surgery, immunotherapy, and targeted therapy. Wilms tumour, a childhood malignancy of the kidney, warrants specialist paediatric oncology management to provide expertise in its unique pathology, staging, and treatment, often with surgery and chemotherapy. Cancer of the bladder and ureters, another tobacco related cancer, may present as either superficial or invasive disease. The former is managed by transurethral resection and intravesical therapy. The latter may require radical surgery, preoperative chemotherapy, or radiotherapy. Prostate cancer, the commonest male cancer, is an androgen dependent malignancy. It has attracted controversy with regards to PSA screening, and potential over treatment with radical prostatectomy. Division into low, intermediate, and high risk disease according to tumour grade, stage, and PSA helps in deciding best treatment, antiandrogen therapy for metastatic disease, radiotherapy and adjuvant hormone therapy for locally advanced disease, either surgery or radiotherapy for early intermediate risk disease, and active monitoring for low risk cases. Testicular cancer divides according to pathology into seminoma, nonseminomatous germ cell tumours (NSGCT), and mixed tumours, the latter two frequently producing tumour markers, alpha-fetoprotein (AFP) and/or human chorionic gonadotrophin (HCG). Stage I disease is managed by inguinal orchidectomy and surveillance or adjuvant chemotherapy. More advanced disease is managed by chemotherapy, with high probability of cure in the majority. Penile cancer, often HPV related, can be excised when it presents early, but delay in presentation may lead to regional and systemic spread with poor prognosis.

The dispersal of Austronesian-speaking farmer-voyagers from Taiwan into Island Southeast Asia (ISEA) and out into the Pacific is one of the great metanarratives of global history. In this chapter, the major lines of multidisciplinary evidence for the “Austronesian” dispersal into ISEA are critically evaluated. Several key points emerge: usage of the term “Austronesian” should be restricted to languages and not be applied to genetic attributes or material culture; the dispersals of genes and Austronesian languages do not correspond within ISEA; and, there is limited evidence for the dispersal of farming across ISEA together with the spread of Austronesian languages from Taiwan. An alternative, multidirectional, distance-decay scenario is advanced for the spread of domesticated animals and plants, cultivation practices, and other material cultural items, in which the inhabitants of ISEA are active participants in the creation of their own history.

As current events around the world have illustrated, epistemological issues are at the center of our political lives. It has become increasingly difficult to discern legitimate sources of evidence, misinformation spreads faster than ever, and the role of truth in politics has allegedly decayed in recent years. It is therefore no coincidence that political discourse is currently saturated with epistemic notions like “post-truth,” “fake news,” “truth decay,” “echo chambers,” and “alternative facts.” This book brings together leading political philosophers and epistemologists to explore ways in which the analytic and conceptual tools of epistemology bear on political philosophy, and vice versa. It is organized around three broad themes: truth and knowledge in politics; epistemic problems for democracy; and disagreement and polarization. This book investigates topics such as: the extent and implications of political ignorance, the value of democratic deliberation, the significance of epistemic considerations for political legitimacy, the epistemology of political disagreement, identity politics, political bullshit, and weaponized skepticism. A premise underlying the development of political epistemology is that, beyond a certain point, progress on certain foundational issues in both political philosophy and epistemology cannot be achieved without sharing insights across fields. By bringing political philosophers into conversation with epistemologists, this volume promotes more cross-pollination of ideas while also highlighting the richness and diversity of political epistemology as a newly emerging field.

An orbitally induced increase in summer insolation during the last glacial-interglacial transition enhanced the thermal contrast between land and sea, with land masses heating up compared to the adjacent ocean surface. In North Africa, warmer land surfaces created a low-pressure zone, driving the northward penetration of monsoonal rains originating from the Atlantic Ocean. As a consequence, regions today among the driest of the world were covered by permanent and deep freshwater lakes, some of them being exceptionally large, such as the “Mega” Lake Chad, which covered some 400 000 square kilometers. A dense network of rivers developed.What were the consequences of this climate change on plant distribution and biodiversity? Pollen grains that accumulated over time in lake sediments are useful tools to reconstruct past vegetation assemblages since they are extremely resistant to decay and are produced in great quantities. In addition, their morphological character allows the determination of most plant families and genera.In response to the postglacial humidity increase, tropical taxa that survived as strongly reduced populations during the last glacial period spread widely, shifting latitudes or elevations, expanding population size, or both. In the Saharan desert, pollen of tropical trees (e.g., Celtis) were found in sites located at up to 25°N in southern Libya. In the Equatorial mountains, trees (e.g., Olea and Podocarpus) migrated to higher elevations to form the present-day Afro-montane forests. Patterns of migration were individualistic, with the entire range of some taxa displaced to higher latitudes or shifted from one elevation belt to another. New combinations of climate/environmental conditions allowed the cooccurrences of taxa growing today in separate regions. Such migrational processes and species-overlapping ranges led to a tremendous increase in biodiversity, particularly in the Saharan desert, where more humid-adapted taxa expanded along water courses, lakes, and wetlands, whereas xerophytic populations persisted in drier areas.At the end of the Holocene era, some 2,500 to 4,500 years ago, the majority of sites in tropical Africa recorded a shift to drier conditions, with many lakes and wetlands drying out. The vegetation response to this shift was the overall disruption of the forests and the wide expansion of open landscapes (wooded grasslands, grasslands, and steppes). This environmental crisis created favorable conditions for further plant exploitation and cereal cultivation in the Congo Basin.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.